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G = C5×C23.81C23order 320 = 26·5

Direct product of C5 and C23.81C23

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

Aliases: C5×C23.81C23, (C2×C20).41Q8, (C2×C20).311D4, C10.39(C4⋊Q8), C22.74(D4×C10), C22.23(Q8×C10), C10.90(C22⋊Q8), C10.141(C4⋊D4), C2.C42.9C10, C23.81(C22×C10), C10.29(C42.C2), (C22×C20).404C22, (C22×C10).462C23, C10.92(C22.D4), C2.5(C5×C4⋊Q8), (C2×C4).4(C5×Q8), (C2×C4).18(C5×D4), (C10×C4⋊C4).39C2, (C2×C4⋊C4).10C10, C2.9(C5×C22⋊Q8), C2.10(C5×C4⋊D4), C2.4(C5×C42.C2), (C2×C10).614(C2×D4), (C2×C10).111(C2×Q8), C22.41(C5×C4○D4), (C22×C4).22(C2×C10), (C2×C10).222(C4○D4), C2.8(C5×C22.D4), (C5×C2.C42).28C2, SmallGroup(320,899)

Series: Derived Chief Lower central Upper central

C1C23 — C5×C23.81C23
C1C2C22C23C22×C10C22×C20C10×C4⋊C4 — C5×C23.81C23
C1C23 — C5×C23.81C23
C1C22×C10 — C5×C23.81C23

Generators and relations for C5×C23.81C23
 G = < a,b,c,d,e,f,g | a5=b2=c2=d2=1, e2=c, f2=g2=b, 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, gfg-1=df=fd, dg=gd >

Subgroups: 234 in 150 conjugacy classes, 78 normal (30 characteristic)
C1, C2 [×3], C2 [×4], C4 [×11], C22 [×3], C22 [×4], C5, C2×C4 [×8], C2×C4 [×17], C23, C10 [×3], C10 [×4], C4⋊C4 [×8], C22×C4 [×3], C22×C4 [×4], C20 [×11], C2×C10 [×3], C2×C10 [×4], C2.C42, C2.C42 [×2], C2×C4⋊C4 [×2], C2×C4⋊C4 [×2], C2×C20 [×8], C2×C20 [×17], C22×C10, C23.81C23, C5×C4⋊C4 [×8], C22×C20 [×3], C22×C20 [×4], C5×C2.C42, C5×C2.C42 [×2], C10×C4⋊C4 [×2], C10×C4⋊C4 [×2], C5×C23.81C23
Quotients: C1, C2 [×7], C22 [×7], C5, D4 [×4], Q8 [×4], C23, C10 [×7], C2×D4 [×2], C2×Q8 [×2], C4○D4 [×3], C2×C10 [×7], C4⋊D4, C22⋊Q8 [×2], C22.D4, C42.C2 [×2], C4⋊Q8, C5×D4 [×4], C5×Q8 [×4], C22×C10, C23.81C23, D4×C10 [×2], Q8×C10 [×2], C5×C4○D4 [×3], C5×C4⋊D4, C5×C22⋊Q8 [×2], C5×C22.D4, C5×C42.C2 [×2], C5×C4⋊Q8, C5×C23.81C23

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

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

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

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

110 conjugacy classes

class 1 2A···2G4A···4N5A5B5C5D10A···10AB20A···20BD
order12···24···4555510···1020···20
size11···14···411111···14···4

110 irreducible representations

dim111111222222
type++++-
imageC1C2C2C5C10C10D4Q8C4○D4C5×D4C5×Q8C5×C4○D4
kernelC5×C23.81C23C5×C2.C42C10×C4⋊C4C23.81C23C2.C42C2×C4⋊C4C2×C20C2×C20C2×C10C2×C4C2×C4C22
# reps13441216446161624

Matrix representation of C5×C23.81C23 in GL6(𝔽41)

1600000
0160000
0016000
0001600
0000160
0000016
,
100000
010000
001000
000100
0000400
0000040
,
4000000
0400000
001000
000100
0000400
0000040
,
100000
010000
0040000
0004000
000010
000001
,
2130000
28390000
001000
000100
0000111
0000130
,
100000
010000
0017100
00402400
000001
0000400
,
010000
100000
000100
001000
000001
0000400

G:=sub<GL(6,GF(41))| [16,0,0,0,0,0,0,16,0,0,0,0,0,0,16,0,0,0,0,0,0,16,0,0,0,0,0,0,16,0,0,0,0,0,0,16],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,40,0,0,0,0,0,0,40],[40,0,0,0,0,0,0,40,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,40,0,0,0,0,0,0,40],[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],[2,28,0,0,0,0,13,39,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,11,1,0,0,0,0,1,30],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,17,40,0,0,0,0,1,24,0,0,0,0,0,0,0,40,0,0,0,0,1,0],[0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,40,0,0,0,0,1,0] >;

C5×C23.81C23 in GAP, Magma, Sage, TeX

C_5\times C_2^3._{81}C_2^3
% in TeX

G:=Group("C5xC2^3.81C2^3");
// GroupNames label

G:=SmallGroup(320,899);
// by ID

G=gap.SmallGroup(320,899);
# by ID

G:=PCGroup([7,-2,-2,-2,-5,-2,-2,-2,560,589,288,1766,1731,226]);
// Polycyclic

G:=Group<a,b,c,d,e,f,g|a^5=b^2=c^2=d^2=1,e^2=c,f^2=g^2=b,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,g*f*g^-1=d*f=f*d,d*g=g*d>;
// generators/relations

׿
×
𝔽