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G = C5×C23.63C23order 320 = 26·5

Direct product of C5 and C23.63C23

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

Aliases: C5×C23.63C23, C4⋊C45C20, C2.6(D4×C20), C2.3(Q8×C20), C10.39(C4×Q8), (C2×C20).50Q8, C10.137(C4×D4), (C2×C20).455D4, (C2×C42).5C10, C22.36(D4×C10), C22.13(Q8×C10), C10.84(C22⋊Q8), C2.C42.3C10, (C22×C20).32C22, C23.60(C22×C10), C22.36(C22×C20), C10.27(C42.C2), C10.32(C422C2), C10.76(C42⋊C2), (C22×C10).451C23, C10.88(C22.D4), (C2×C4×C20).7C2, (C5×C4⋊C4)⋊19C4, (C2×C4⋊C4).6C10, (C10×C4⋊C4).35C2, (C2×C4).10(C5×Q8), (C2×C4).33(C2×C20), C2.3(C5×C22⋊Q8), (C2×C4).100(C5×D4), (C2×C20).363(C2×C4), C2.2(C5×C42.C2), (C2×C10).603(C2×D4), C2.9(C5×C42⋊C2), C2.2(C5×C422C2), (C2×C10).105(C2×Q8), C22.21(C5×C4○D4), (C22×C4).20(C2×C10), (C2×C10).211(C4○D4), C2.4(C5×C22.D4), (C2×C10).324(C22×C4), (C5×C2.C42).5C2, SmallGroup(320,888)

Series: Derived Chief Lower central Upper central

C1C22 — C5×C23.63C23
C1C2C22C23C22×C10C22×C20C10×C4⋊C4 — C5×C23.63C23
C1C22 — C5×C23.63C23
C1C22×C10 — C5×C23.63C23

Generators and relations for C5×C23.63C23
 G = < a,b,c,d,e,f,g | a5=b2=c2=d2=1, e2=f2=d, 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, df=fd, dg=gd, fg=gf >

Subgroups: 226 in 154 conjugacy classes, 90 normal (62 characteristic)
C1, C2 [×7], C4 [×12], C22 [×7], C5, C2×C4 [×10], C2×C4 [×16], C23, C10 [×7], C42 [×2], C4⋊C4 [×4], C4⋊C4 [×2], C22×C4 [×7], C20 [×12], C2×C10 [×7], C2.C42 [×4], C2×C42, C2×C4⋊C4 [×2], C2×C20 [×10], C2×C20 [×16], C22×C10, C23.63C23, C4×C20 [×2], C5×C4⋊C4 [×4], C5×C4⋊C4 [×2], C22×C20 [×7], C5×C2.C42 [×4], C2×C4×C20, C10×C4⋊C4 [×2], C5×C23.63C23
Quotients: C1, C2 [×7], C4 [×4], C22 [×7], C5, C2×C4 [×6], D4 [×2], Q8 [×2], C23, C10 [×7], C22×C4, C2×D4, C2×Q8, C4○D4 [×4], C20 [×4], C2×C10 [×7], C42⋊C2, C4×D4, C4×Q8, C22⋊Q8, C22.D4, C42.C2, C422C2, C2×C20 [×6], C5×D4 [×2], C5×Q8 [×2], C22×C10, C23.63C23, C22×C20, D4×C10, Q8×C10, C5×C4○D4 [×4], C5×C42⋊C2, D4×C20, Q8×C20, C5×C22⋊Q8, C5×C22.D4, C5×C42.C2, C5×C422C2, C5×C23.63C23

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

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

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

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

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×C23.63C23C5×C2.C42C2×C4×C20C10×C4⋊C4C5×C4⋊C4C23.63C23C2.C42C2×C42C2×C4⋊C4C4⋊C4C2×C20C2×C20C2×C10C2×C4C2×C4C22
# reps1412841648322288832

Matrix representation of C5×C23.63C23 in GL5(𝔽41)

160000
018000
001800
000100
000010
,
10000
01000
00100
000400
000040
,
10000
040000
004000
00010
00001
,
400000
01000
00100
00010
00001
,
320000
092500
053200
00071
0003434
,
90000
040000
004000
0004039
00001
,
10000
040000
04100
000320
000032

G:=sub<GL(5,GF(41))| [16,0,0,0,0,0,18,0,0,0,0,0,18,0,0,0,0,0,10,0,0,0,0,0,10],[1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,40,0,0,0,0,0,40],[1,0,0,0,0,0,40,0,0,0,0,0,40,0,0,0,0,0,1,0,0,0,0,0,1],[40,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1],[32,0,0,0,0,0,9,5,0,0,0,25,32,0,0,0,0,0,7,34,0,0,0,1,34],[9,0,0,0,0,0,40,0,0,0,0,0,40,0,0,0,0,0,40,0,0,0,0,39,1],[1,0,0,0,0,0,40,4,0,0,0,0,1,0,0,0,0,0,32,0,0,0,0,0,32] >;

C5×C23.63C23 in GAP, Magma, Sage, TeX

C_5\times C_2^3._{63}C_2^3
% in TeX

G:=Group("C5xC2^3.63C2^3");
// GroupNames label

G:=SmallGroup(320,888);
// by ID

G=gap.SmallGroup(320,888);
# by ID

G:=PCGroup([7,-2,-2,-2,-5,-2,-2,-2,1120,589,1128,1766,226]);
// 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=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,d*f=f*d,d*g=g*d,f*g=g*f>;
// generators/relations

׿
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𝔽