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G = C5×C23.65C23  order 320 = 26·5

Direct product of C5 and C23.65C23

direct product, metabelian, nilpotent (class 2), monomial, 2-elementary

Aliases: C5×C23.65C23, C4⋊C4⋊6C20, C20⋊12(C4⋊C4), C2.8(D4×C20), C2.4(Q8×C20), C10.40(C4×Q8), (C2×C20).73Q8, (C2×C20).359D4, C10.139(C4×D4), C10.36(C4⋊Q8), (C2×C42).10C10, C22.38(D4×C10), C22.14(Q8×C10), C10.85(C22⋊Q8), C10.135(C4⋊D4), C2.C42.6C10, C23.62(C22×C10), C22.38(C22×C20), C10.28(C42.C2), (C22×C10).453C23, (C22×C20).575C22, C4⋊2(C5×C4⋊C4), (C5×C4⋊C4)⋊20C4, C2.2(C5×C4⋊Q8), C2.8(C10×C4⋊C4), (C2×C4×C20).33C2, (C2×C4⋊C4).7C10, C10.86(C2×C4⋊C4), C2.4(C5×C4⋊D4), (C10×C4⋊C4).36C2, (C2×C4).11(C5×Q8), (C2×C4).16(C2×C20), C2.4(C5×C22⋊Q8), (C2×C4).117(C5×D4), (C2×C20).437(C2×C4), C2.3(C5×C42.C2), (C2×C10).605(C2×D4), (C2×C10).106(C2×Q8), C22.23(C5×C4○D4), (C22×C4).89(C2×C10), (C2×C10).213(C4○D4), (C2×C10).326(C22×C4), (C5×C2.C42).25C2, SmallGroup(320,890)

Series: Derived ►Chief ►Lower central ►Upper central

Derived series
C1 — C22 — C5×C23.65C23
Chief series
C1 — C2 — C22 — C23 — C22×C10 — C22×C20 — C10×C4⋊C4 — C5×C23.65C23
Lower central
C1 — C22 — C5×C23.65C23
Upper central
C1 — C22×C10 — C5×C23.65C23

Generators and relations for C5×C23.65C23
 G = < a,b,c,d,e,f,g | a5=b2=c2=d2=1, e2=f2=d, g2=c, ab=ba, ac=ca, ad=da, ae=ea, af=fa, ag=ga, bc=cb, bd=db, fef-1=be=eb, bf=fb, bg=gb, cd=dc, geg-1=ce=ec, cf=fc, cg=gc, de=ed, df=fd, dg=gd, fg=gf >

Subgroups: 242 in 170 conjugacy classes, 106 normal (46 characteristic)
C1, C2, C4, C4, C22, C5, C2×C4, C2×C4, C23, C10, C42, C4⋊C4, C4⋊C4, C22×C4, C22×C4, C20, C20, C2×C10, C2.C42, C2×C42, C2×C4⋊C4, C2×C4⋊C4, C2×C20, C2×C20, C22×C10, C23.65C23, C4×C20, C5×C4⋊C4, C5×C4⋊C4, C22×C20, C22×C20, C5×C2.C42, C2×C4×C20, C10×C4⋊C4, C10×C4⋊C4, C5×C23.65C23
Quotients: C1, C2, C4, C22, C5, C2×C4, D4, Q8, C23, C10, C4⋊C4, C22×C4, C2×D4, C2×Q8, C4○D4, C20, C2×C10, C2×C4⋊C4, C4×D4, C4×Q8, C4⋊D4, C22⋊Q8, C42.C2, C4⋊Q8, C2×C20, C5×D4, C5×Q8, C22×C10, C23.65C23, C5×C4⋊C4, C22×C20, D4×C10, Q8×C10, C5×C4○D4, C10×C4⋊C4, D4×C20, Q8×C20, C5×C4⋊D4, C5×C22⋊Q8, C5×C42.C2, C5×C4⋊Q8, C5×C23.65C23

Smallest permutation representation of C5×C23.65C23
►Regular action on 320 points
Generators in S320
(1 2 3 4 5)(6 7 8 9 10)(11 12 13 14 15)(16 17 18 19 20)(21 22 23 24 25)(26 27 28 29 30)(31 32 33 34 35)(36 37 38 39 40)(41 42 43 44 45)(46 47 48 49 50)(51 52 53 54 55)(56 57 58 59 60)(61 62 63 64 65)(66 67 68 69 70)(71 72 73 74 75)(76 77 78 79 80)(81 82 83 84 85)(86 87 88 89 90)(91 92 93 94 95)(96 97 98 99 100)(101 102 103 104 105)(106 107 108 109 110)(111 112 113 114 115)(116 117 118 119 120)(121 122 123 124 125)(126 127 128 129 130)(131 132 133 134 135)(136 137 138 139 140)(141 142 143 144 145)(146 147 148 149 150)(151 152 153 154 155)(156 157 158 159 160)(161 162 163 164 165)(166 167 168 169 170)(171 172 173 174 175)(176 177 178 179 180)(181 182 183 184 185)(186 187 188 189 190)(191 192 193 194 195)(196 197 198 199 200)(201 202 203 204 205)(206 207 208 209 210)(211 212 213 214 215)(216 217 218 219 220)(221 222 223 224 225)(226 227 228 229 230)(231 232 233 234 235)(236 237 238 239 240)(241 242 243 244 245)(246 247 248 249 250)(251 252 253 254 255)(256 257 258 259 260)(261 262 263 264 265)(266 267 268 269 270)(271 272 273 274 275)(276 277 278 279 280)(281 282 283 284 285)(286 287 288 289 290)(291 292 293 294 295)(296 297 298 299 300)(301 302 303 304 305)(306 307 308 309 310)(311 312 313 314 315)(316 317 318 319 320)

(1 30)(2 26)(3 27)(4 28)(5 29)(6 311)(7 312)(8 313)(9 314)(10 315)(11 45)(12 41)(13 42)(14 43)(15 44)(16 305)(17 301)(18 302)(19 303)(20 304)(21 287)(22 288)(23 289)(24 290)(25 286)(31 316)(32 317)(33 318)(34 319)(35 320)(36 59)(37 60)(38 56)(39 57)(40 58)(46 83)(47 84)(48 85)(49 81)(50 82)(51 67)(52 68)(53 69)(54 70)(55 66)(61 91)(62 92)(63 93)(64 94)(65 95)(71 109)(72 110)(73 106)(74 107)(75 108)(76 99)(77 100)(78 96)(79 97)(80 98)(86 123)(87 124)(88 125)(89 121)(90 122)(101 131)(102 132)(103 133)(104 134)(105 135)(111 149)(112 150)(113 146)(114 147)(115 148)(116 139)(117 140)(118 136)(119 137)(120 138)(126 163)(127 164)(128 165)(129 161)(130 162)(141 171)(142 172)(143 173)(144 174)(145 175)(151 189)(152 190)(153 186)(154 187)(155 188)(156 179)(157 180)(158 176)(159 177)(160 178)(166 203)(167 204)(168 205)(169 201)(170 202)(181 211)(182 212)(183 213)(184 214)(185 215)(191 229)(192 230)(193 226)(194 227)(195 228)(196 219)(197 220)(198 216)(199 217)(200 218)(206 243)(207 244)(208 245)(209 241)(210 242)(221 251)(222 252)(223 253)(224 254)(225 255)(231 269)(232 270)(233 266)(234 267)(235 268)(236 259)(237 260)(238 256)(239 257)(240 258)(246 283)(247 284)(248 285)(249 281)(250 282)(261 291)(262 292)(263 293)(264 294)(265 295)(271 309)(272 310)(273 306)(274 307)(275 308)(276 299)(277 300)(278 296)(279 297)(280 298)

(1 66)(2 67)(3 68)(4 69)(5 70)(6 18)(7 19)(8 20)(9 16)(10 17)(11 36)(12 37)(13 38)(14 39)(15 40)(21 35)(22 31)(23 32)(24 33)(25 34)(26 51)(27 52)(28 53)(29 54)(30 55)(41 60)(42 56)(43 57)(44 58)(45 59)(46 79)(47 80)(48 76)(49 77)(50 78)(61 75)(62 71)(63 72)(64 73)(65 74)(81 100)(82 96)(83 97)(84 98)(85 99)(86 119)(87 120)(88 116)(89 117)(90 118)(91 108)(92 109)(93 110)(94 106)(95 107)(101 115)(102 111)(103 112)(104 113)(105 114)(121 140)(122 136)(123 137)(124 138)(125 139)(126 159)(127 160)(128 156)(129 157)(130 158)(131 148)(132 149)(133 150)(134 146)(135 147)(141 155)(142 151)(143 152)(144 153)(145 154)(161 180)(162 176)(163 177)(164 178)(165 179)(166 199)(167 200)(168 196)(169 197)(170 198)(171 188)(172 189)(173 190)(174 186)(175 187)(181 195)(182 191)(183 192)(184 193)(185 194)(201 220)(202 216)(203 217)(204 218)(205 219)(206 239)(207 240)(208 236)(209 237)(210 238)(211 228)(212 229)(213 230)(214 226)(215 227)(221 235)(222 231)(223 232)(224 233)(225 234)(241 260)(242 256)(243 257)(244 258)(245 259)(246 279)(247 280)(248 276)(249 277)(250 278)(251 268)(252 269)(253 270)(254 266)(255 267)(261 275)(262 271)(263 272)(264 273)(265 274)(281 300)(282 296)(283 297)(284 298)(285 299)(286 319)(287 320)(288 316)(289 317)(290 318)(291 308)(292 309)(293 310)(294 306)(295 307)(301 315)(302 311)(303 312)(304 313)(305 314)

(1 12)(2 13)(3 14)(4 15)(5 11)(6 320)(7 316)(8 317)(9 318)(10 319)(16 290)(17 286)(18 287)(19 288)(20 289)(21 302)(22 303)(23 304)(24 305)(25 301)(26 42)(27 43)(28 44)(29 45)(30 41)(31 312)(32 313)(33 314)(34 315)(35 311)(36 70)(37 66)(38 67)(39 68)(40 69)(46 91)(47 92)(48 93)(49 94)(50 95)(51 56)(52 57)(53 58)(54 59)(55 60)(61 83)(62 84)(63 85)(64 81)(65 82)(71 98)(72 99)(73 100)(74 96)(75 97)(76 110)(77 106)(78 107)(79 108)(80 109)(86 131)(87 132)(88 133)(89 134)(90 135)(101 123)(102 124)(103 125)(104 121)(105 122)(111 138)(112 139)(113 140)(114 136)(115 137)(116 150)(117 146)(118 147)(119 148)(120 149)(126 171)(127 172)(128 173)(129 174)(130 175)(141 163)(142 164)(143 165)(144 161)(145 162)(151 178)(152 179)(153 180)(154 176)(155 177)(156 190)(157 186)(158 187)(159 188)(160 189)(166 211)(167 212)(168 213)(169 214)(170 215)(181 203)(182 204)(183 205)(184 201)(185 202)(191 218)(192 219)(193 220)(194 216)(195 217)(196 230)(197 226)(198 227)(199 228)(200 229)(206 251)(207 252)(208 253)(209 254)(210 255)(221 243)(222 244)(223 245)(224 241)(225 242)(231 258)(232 259)(233 260)(234 256)(235 257)(236 270)(237 266)(238 267)(239 268)(240 269)(246 291)(247 292)(248 293)(249 294)(250 295)(261 283)(262 284)(263 285)(264 281)(265 282)(271 298)(272 299)(273 300)(274 296)(275 297)(276 310)(277 306)(278 307)(279 308)(280 309)

(1 169 12 214)(2 170 13 215)(3 166 14 211)(4 167 15 212)(5 168 11 213)(6 189 320 160)(7 190 316 156)(8 186 317 157)(9 187 318 158)(10 188 319 159)(16 175 290 130)(17 171 286 126)(18 172 287 127)(19 173 288 128)(20 174 289 129)(21 164 302 142)(22 165 303 143)(23 161 304 144)(24 162 305 145)(25 163 301 141)(26 202 42 185)(27 203 43 181)(28 204 44 182)(29 205 45 183)(30 201 41 184)(31 179 312 152)(32 180 313 153)(33 176 314 154)(34 177 315 155)(35 178 311 151)(36 230 70 196)(37 226 66 197)(38 227 67 198)(39 228 68 199)(40 229 69 200)(46 251 91 206)(47 252 92 207)(48 253 93 208)(49 254 94 209)(50 255 95 210)(51 216 56 194)(52 217 57 195)(53 218 58 191)(54 219 59 192)(55 220 60 193)(61 243 83 221)(62 244 84 222)(63 245 85 223)(64 241 81 224)(65 242 82 225)(71 258 98 231)(72 259 99 232)(73 260 100 233)(74 256 96 234)(75 257 97 235)(76 270 110 236)(77 266 106 237)(78 267 107 238)(79 268 108 239)(80 269 109 240)(86 291 131 246)(87 292 132 247)(88 293 133 248)(89 294 134 249)(90 295 135 250)(101 283 123 261)(102 284 124 262)(103 285 125 263)(104 281 121 264)(105 282 122 265)(111 298 138 271)(112 299 139 272)(113 300 140 273)(114 296 136 274)(115 297 137 275)(116 310 150 276)(117 306 146 277)(118 307 147 278)(119 308 148 279)(120 309 149 280)

(1 89 12 134)(2 90 13 135)(3 86 14 131)(4 87 15 132)(5 88 11 133)(6 231 320 258)(7 232 316 259)(8 233 317 260)(9 234 318 256)(10 235 319 257)(16 225 290 242)(17 221 286 243)(18 222 287 244)(19 223 288 245)(20 224 289 241)(21 207 302 252)(22 208 303 253)(23 209 304 254)(24 210 305 255)(25 206 301 251)(26 122 42 105)(27 123 43 101)(28 124 44 102)(29 125 45 103)(30 121 41 104)(31 236 312 270)(32 237 313 266)(33 238 314 267)(34 239 315 268)(35 240 311 269)(36 150 70 116)(37 146 66 117)(38 147 67 118)(39 148 68 119)(40 149 69 120)(46 171 91 126)(47 172 92 127)(48 173 93 128)(49 174 94 129)(50 175 95 130)(51 136 56 114)(52 137 57 115)(53 138 58 111)(54 139 59 112)(55 140 60 113)(61 163 83 141)(62 164 84 142)(63 165 85 143)(64 161 81 144)(65 162 82 145)(71 178 98 151)(72 179 99 152)(73 180 100 153)(74 176 96 154)(75 177 97 155)(76 190 110 156)(77 186 106 157)(78 187 107 158)(79 188 108 159)(80 189 109 160)(166 261 211 283)(167 262 212 284)(168 263 213 285)(169 264 214 281)(170 265 215 282)(181 246 203 291)(182 247 204 292)(183 248 205 293)(184 249 201 294)(185 250 202 295)(191 280 218 309)(192 276 219 310)(193 277 220 306)(194 278 216 307)(195 279 217 308)(196 272 230 299)(197 273 226 300)(198 274 227 296)(199 275 228 297)(200 271 229 298)

(1 106 66 94)(2 107 67 95)(3 108 68 91)(4 109 69 92)(5 110 70 93)(6 292 18 309)(7 293 19 310)(8 294 20 306)(9 295 16 307)(10 291 17 308)(11 76 36 48)(12 77 37 49)(13 78 38 50)(14 79 39 46)(15 80 40 47)(21 298 35 284)(22 299 31 285)(23 300 32 281)(24 296 33 282)(25 297 34 283)(26 74 51 65)(27 75 52 61)(28 71 53 62)(29 72 54 63)(30 73 55 64)(41 100 60 81)(42 96 56 82)(43 97 57 83)(44 98 58 84)(45 99 59 85)(86 159 119 126)(87 160 120 127)(88 156 116 128)(89 157 117 129)(90 158 118 130)(101 155 115 141)(102 151 111 142)(103 152 112 143)(104 153 113 144)(105 154 114 145)(121 180 140 161)(122 176 136 162)(123 177 137 163)(124 178 138 164)(125 179 139 165)(131 188 148 171)(132 189 149 172)(133 190 150 173)(134 186 146 174)(135 187 147 175)(166 206 199 239)(167 207 200 240)(168 208 196 236)(169 209 197 237)(170 210 198 238)(181 221 195 235)(182 222 191 231)(183 223 192 232)(184 224 193 233)(185 225 194 234)(201 241 220 260)(202 242 216 256)(203 243 217 257)(204 244 218 258)(205 245 219 259)(211 251 228 268)(212 252 229 269)(213 253 230 270)(214 254 226 266)(215 255 227 267)(246 286 279 319)(247 287 280 320)(248 288 276 316)(249 289 277 317)(250 290 278 318)(261 301 275 315)(262 302 271 311)(263 303 272 312)(264 304 273 313)(265 305 274 314)
 
G:=sub<Sym(320)| (1,2,3,4,5)(6,7,8,9,10)(11,12,13,14,15)(16,17,18,19,20)(21,22,23,24,25)(26,27,28,29,30)(31,32,33,34,35)(36,37,38,39,40)(41,42,43,44,45)(46,47,48,49,50)(51,52,53,54,55)(56,57,58,59,60)(61,62,63,64,65)(66,67,68,69,70)(71,72,73,74,75)(76,77,78,79,80)(81,82,83,84,85)(86,87,88,89,90)(91,92,93,94,95)(96,97,98,99,100)(101,102,103,104,105)(106,107,108,109,110)(111,112,113,114,115)(116,117,118,119,120)(121,122,123,124,125)(126,127,128,129,130)(131,132,133,134,135)(136,137,138,139,140)(141,142,143,144,145)(146,147,148,149,150)(151,152,153,154,155)(156,157,158,159,160)(161,162,163,164,165)(166,167,168,169,170)(171,172,173,174,175)(176,177,178,179,180)(181,182,183,184,185)(186,187,188,189,190)(191,192,193,194,195)(196,197,198,199,200)(201,202,203,204,205)(206,207,208,209,210)(211,212,213,214,215)(216,217,218,219,220)(221,222,223,224,225)(226,227,228,229,230)(231,232,233,234,235)(236,237,238,239,240)(241,242,243,244,245)(246,247,248,249,250)(251,252,253,254,255)(256,257,258,259,260)(261,262,263,264,265)(266,267,268,269,270)(271,272,273,274,275)(276,277,278,279,280)(281,282,283,284,285)(286,287,288,289,290)(291,292,293,294,295)(296,297,298,299,300)(301,302,303,304,305)(306,307,308,309,310)(311,312,313,314,315)(316,317,318,319,320), (1,30)(2,26)(3,27)(4,28)(5,29)(6,311)(7,312)(8,313)(9,314)(10,315)(11,45)(12,41)(13,42)(14,43)(15,44)(16,305)(17,301)(18,302)(19,303)(20,304)(21,287)(22,288)(23,289)(24,290)(25,286)(31,316)(32,317)(33,318)(34,319)(35,320)(36,59)(37,60)(38,56)(39,57)(40,58)(46,83)(47,84)(48,85)(49,81)(50,82)(51,67)(52,68)(53,69)(54,70)(55,66)(61,91)(62,92)(63,93)(64,94)(65,95)(71,109)(72,110)(73,106)(74,107)(75,108)(76,99)(77,100)(78,96)(79,97)(80,98)(86,123)(87,124)(88,125)(89,121)(90,122)(101,131)(102,132)(103,133)(104,134)(105,135)(111,149)(112,150)(113,146)(114,147)(115,148)(116,139)(117,140)(118,136)(119,137)(120,138)(126,163)(127,164)(128,165)(129,161)(130,162)(141,171)(142,172)(143,173)(144,174)(145,175)(151,189)(152,190)(153,186)(154,187)(155,188)(156,179)(157,180)(158,176)(159,177)(160,178)(166,203)(167,204)(168,205)(169,201)(170,202)(181,211)(182,212)(183,213)(184,214)(185,215)(191,229)(192,230)(193,226)(194,227)(195,228)(196,219)(197,220)(198,216)(199,217)(200,218)(206,243)(207,244)(208,245)(209,241)(210,242)(221,251)(222,252)(223,253)(224,254)(225,255)(231,269)(232,270)(233,266)(234,267)(235,268)(236,259)(237,260)(238,256)(239,257)(240,258)(246,283)(247,284)(248,285)(249,281)(250,282)(261,291)(262,292)(263,293)(264,294)(265,295)(271,309)(272,310)(273,306)(274,307)(275,308)(276,299)(277,300)(278,296)(279,297)(280,298), (1,66)(2,67)(3,68)(4,69)(5,70)(6,18)(7,19)(8,20)(9,16)(10,17)(11,36)(12,37)(13,38)(14,39)(15,40)(21,35)(22,31)(23,32)(24,33)(25,34)(26,51)(27,52)(28,53)(29,54)(30,55)(41,60)(42,56)(43,57)(44,58)(45,59)(46,79)(47,80)(48,76)(49,77)(50,78)(61,75)(62,71)(63,72)(64,73)(65,74)(81,100)(82,96)(83,97)(84,98)(85,99)(86,119)(87,120)(88,116)(89,117)(90,118)(91,108)(92,109)(93,110)(94,106)(95,107)(101,115)(102,111)(103,112)(104,113)(105,114)(121,140)(122,136)(123,137)(124,138)(125,139)(126,159)(127,160)(128,156)(129,157)(130,158)(131,148)(132,149)(133,150)(134,146)(135,147)(141,155)(142,151)(143,152)(144,153)(145,154)(161,180)(162,176)(163,177)(164,178)(165,179)(166,199)(167,200)(168,196)(169,197)(170,198)(171,188)(172,189)(173,190)(174,186)(175,187)(181,195)(182,191)(183,192)(184,193)(185,194)(201,220)(202,216)(203,217)(204,218)(205,219)(206,239)(207,240)(208,236)(209,237)(210,238)(211,228)(212,229)(213,230)(214,226)(215,227)(221,235)(222,231)(223,232)(224,233)(225,234)(241,260)(242,256)(243,257)(244,258)(245,259)(246,279)(247,280)(248,276)(249,277)(250,278)(251,268)(252,269)(253,270)(254,266)(255,267)(261,275)(262,271)(263,272)(264,273)(265,274)(281,300)(282,296)(283,297)(284,298)(285,299)(286,319)(287,320)(288,316)(289,317)(290,318)(291,308)(292,309)(293,310)(294,306)(295,307)(301,315)(302,311)(303,312)(304,313)(305,314), (1,12)(2,13)(3,14)(4,15)(5,11)(6,320)(7,316)(8,317)(9,318)(10,319)(16,290)(17,286)(18,287)(19,288)(20,289)(21,302)(22,303)(23,304)(24,305)(25,301)(26,42)(27,43)(28,44)(29,45)(30,41)(31,312)(32,313)(33,314)(34,315)(35,311)(36,70)(37,66)(38,67)(39,68)(40,69)(46,91)(47,92)(48,93)(49,94)(50,95)(51,56)(52,57)(53,58)(54,59)(55,60)(61,83)(62,84)(63,85)(64,81)(65,82)(71,98)(72,99)(73,100)(74,96)(75,97)(76,110)(77,106)(78,107)(79,108)(80,109)(86,131)(87,132)(88,133)(89,134)(90,135)(101,123)(102,124)(103,125)(104,121)(105,122)(111,138)(112,139)(113,140)(114,136)(115,137)(116,150)(117,146)(118,147)(119,148)(120,149)(126,171)(127,172)(128,173)(129,174)(130,175)(141,163)(142,164)(143,165)(144,161)(145,162)(151,178)(152,179)(153,180)(154,176)(155,177)(156,190)(157,186)(158,187)(159,188)(160,189)(166,211)(167,212)(168,213)(169,214)(170,215)(181,203)(182,204)(183,205)(184,201)(185,202)(191,218)(192,219)(193,220)(194,216)(195,217)(196,230)(197,226)(198,227)(199,228)(200,229)(206,251)(207,252)(208,253)(209,254)(210,255)(221,243)(222,244)(223,245)(224,241)(225,242)(231,258)(232,259)(233,260)(234,256)(235,257)(236,270)(237,266)(238,267)(239,268)(240,269)(246,291)(247,292)(248,293)(249,294)(250,295)(261,283)(262,284)(263,285)(264,281)(265,282)(271,298)(272,299)(273,300)(274,296)(275,297)(276,310)(277,306)(278,307)(279,308)(280,309), (1,169,12,214)(2,170,13,215)(3,166,14,211)(4,167,15,212)(5,168,11,213)(6,189,320,160)(7,190,316,156)(8,186,317,157)(9,187,318,158)(10,188,319,159)(16,175,290,130)(17,171,286,126)(18,172,287,127)(19,173,288,128)(20,174,289,129)(21,164,302,142)(22,165,303,143)(23,161,304,144)(24,162,305,145)(25,163,301,141)(26,202,42,185)(27,203,43,181)(28,204,44,182)(29,205,45,183)(30,201,41,184)(31,179,312,152)(32,180,313,153)(33,176,314,154)(34,177,315,155)(35,178,311,151)(36,230,70,196)(37,226,66,197)(38,227,67,198)(39,228,68,199)(40,229,69,200)(46,251,91,206)(47,252,92,207)(48,253,93,208)(49,254,94,209)(50,255,95,210)(51,216,56,194)(52,217,57,195)(53,218,58,191)(54,219,59,192)(55,220,60,193)(61,243,83,221)(62,244,84,222)(63,245,85,223)(64,241,81,224)(65,242,82,225)(71,258,98,231)(72,259,99,232)(73,260,100,233)(74,256,96,234)(75,257,97,235)(76,270,110,236)(77,266,106,237)(78,267,107,238)(79,268,108,239)(80,269,109,240)(86,291,131,246)(87,292,132,247)(88,293,133,248)(89,294,134,249)(90,295,135,250)(101,283,123,261)(102,284,124,262)(103,285,125,263)(104,281,121,264)(105,282,122,265)(111,298,138,271)(112,299,139,272)(113,300,140,273)(114,296,136,274)(115,297,137,275)(116,310,150,276)(117,306,146,277)(118,307,147,278)(119,308,148,279)(120,309,149,280), (1,89,12,134)(2,90,13,135)(3,86,14,131)(4,87,15,132)(5,88,11,133)(6,231,320,258)(7,232,316,259)(8,233,317,260)(9,234,318,256)(10,235,319,257)(16,225,290,242)(17,221,286,243)(18,222,287,244)(19,223,288,245)(20,224,289,241)(21,207,302,252)(22,208,303,253)(23,209,304,254)(24,210,305,255)(25,206,301,251)(26,122,42,105)(27,123,43,101)(28,124,44,102)(29,125,45,103)(30,121,41,104)(31,236,312,270)(32,237,313,266)(33,238,314,267)(34,239,315,268)(35,240,311,269)(36,150,70,116)(37,146,66,117)(38,147,67,118)(39,148,68,119)(40,149,69,120)(46,171,91,126)(47,172,92,127)(48,173,93,128)(49,174,94,129)(50,175,95,130)(51,136,56,114)(52,137,57,115)(53,138,58,111)(54,139,59,112)(55,140,60,113)(61,163,83,141)(62,164,84,142)(63,165,85,143)(64,161,81,144)(65,162,82,145)(71,178,98,151)(72,179,99,152)(73,180,100,153)(74,176,96,154)(75,177,97,155)(76,190,110,156)(77,186,106,157)(78,187,107,158)(79,188,108,159)(80,189,109,160)(166,261,211,283)(167,262,212,284)(168,263,213,285)(169,264,214,281)(170,265,215,282)(181,246,203,291)(182,247,204,292)(183,248,205,293)(184,249,201,294)(185,250,202,295)(191,280,218,309)(192,276,219,310)(193,277,220,306)(194,278,216,307)(195,279,217,308)(196,272,230,299)(197,273,226,300)(198,274,227,296)(199,275,228,297)(200,271,229,298), (1,106,66,94)(2,107,67,95)(3,108,68,91)(4,109,69,92)(5,110,70,93)(6,292,18,309)(7,293,19,310)(8,294,20,306)(9,295,16,307)(10,291,17,308)(11,76,36,48)(12,77,37,49)(13,78,38,50)(14,79,39,46)(15,80,40,47)(21,298,35,284)(22,299,31,285)(23,300,32,281)(24,296,33,282)(25,297,34,283)(26,74,51,65)(27,75,52,61)(28,71,53,62)(29,72,54,63)(30,73,55,64)(41,100,60,81)(42,96,56,82)(43,97,57,83)(44,98,58,84)(45,99,59,85)(86,159,119,126)(87,160,120,127)(88,156,116,128)(89,157,117,129)(90,158,118,130)(101,155,115,141)(102,151,111,142)(103,152,112,143)(104,153,113,144)(105,154,114,145)(121,180,140,161)(122,176,136,162)(123,177,137,163)(124,178,138,164)(125,179,139,165)(131,188,148,171)(132,189,149,172)(133,190,150,173)(134,186,146,174)(135,187,147,175)(166,206,199,239)(167,207,200,240)(168,208,196,236)(169,209,197,237)(170,210,198,238)(181,221,195,235)(182,222,191,231)(183,223,192,232)(184,224,193,233)(185,225,194,234)(201,241,220,260)(202,242,216,256)(203,243,217,257)(204,244,218,258)(205,245,219,259)(211,251,228,268)(212,252,229,269)(213,253,230,270)(214,254,226,266)(215,255,227,267)(246,286,279,319)(247,287,280,320)(248,288,276,316)(249,289,277,317)(250,290,278,318)(261,301,275,315)(262,302,271,311)(263,303,272,312)(264,304,273,313)(265,305,274,314)>;
 
G:=Group( (1,2,3,4,5)(6,7,8,9,10)(11,12,13,14,15)(16,17,18,19,20)(21,22,23,24,25)(26,27,28,29,30)(31,32,33,34,35)(36,37,38,39,40)(41,42,43,44,45)(46,47,48,49,50)(51,52,53,54,55)(56,57,58,59,60)(61,62,63,64,65)(66,67,68,69,70)(71,72,73,74,75)(76,77,78,79,80)(81,82,83,84,85)(86,87,88,89,90)(91,92,93,94,95)(96,97,98,99,100)(101,102,103,104,105)(106,107,108,109,110)(111,112,113,114,115)(116,117,118,119,120)(121,122,123,124,125)(126,127,128,129,130)(131,132,133,134,135)(136,137,138,139,140)(141,142,143,144,145)(146,147,148,149,150)(151,152,153,154,155)(156,157,158,159,160)(161,162,163,164,165)(166,167,168,169,170)(171,172,173,174,175)(176,177,178,179,180)(181,182,183,184,185)(186,187,188,189,190)(191,192,193,194,195)(196,197,198,199,200)(201,202,203,204,205)(206,207,208,209,210)(211,212,213,214,215)(216,217,218,219,220)(221,222,223,224,225)(226,227,228,229,230)(231,232,233,234,235)(236,237,238,239,240)(241,242,243,244,245)(246,247,248,249,250)(251,252,253,254,255)(256,257,258,259,260)(261,262,263,264,265)(266,267,268,269,270)(271,272,273,274,275)(276,277,278,279,280)(281,282,283,284,285)(286,287,288,289,290)(291,292,293,294,295)(296,297,298,299,300)(301,302,303,304,305)(306,307,308,309,310)(311,312,313,314,315)(316,317,318,319,320), (1,30)(2,26)(3,27)(4,28)(5,29)(6,311)(7,312)(8,313)(9,314)(10,315)(11,45)(12,41)(13,42)(14,43)(15,44)(16,305)(17,301)(18,302)(19,303)(20,304)(21,287)(22,288)(23,289)(24,290)(25,286)(31,316)(32,317)(33,318)(34,319)(35,320)(36,59)(37,60)(38,56)(39,57)(40,58)(46,83)(47,84)(48,85)(49,81)(50,82)(51,67)(52,68)(53,69)(54,70)(55,66)(61,91)(62,92)(63,93)(64,94)(65,95)(71,109)(72,110)(73,106)(74,107)(75,108)(76,99)(77,100)(78,96)(79,97)(80,98)(86,123)(87,124)(88,125)(89,121)(90,122)(101,131)(102,132)(103,133)(104,134)(105,135)(111,149)(112,150)(113,146)(114,147)(115,148)(116,139)(117,140)(118,136)(119,137)(120,138)(126,163)(127,164)(128,165)(129,161)(130,162)(141,171)(142,172)(143,173)(144,174)(145,175)(151,189)(152,190)(153,186)(154,187)(155,188)(156,179)(157,180)(158,176)(159,177)(160,178)(166,203)(167,204)(168,205)(169,201)(170,202)(181,211)(182,212)(183,213)(184,214)(185,215)(191,229)(192,230)(193,226)(194,227)(195,228)(196,219)(197,220)(198,216)(199,217)(200,218)(206,243)(207,244)(208,245)(209,241)(210,242)(221,251)(222,252)(223,253)(224,254)(225,255)(231,269)(232,270)(233,266)(234,267)(235,268)(236,259)(237,260)(238,256)(239,257)(240,258)(246,283)(247,284)(248,285)(249,281)(250,282)(261,291)(262,292)(263,293)(264,294)(265,295)(271,309)(272,310)(273,306)(274,307)(275,308)(276,299)(277,300)(278,296)(279,297)(280,298), (1,66)(2,67)(3,68)(4,69)(5,70)(6,18)(7,19)(8,20)(9,16)(10,17)(11,36)(12,37)(13,38)(14,39)(15,40)(21,35)(22,31)(23,32)(24,33)(25,34)(26,51)(27,52)(28,53)(29,54)(30,55)(41,60)(42,56)(43,57)(44,58)(45,59)(46,79)(47,80)(48,76)(49,77)(50,78)(61,75)(62,71)(63,72)(64,73)(65,74)(81,100)(82,96)(83,97)(84,98)(85,99)(86,119)(87,120)(88,116)(89,117)(90,118)(91,108)(92,109)(93,110)(94,106)(95,107)(101,115)(102,111)(103,112)(104,113)(105,114)(121,140)(122,136)(123,137)(124,138)(125,139)(126,159)(127,160)(128,156)(129,157)(130,158)(131,148)(132,149)(133,150)(134,146)(135,147)(141,155)(142,151)(143,152)(144,153)(145,154)(161,180)(162,176)(163,177)(164,178)(165,179)(166,199)(167,200)(168,196)(169,197)(170,198)(171,188)(172,189)(173,190)(174,186)(175,187)(181,195)(182,191)(183,192)(184,193)(185,194)(201,220)(202,216)(203,217)(204,218)(205,219)(206,239)(207,240)(208,236)(209,237)(210,238)(211,228)(212,229)(213,230)(214,226)(215,227)(221,235)(222,231)(223,232)(224,233)(225,234)(241,260)(242,256)(243,257)(244,258)(245,259)(246,279)(247,280)(248,276)(249,277)(250,278)(251,268)(252,269)(253,270)(254,266)(255,267)(261,275)(262,271)(263,272)(264,273)(265,274)(281,300)(282,296)(283,297)(284,298)(285,299)(286,319)(287,320)(288,316)(289,317)(290,318)(291,308)(292,309)(293,310)(294,306)(295,307)(301,315)(302,311)(303,312)(304,313)(305,314), (1,12)(2,13)(3,14)(4,15)(5,11)(6,320)(7,316)(8,317)(9,318)(10,319)(16,290)(17,286)(18,287)(19,288)(20,289)(21,302)(22,303)(23,304)(24,305)(25,301)(26,42)(27,43)(28,44)(29,45)(30,41)(31,312)(32,313)(33,314)(34,315)(35,311)(36,70)(37,66)(38,67)(39,68)(40,69)(46,91)(47,92)(48,93)(49,94)(50,95)(51,56)(52,57)(53,58)(54,59)(55,60)(61,83)(62,84)(63,85)(64,81)(65,82)(71,98)(72,99)(73,100)(74,96)(75,97)(76,110)(77,106)(78,107)(79,108)(80,109)(86,131)(87,132)(88,133)(89,134)(90,135)(101,123)(102,124)(103,125)(104,121)(105,122)(111,138)(112,139)(113,140)(114,136)(115,137)(116,150)(117,146)(118,147)(119,148)(120,149)(126,171)(127,172)(128,173)(129,174)(130,175)(141,163)(142,164)(143,165)(144,161)(145,162)(151,178)(152,179)(153,180)(154,176)(155,177)(156,190)(157,186)(158,187)(159,188)(160,189)(166,211)(167,212)(168,213)(169,214)(170,215)(181,203)(182,204)(183,205)(184,201)(185,202)(191,218)(192,219)(193,220)(194,216)(195,217)(196,230)(197,226)(198,227)(199,228)(200,229)(206,251)(207,252)(208,253)(209,254)(210,255)(221,243)(222,244)(223,245)(224,241)(225,242)(231,258)(232,259)(233,260)(234,256)(235,257)(236,270)(237,266)(238,267)(239,268)(240,269)(246,291)(247,292)(248,293)(249,294)(250,295)(261,283)(262,284)(263,285)(264,281)(265,282)(271,298)(272,299)(273,300)(274,296)(275,297)(276,310)(277,306)(278,307)(279,308)(280,309), (1,169,12,214)(2,170,13,215)(3,166,14,211)(4,167,15,212)(5,168,11,213)(6,189,320,160)(7,190,316,156)(8,186,317,157)(9,187,318,158)(10,188,319,159)(16,175,290,130)(17,171,286,126)(18,172,287,127)(19,173,288,128)(20,174,289,129)(21,164,302,142)(22,165,303,143)(23,161,304,144)(24,162,305,145)(25,163,301,141)(26,202,42,185)(27,203,43,181)(28,204,44,182)(29,205,45,183)(30,201,41,184)(31,179,312,152)(32,180,313,153)(33,176,314,154)(34,177,315,155)(35,178,311,151)(36,230,70,196)(37,226,66,197)(38,227,67,198)(39,228,68,199)(40,229,69,200)(46,251,91,206)(47,252,92,207)(48,253,93,208)(49,254,94,209)(50,255,95,210)(51,216,56,194)(52,217,57,195)(53,218,58,191)(54,219,59,192)(55,220,60,193)(61,243,83,221)(62,244,84,222)(63,245,85,223)(64,241,81,224)(65,242,82,225)(71,258,98,231)(72,259,99,232)(73,260,100,233)(74,256,96,234)(75,257,97,235)(76,270,110,236)(77,266,106,237)(78,267,107,238)(79,268,108,239)(80,269,109,240)(86,291,131,246)(87,292,132,247)(88,293,133,248)(89,294,134,249)(90,295,135,250)(101,283,123,261)(102,284,124,262)(103,285,125,263)(104,281,121,264)(105,282,122,265)(111,298,138,271)(112,299,139,272)(113,300,140,273)(114,296,136,274)(115,297,137,275)(116,310,150,276)(117,306,146,277)(118,307,147,278)(119,308,148,279)(120,309,149,280), (1,89,12,134)(2,90,13,135)(3,86,14,131)(4,87,15,132)(5,88,11,133)(6,231,320,258)(7,232,316,259)(8,233,317,260)(9,234,318,256)(10,235,319,257)(16,225,290,242)(17,221,286,243)(18,222,287,244)(19,223,288,245)(20,224,289,241)(21,207,302,252)(22,208,303,253)(23,209,304,254)(24,210,305,255)(25,206,301,251)(26,122,42,105)(27,123,43,101)(28,124,44,102)(29,125,45,103)(30,121,41,104)(31,236,312,270)(32,237,313,266)(33,238,314,267)(34,239,315,268)(35,240,311,269)(36,150,70,116)(37,146,66,117)(38,147,67,118)(39,148,68,119)(40,149,69,120)(46,171,91,126)(47,172,92,127)(48,173,93,128)(49,174,94,129)(50,175,95,130)(51,136,56,114)(52,137,57,115)(53,138,58,111)(54,139,59,112)(55,140,60,113)(61,163,83,141)(62,164,84,142)(63,165,85,143)(64,161,81,144)(65,162,82,145)(71,178,98,151)(72,179,99,152)(73,180,100,153)(74,176,96,154)(75,177,97,155)(76,190,110,156)(77,186,106,157)(78,187,107,158)(79,188,108,159)(80,189,109,160)(166,261,211,283)(167,262,212,284)(168,263,213,285)(169,264,214,281)(170,265,215,282)(181,246,203,291)(182,247,204,292)(183,248,205,293)(184,249,201,294)(185,250,202,295)(191,280,218,309)(192,276,219,310)(193,277,220,306)(194,278,216,307)(195,279,217,308)(196,272,230,299)(197,273,226,300)(198,274,227,296)(199,275,228,297)(200,271,229,298), (1,106,66,94)(2,107,67,95)(3,108,68,91)(4,109,69,92)(5,110,70,93)(6,292,18,309)(7,293,19,310)(8,294,20,306)(9,295,16,307)(10,291,17,308)(11,76,36,48)(12,77,37,49)(13,78,38,50)(14,79,39,46)(15,80,40,47)(21,298,35,284)(22,299,31,285)(23,300,32,281)(24,296,33,282)(25,297,34,283)(26,74,51,65)(27,75,52,61)(28,71,53,62)(29,72,54,63)(30,73,55,64)(41,100,60,81)(42,96,56,82)(43,97,57,83)(44,98,58,84)(45,99,59,85)(86,159,119,126)(87,160,120,127)(88,156,116,128)(89,157,117,129)(90,158,118,130)(101,155,115,141)(102,151,111,142)(103,152,112,143)(104,153,113,144)(105,154,114,145)(121,180,140,161)(122,176,136,162)(123,177,137,163)(124,178,138,164)(125,179,139,165)(131,188,148,171)(132,189,149,172)(133,190,150,173)(134,186,146,174)(135,187,147,175)(166,206,199,239)(167,207,200,240)(168,208,196,236)(169,209,197,237)(170,210,198,238)(181,221,195,235)(182,222,191,231)(183,223,192,232)(184,224,193,233)(185,225,194,234)(201,241,220,260)(202,242,216,256)(203,243,217,257)(204,244,218,258)(205,245,219,259)(211,251,228,268)(212,252,229,269)(213,253,230,270)(214,254,226,266)(215,255,227,267)(246,286,279,319)(247,287,280,320)(248,288,276,316)(249,289,277,317)(250,290,278,318)(261,301,275,315)(262,302,271,311)(263,303,272,312)(264,304,273,313)(265,305,274,314) );
 
G=PermutationGroup([[(1,2,3,4,5),(6,7,8,9,10),(11,12,13,14,15),(16,17,18,19,20),(21,22,23,24,25),(26,27,28,29,30),(31,32,33,34,35),(36,37,38,39,40),(41,42,43,44,45),(46,47,48,49,50),(51,52,53,54,55),(56,57,58,59,60),(61,62,63,64,65),(66,67,68,69,70),(71,72,73,74,75),(76,77,78,79,80),(81,82,83,84,85),(86,87,88,89,90),(91,92,93,94,95),(96,97,98,99,100),(101,102,103,104,105),(106,107,108,109,110),(111,112,113,114,115),(116,117,118,119,120),(121,122,123,124,125),(126,127,128,129,130),(131,132,133,134,135),(136,137,138,139,140),(141,142,143,144,145),(146,147,148,149,150),(151,152,153,154,155),(156,157,158,159,160),(161,162,163,164,165),(166,167,168,169,170),(171,172,173,174,175),(176,177,178,179,180),(181,182,183,184,185),(186,187,188,189,190),(191,192,193,194,195),(196,197,198,199,200),(201,202,203,204,205),(206,207,208,209,210),(211,212,213,214,215),(216,217,218,219,220),(221,222,223,224,225),(226,227,228,229,230),(231,232,233,234,235),(236,237,238,239,240),(241,242,243,244,245),(246,247,248,249,250),(251,252,253,254,255),(256,257,258,259,260),(261,262,263,264,265),(266,267,268,269,270),(271,272,273,274,275),(276,277,278,279,280),(281,282,283,284,285),(286,287,288,289,290),(291,292,293,294,295),(296,297,298,299,300),(301,302,303,304,305),(306,307,308,309,310),(311,312,313,314,315),(316,317,318,319,320)], [(1,30),(2,26),(3,27),(4,28),(5,29),(6,311),(7,312),(8,313),(9,314),(10,315),(11,45),(12,41),(13,42),(14,43),(15,44),(16,305),(17,301),(18,302),(19,303),(20,304),(21,287),(22,288),(23,289),(24,290),(25,286),(31,316),(32,317),(33,318),(34,319),(35,320),(36,59),(37,60),(38,56),(39,57),(40,58),(46,83),(47,84),(48,85),(49,81),(50,82),(51,67),(52,68),(53,69),(54,70),(55,66),(61,91),(62,92),(63,93),(64,94),(65,95),(71,109),(72,110),(73,106),(74,107),(75,108),(76,99),(77,100),(78,96),(79,97),(80,98),(86,123),(87,124),(88,125),(89,121),(90,122),(101,131),(102,132),(103,133),(104,134),(105,135),(111,149),(112,150),(113,146),(114,147),(115,148),(116,139),(117,140),(118,136),(119,137),(120,138),(126,163),(127,164),(128,165),(129,161),(130,162),(141,171),(142,172),(143,173),(144,174),(145,175),(151,189),(152,190),(153,186),(154,187),(155,188),(156,179),(157,180),(158,176),(159,177),(160,178),(166,203),(167,204),(168,205),(169,201),(170,202),(181,211),(182,212),(183,213),(184,214),(185,215),(191,229),(192,230),(193,226),(194,227),(195,228),(196,219),(197,220),(198,216),(199,217),(200,218),(206,243),(207,244),(208,245),(209,241),(210,242),(221,251),(222,252),(223,253),(224,254),(225,255),(231,269),(232,270),(233,266),(234,267),(235,268),(236,259),(237,260),(238,256),(239,257),(240,258),(246,283),(247,284),(248,285),(249,281),(250,282),(261,291),(262,292),(263,293),(264,294),(265,295),(271,309),(272,310),(273,306),(274,307),(275,308),(276,299),(277,300),(278,296),(279,297),(280,298)], [(1,66),(2,67),(3,68),(4,69),(5,70),(6,18),(7,19),(8,20),(9,16),(10,17),(11,36),(12,37),(13,38),(14,39),(15,40),(21,35),(22,31),(23,32),(24,33),(25,34),(26,51),(27,52),(28,53),(29,54),(30,55),(41,60),(42,56),(43,57),(44,58),(45,59),(46,79),(47,80),(48,76),(49,77),(50,78),(61,75),(62,71),(63,72),(64,73),(65,74),(81,100),(82,96),(83,97),(84,98),(85,99),(86,119),(87,120),(88,116),(89,117),(90,118),(91,108),(92,109),(93,110),(94,106),(95,107),(101,115),(102,111),(103,112),(104,113),(105,114),(121,140),(122,136),(123,137),(124,138),(125,139),(126,159),(127,160),(128,156),(129,157),(130,158),(131,148),(132,149),(133,150),(134,146),(135,147),(141,155),(142,151),(143,152),(144,153),(145,154),(161,180),(162,176),(163,177),(164,178),(165,179),(166,199),(167,200),(168,196),(169,197),(170,198),(171,188),(172,189),(173,190),(174,186),(175,187),(181,195),(182,191),(183,192),(184,193),(185,194),(201,220),(202,216),(203,217),(204,218),(205,219),(206,239),(207,240),(208,236),(209,237),(210,238),(211,228),(212,229),(213,230),(214,226),(215,227),(221,235),(222,231),(223,232),(224,233),(225,234),(241,260),(242,256),(243,257),(244,258),(245,259),(246,279),(247,280),(248,276),(249,277),(250,278),(251,268),(252,269),(253,270),(254,266),(255,267),(261,275),(262,271),(263,272),(264,273),(265,274),(281,300),(282,296),(283,297),(284,298),(285,299),(286,319),(287,320),(288,316),(289,317),(290,318),(291,308),(292,309),(293,310),(294,306),(295,307),(301,315),(302,311),(303,312),(304,313),(305,314)], [(1,12),(2,13),(3,14),(4,15),(5,11),(6,320),(7,316),(8,317),(9,318),(10,319),(16,290),(17,286),(18,287),(19,288),(20,289),(21,302),(22,303),(23,304),(24,305),(25,301),(26,42),(27,43),(28,44),(29,45),(30,41),(31,312),(32,313),(33,314),(34,315),(35,311),(36,70),(37,66),(38,67),(39,68),(40,69),(46,91),(47,92),(48,93),(49,94),(50,95),(51,56),(52,57),(53,58),(54,59),(55,60),(61,83),(62,84),(63,85),(64,81),(65,82),(71,98),(72,99),(73,100),(74,96),(75,97),(76,110),(77,106),(78,107),(79,108),(80,109),(86,131),(87,132),(88,133),(89,134),(90,135),(101,123),(102,124),(103,125),(104,121),(105,122),(111,138),(112,139),(113,140),(114,136),(115,137),(116,150),(117,146),(118,147),(119,148),(120,149),(126,171),(127,172),(128,173),(129,174),(130,175),(141,163),(142,164),(143,165),(144,161),(145,162),(151,178),(152,179),(153,180),(154,176),(155,177),(156,190),(157,186),(158,187),(159,188),(160,189),(166,211),(167,212),(168,213),(169,214),(170,215),(181,203),(182,204),(183,205),(184,201),(185,202),(191,218),(192,219),(193,220),(194,216),(195,217),(196,230),(197,226),(198,227),(199,228),(200,229),(206,251),(207,252),(208,253),(209,254),(210,255),(221,243),(222,244),(223,245),(224,241),(225,242),(231,258),(232,259),(233,260),(234,256),(235,257),(236,270),(237,266),(238,267),(239,268),(240,269),(246,291),(247,292),(248,293),(249,294),(250,295),(261,283),(262,284),(263,285),(264,281),(265,282),(271,298),(272,299),(273,300),(274,296),(275,297),(276,310),(277,306),(278,307),(279,308),(280,309)], [(1,169,12,214),(2,170,13,215),(3,166,14,211),(4,167,15,212),(5,168,11,213),(6,189,320,160),(7,190,316,156),(8,186,317,157),(9,187,318,158),(10,188,319,159),(16,175,290,130),(17,171,286,126),(18,172,287,127),(19,173,288,128),(20,174,289,129),(21,164,302,142),(22,165,303,143),(23,161,304,144),(24,162,305,145),(25,163,301,141),(26,202,42,185),(27,203,43,181),(28,204,44,182),(29,205,45,183),(30,201,41,184),(31,179,312,152),(32,180,313,153),(33,176,314,154),(34,177,315,155),(35,178,311,151),(36,230,70,196),(37,226,66,197),(38,227,67,198),(39,228,68,199),(40,229,69,200),(46,251,91,206),(47,252,92,207),(48,253,93,208),(49,254,94,209),(50,255,95,210),(51,216,56,194),(52,217,57,195),(53,218,58,191),(54,219,59,192),(55,220,60,193),(61,243,83,221),(62,244,84,222),(63,245,85,223),(64,241,81,224),(65,242,82,225),(71,258,98,231),(72,259,99,232),(73,260,100,233),(74,256,96,234),(75,257,97,235),(76,270,110,236),(77,266,106,237),(78,267,107,238),(79,268,108,239),(80,269,109,240),(86,291,131,246),(87,292,132,247),(88,293,133,248),(89,294,134,249),(90,295,135,250),(101,283,123,261),(102,284,124,262),(103,285,125,263),(104,281,121,264),(105,282,122,265),(111,298,138,271),(112,299,139,272),(113,300,140,273),(114,296,136,274),(115,297,137,275),(116,310,150,276),(117,306,146,277),(118,307,147,278),(119,308,148,279),(120,309,149,280)], [(1,89,12,134),(2,90,13,135),(3,86,14,131),(4,87,15,132),(5,88,11,133),(6,231,320,258),(7,232,316,259),(8,233,317,260),(9,234,318,256),(10,235,319,257),(16,225,290,242),(17,221,286,243),(18,222,287,244),(19,223,288,245),(20,224,289,241),(21,207,302,252),(22,208,303,253),(23,209,304,254),(24,210,305,255),(25,206,301,251),(26,122,42,105),(27,123,43,101),(28,124,44,102),(29,125,45,103),(30,121,41,104),(31,236,312,270),(32,237,313,266),(33,238,314,267),(34,239,315,268),(35,240,311,269),(36,150,70,116),(37,146,66,117),(38,147,67,118),(39,148,68,119),(40,149,69,120),(46,171,91,126),(47,172,92,127),(48,173,93,128),(49,174,94,129),(50,175,95,130),(51,136,56,114),(52,137,57,115),(53,138,58,111),(54,139,59,112),(55,140,60,113),(61,163,83,141),(62,164,84,142),(63,165,85,143),(64,161,81,144),(65,162,82,145),(71,178,98,151),(72,179,99,152),(73,180,100,153),(74,176,96,154),(75,177,97,155),(76,190,110,156),(77,186,106,157),(78,187,107,158),(79,188,108,159),(80,189,109,160),(166,261,211,283),(167,262,212,284),(168,263,213,285),(169,264,214,281),(170,265,215,282),(181,246,203,291),(182,247,204,292),(183,248,205,293),(184,249,201,294),(185,250,202,295),(191,280,218,309),(192,276,219,310),(193,277,220,306),(194,278,216,307),(195,279,217,308),(196,272,230,299),(197,273,226,300),(198,274,227,296),(199,275,228,297),(200,271,229,298)], [(1,106,66,94),(2,107,67,95),(3,108,68,91),(4,109,69,92),(5,110,70,93),(6,292,18,309),(7,293,19,310),(8,294,20,306),(9,295,16,307),(10,291,17,308),(11,76,36,48),(12,77,37,49),(13,78,38,50),(14,79,39,46),(15,80,40,47),(21,298,35,284),(22,299,31,285),(23,300,32,281),(24,296,33,282),(25,297,34,283),(26,74,51,65),(27,75,52,61),(28,71,53,62),(29,72,54,63),(30,73,55,64),(41,100,60,81),(42,96,56,82),(43,97,57,83),(44,98,58,84),(45,99,59,85),(86,159,119,126),(87,160,120,127),(88,156,116,128),(89,157,117,129),(90,158,118,130),(101,155,115,141),(102,151,111,142),(103,152,112,143),(104,153,113,144),(105,154,114,145),(121,180,140,161),(122,176,136,162),(123,177,137,163),(124,178,138,164),(125,179,139,165),(131,188,148,171),(132,189,149,172),(133,190,150,173),(134,186,146,174),(135,187,147,175),(166,206,199,239),(167,207,200,240),(168,208,196,236),(169,209,197,237),(170,210,198,238),(181,221,195,235),(182,222,191,231),(183,223,192,232),(184,224,193,233),(185,225,194,234),(201,241,220,260),(202,242,216,256),(203,243,217,257),(204,244,218,258),(205,245,219,259),(211,251,228,268),(212,252,229,269),(213,253,230,270),(214,254,226,266),(215,255,227,267),(246,286,279,319),(247,287,280,320),(248,288,276,316),(249,289,277,317),(250,290,278,318),(261,301,275,315),(262,302,271,311),(263,303,272,312),(264,304,273,313),(265,305,274,314)]])
 

140 conjugacy classes

class 1 2A···2G4A···4L4M···4T5A5B5C5D10A···10AB20A···20AV20AW···20CB
order12···24···44···4555510···1020···2020···20
size11···12···24···411111···12···24···4

140 irreducible representations

dim1111111111222222
type+++++-
imageC1C2C2C2C4C5C10C10C10C20D4Q8C4○D4C5×D4C5×Q8C5×C4○D4
kernelC5×C23.65C23C5×C2.C42C2×C4×C20C10×C4⋊C4C5×C4⋊C4C23.65C23C2.C42C2×C42C2×C4⋊C4C4⋊C4C2×C20C2×C20C2×C10C2×C4C2×C4C22
# reps121484841632444161616

Matrix representation of C5×C23.65C23 ►in GL6(𝔽41)

1600000
010000
001000
000100
000010
000001
,
100000
010000
0040000
0004000
000010
000001
,
100000
010000
0040000
0004000
0000400
0000040
,
100000
0400000
0040000
0004000
0000400
0000040
,
4000000
090000
00143400
00342700
0000320
000009
,
100000
0320000
000100
0040000
000090
000009
,
100000
010000
000100
0040000
000001
0000400

G:=sub<GL(6,GF(41))| [16,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40],[1,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40,0,0,0,0,0,0,40],[40,0,0,0,0,0,0,9,0,0,0,0,0,0,14,34,0,0,0,0,34,27,0,0,0,0,0,0,32,0,0,0,0,0,0,9],[1,0,0,0,0,0,0,32,0,0,0,0,0,0,0,40,0,0,0,0,1,0,0,0,0,0,0,0,9,0,0,0,0,0,0,9],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,40,0,0,0,0,1,0,0,0,0,0,0,0,0,40,0,0,0,0,1,0] >;
 

C5×C23.65C23 in GAP, Magma, Sage, TeX 

C_5\times C_2^3._{65}C_2^3
 
% in TeX
 
G:=Group("C5xC2^3.65C2^3");
 
// GroupNames label
 
G:=SmallGroup(320,890);
 
// by ID
 
G=gap.SmallGroup(320,890);
 
# by ID
 
G:=PCGroup([7,-2,-2,-2,-5,-2,-2,-2,1120,589,1128,1766,436]);
 
// Polycyclic
 
G:=Group<a,b,c,d,e,f,g|a^5=b^2=c^2=d^2=1,e^2=f^2=d,g^2=c,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,a*f=f*a,a*g=g*a,b*c=c*b,b*d=d*b,f*e*f^-1=b*e=e*b,b*f=f*b,b*g=g*b,c*d=d*c,g*e*g^-1=c*e=e*c,c*f=f*c,c*g=g*c,d*e=e*d,d*f=f*d,d*g=g*d,f*g=g*f>;
 
// generators/relations
 

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