direct product, metabelian, supersoluble, monomial, A-group, 2-hyperelementary
Aliases: C22×C15⋊C8, C30⋊8(C2×C8), (C2×C30)⋊2C8, C15⋊10(C22×C8), C23.5(C3⋊F5), (C22×C6).6F5, (C22×C30).6C4, C6.42(C22×F5), C30.80(C22×C4), (C6×Dic5).22C4, (C2×Dic5).209D6, (C22×C10).8Dic3, (C2×Dic5).13Dic3, Dic5.18(C2×Dic3), (C22×Dic5).11S3, Dic5.53(C22×S3), (C3×Dic5).67C23, C10.11(C22×Dic3), (C6×Dic5).268C22, C6⋊2(C2×C5⋊C8), C10⋊2(C2×C3⋊C8), C5⋊2(C22×C3⋊C8), C3⋊2(C22×C5⋊C8), (C2×C6)⋊3(C5⋊C8), (C2×C10)⋊5(C3⋊C8), C2.3(C22×C3⋊F5), (C2×C6).49(C2×F5), (C2×C30).43(C2×C4), C22.20(C2×C3⋊F5), (C2×C6×Dic5).16C2, (C3×Dic5).68(C2×C4), (C2×C10).19(C2×Dic3), SmallGroup(480,1070)
Series: Derived ►Chief ►Lower central ►Upper central
| C15 — C22×C15⋊C8 |
Subgroups: 460 in 152 conjugacy classes, 97 normal (17 characteristic)
C1, C2, C2 [×6], C3, C4 [×4], C22 [×7], C5, C6, C6 [×6], C8 [×4], C2×C4 [×6], C23, C10, C10 [×6], C12 [×4], C2×C6 [×7], C15, C2×C8 [×6], C22×C4, Dic5, Dic5 [×3], C2×C10 [×7], C3⋊C8 [×4], C2×C12 [×6], C22×C6, C30, C30 [×6], C22×C8, C5⋊C8 [×4], C2×Dic5 [×6], C22×C10, C2×C3⋊C8 [×6], C22×C12, C3×Dic5, C3×Dic5 [×3], C2×C30 [×7], C2×C5⋊C8 [×6], C22×Dic5, C22×C3⋊C8, C15⋊C8 [×4], C6×Dic5 [×6], C22×C30, C22×C5⋊C8, C2×C15⋊C8 [×6], C2×C6×Dic5, C22×C15⋊C8
Quotients:
C1, C2 [×7], C4 [×4], C22 [×7], S3, C8 [×4], C2×C4 [×6], C23, Dic3 [×4], D6 [×3], C2×C8 [×6], C22×C4, F5, C3⋊C8 [×4], C2×Dic3 [×6], C22×S3, C22×C8, C5⋊C8 [×4], C2×F5 [×3], C2×C3⋊C8 [×6], C22×Dic3, C3⋊F5, C2×C5⋊C8 [×6], C22×F5, C22×C3⋊C8, C15⋊C8 [×4], C2×C3⋊F5 [×3], C22×C5⋊C8, C2×C15⋊C8 [×6], C22×C3⋊F5, C22×C15⋊C8
Generators and relations
G = < a,b,c,d | a2=b2=c15=d8=1, ab=ba, ac=ca, ad=da, bc=cb, bd=db, dcd-1=c2 >
►Regular action on 480 points
Generators in S480
(1 134)(2 135)(3 121)(4 122)(5 123)(6 124)(7 125)(8 126)(9 127)(10 128)(11 129)(12 130)(13 131)(14 132)(15 133)(16 142)(17 143)(18 144)(19 145)(20 146)(21 147)(22 148)(23 149)(24 150)(25 136)(26 137)(27 138)(28 139)(29 140)(30 141)(31 165)(32 151)(33 152)(34 153)(35 154)(36 155)(37 156)(38 157)(39 158)(40 159)(41 160)(42 161)(43 162)(44 163)(45 164)(46 180)(47 166)(48 167)(49 168)(50 169)(51 170)(52 171)(53 172)(54 173)(55 174)(56 175)(57 176)(58 177)(59 178)(60 179)(61 191)(62 192)(63 193)(64 194)(65 195)(66 181)(67 182)(68 183)(69 184)(70 185)(71 186)(72 187)(73 188)(74 189)(75 190)(76 200)(77 201)(78 202)(79 203)(80 204)(81 205)(82 206)(83 207)(84 208)(85 209)(86 210)(87 196)(88 197)(89 198)(90 199)(91 211)(92 212)(93 213)(94 214)(95 215)(96 216)(97 217)(98 218)(99 219)(100 220)(101 221)(102 222)(103 223)(104 224)(105 225)(106 230)(107 231)(108 232)(109 233)(110 234)(111 235)(112 236)(113 237)(114 238)(115 239)(116 240)(117 226)(118 227)(119 228)(120 229)(241 361)(242 362)(243 363)(244 364)(245 365)(246 366)(247 367)(248 368)(249 369)(250 370)(251 371)(252 372)(253 373)(254 374)(255 375)(256 381)(257 382)(258 383)(259 384)(260 385)(261 386)(262 387)(263 388)(264 389)(265 390)(266 376)(267 377)(268 378)(269 379)(270 380)(271 405)(272 391)(273 392)(274 393)(275 394)(276 395)(277 396)(278 397)(279 398)(280 399)(281 400)(282 401)(283 402)(284 403)(285 404)(286 407)(287 408)(288 409)(289 410)(290 411)(291 412)(292 413)(293 414)(294 415)(295 416)(296 417)(297 418)(298 419)(299 420)(300 406)(301 431)(302 432)(303 433)(304 434)(305 435)(306 421)(307 422)(308 423)(309 424)(310 425)(311 426)(312 427)(313 428)(314 429)(315 430)(316 436)(317 437)(318 438)(319 439)(320 440)(321 441)(322 442)(323 443)(324 444)(325 445)(326 446)(327 447)(328 448)(329 449)(330 450)(331 451)(332 452)(333 453)(334 454)(335 455)(336 456)(337 457)(338 458)(339 459)(340 460)(341 461)(342 462)(343 463)(344 464)(345 465)(346 472)(347 473)(348 474)(349 475)(350 476)(351 477)(352 478)(353 479)(354 480)(355 466)(356 467)(357 468)(358 469)(359 470)(360 471)
(1 86)(2 87)(3 88)(4 89)(5 90)(6 76)(7 77)(8 78)(9 79)(10 80)(11 81)(12 82)(13 83)(14 84)(15 85)(16 62)(17 63)(18 64)(19 65)(20 66)(21 67)(22 68)(23 69)(24 70)(25 71)(26 72)(27 73)(28 74)(29 75)(30 61)(31 106)(32 107)(33 108)(34 109)(35 110)(36 111)(37 112)(38 113)(39 114)(40 115)(41 116)(42 117)(43 118)(44 119)(45 120)(46 98)(47 99)(48 100)(49 101)(50 102)(51 103)(52 104)(53 105)(54 91)(55 92)(56 93)(57 94)(58 95)(59 96)(60 97)(121 197)(122 198)(123 199)(124 200)(125 201)(126 202)(127 203)(128 204)(129 205)(130 206)(131 207)(132 208)(133 209)(134 210)(135 196)(136 186)(137 187)(138 188)(139 189)(140 190)(141 191)(142 192)(143 193)(144 194)(145 195)(146 181)(147 182)(148 183)(149 184)(150 185)(151 231)(152 232)(153 233)(154 234)(155 235)(156 236)(157 237)(158 238)(159 239)(160 240)(161 226)(162 227)(163 228)(164 229)(165 230)(166 219)(167 220)(168 221)(169 222)(170 223)(171 224)(172 225)(173 211)(174 212)(175 213)(176 214)(177 215)(178 216)(179 217)(180 218)(241 321)(242 322)(243 323)(244 324)(245 325)(246 326)(247 327)(248 328)(249 329)(250 330)(251 316)(252 317)(253 318)(254 319)(255 320)(256 301)(257 302)(258 303)(259 304)(260 305)(261 306)(262 307)(263 308)(264 309)(265 310)(266 311)(267 312)(268 313)(269 314)(270 315)(271 354)(272 355)(273 356)(274 357)(275 358)(276 359)(277 360)(278 346)(279 347)(280 348)(281 349)(282 350)(283 351)(284 352)(285 353)(286 332)(287 333)(288 334)(289 335)(290 336)(291 337)(292 338)(293 339)(294 340)(295 341)(296 342)(297 343)(298 344)(299 345)(300 331)(361 441)(362 442)(363 443)(364 444)(365 445)(366 446)(367 447)(368 448)(369 449)(370 450)(371 436)(372 437)(373 438)(374 439)(375 440)(376 426)(377 427)(378 428)(379 429)(380 430)(381 431)(382 432)(383 433)(384 434)(385 435)(386 421)(387 422)(388 423)(389 424)(390 425)(391 466)(392 467)(393 468)(394 469)(395 470)(396 471)(397 472)(398 473)(399 474)(400 475)(401 476)(402 477)(403 478)(404 479)(405 480)(406 451)(407 452)(408 453)(409 454)(410 455)(411 456)(412 457)(413 458)(414 459)(415 460)(416 461)(417 462)(418 463)(419 464)(420 465)
(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)(316 317 318 319 320 321 322 323 324 325 326 327 328 329 330)(331 332 333 334 335 336 337 338 339 340 341 342 343 344 345)(346 347 348 349 350 351 352 353 354 355 356 357 358 359 360)(361 362 363 364 365 366 367 368 369 370 371 372 373 374 375)(376 377 378 379 380 381 382 383 384 385 386 387 388 389 390)(391 392 393 394 395 396 397 398 399 400 401 402 403 404 405)(406 407 408 409 410 411 412 413 414 415 416 417 418 419 420)(421 422 423 424 425 426 427 428 429 430 431 432 433 434 435)(436 437 438 439 440 441 442 443 444 445 446 447 448 449 450)(451 452 453 454 455 456 457 458 459 460 461 462 463 464 465)(466 467 468 469 470 471 472 473 474 475 476 477 478 479 480)
(1 413 57 381 28 404 32 371)(2 406 46 383 29 397 36 373)(3 414 50 385 30 405 40 375)(4 407 54 387 16 398 44 362)(5 415 58 389 17 391 33 364)(6 408 47 376 18 399 37 366)(7 416 51 378 19 392 41 368)(8 409 55 380 20 400 45 370)(9 417 59 382 21 393 34 372)(10 410 48 384 22 401 38 374)(11 418 52 386 23 394 42 361)(12 411 56 388 24 402 31 363)(13 419 60 390 25 395 35 365)(14 412 49 377 26 403 39 367)(15 420 53 379 27 396 43 369)(61 480 115 440 88 459 102 435)(62 473 119 442 89 452 91 422)(63 466 108 444 90 460 95 424)(64 474 112 446 76 453 99 426)(65 467 116 448 77 461 103 428)(66 475 120 450 78 454 92 430)(67 468 109 437 79 462 96 432)(68 476 113 439 80 455 100 434)(69 469 117 441 81 463 104 421)(70 477 106 443 82 456 93 423)(71 470 110 445 83 464 97 425)(72 478 114 447 84 457 101 427)(73 471 118 449 85 465 105 429)(74 479 107 436 86 458 94 431)(75 472 111 438 87 451 98 433)(121 293 169 260 141 271 159 255)(122 286 173 262 142 279 163 242)(123 294 177 264 143 272 152 244)(124 287 166 266 144 280 156 246)(125 295 170 268 145 273 160 248)(126 288 174 270 146 281 164 250)(127 296 178 257 147 274 153 252)(128 289 167 259 148 282 157 254)(129 297 171 261 149 275 161 241)(130 290 175 263 150 283 165 243)(131 298 179 265 136 276 154 245)(132 291 168 267 137 284 158 247)(133 299 172 269 138 277 162 249)(134 292 176 256 139 285 151 251)(135 300 180 258 140 278 155 253)(181 349 229 330 202 334 212 315)(182 357 233 317 203 342 216 302)(183 350 237 319 204 335 220 304)(184 358 226 321 205 343 224 306)(185 351 230 323 206 336 213 308)(186 359 234 325 207 344 217 310)(187 352 238 327 208 337 221 312)(188 360 227 329 209 345 225 314)(189 353 231 316 210 338 214 301)(190 346 235 318 196 331 218 303)(191 354 239 320 197 339 222 305)(192 347 228 322 198 332 211 307)(193 355 232 324 199 340 215 309)(194 348 236 326 200 333 219 311)(195 356 240 328 201 341 223 313)
G:=sub<Sym(480)| (1,134)(2,135)(3,121)(4,122)(5,123)(6,124)(7,125)(8,126)(9,127)(10,128)(11,129)(12,130)(13,131)(14,132)(15,133)(16,142)(17,143)(18,144)(19,145)(20,146)(21,147)(22,148)(23,149)(24,150)(25,136)(26,137)(27,138)(28,139)(29,140)(30,141)(31,165)(32,151)(33,152)(34,153)(35,154)(36,155)(37,156)(38,157)(39,158)(40,159)(41,160)(42,161)(43,162)(44,163)(45,164)(46,180)(47,166)(48,167)(49,168)(50,169)(51,170)(52,171)(53,172)(54,173)(55,174)(56,175)(57,176)(58,177)(59,178)(60,179)(61,191)(62,192)(63,193)(64,194)(65,195)(66,181)(67,182)(68,183)(69,184)(70,185)(71,186)(72,187)(73,188)(74,189)(75,190)(76,200)(77,201)(78,202)(79,203)(80,204)(81,205)(82,206)(83,207)(84,208)(85,209)(86,210)(87,196)(88,197)(89,198)(90,199)(91,211)(92,212)(93,213)(94,214)(95,215)(96,216)(97,217)(98,218)(99,219)(100,220)(101,221)(102,222)(103,223)(104,224)(105,225)(106,230)(107,231)(108,232)(109,233)(110,234)(111,235)(112,236)(113,237)(114,238)(115,239)(116,240)(117,226)(118,227)(119,228)(120,229)(241,361)(242,362)(243,363)(244,364)(245,365)(246,366)(247,367)(248,368)(249,369)(250,370)(251,371)(252,372)(253,373)(254,374)(255,375)(256,381)(257,382)(258,383)(259,384)(260,385)(261,386)(262,387)(263,388)(264,389)(265,390)(266,376)(267,377)(268,378)(269,379)(270,380)(271,405)(272,391)(273,392)(274,393)(275,394)(276,395)(277,396)(278,397)(279,398)(280,399)(281,400)(282,401)(283,402)(284,403)(285,404)(286,407)(287,408)(288,409)(289,410)(290,411)(291,412)(292,413)(293,414)(294,415)(295,416)(296,417)(297,418)(298,419)(299,420)(300,406)(301,431)(302,432)(303,433)(304,434)(305,435)(306,421)(307,422)(308,423)(309,424)(310,425)(311,426)(312,427)(313,428)(314,429)(315,430)(316,436)(317,437)(318,438)(319,439)(320,440)(321,441)(322,442)(323,443)(324,444)(325,445)(326,446)(327,447)(328,448)(329,449)(330,450)(331,451)(332,452)(333,453)(334,454)(335,455)(336,456)(337,457)(338,458)(339,459)(340,460)(341,461)(342,462)(343,463)(344,464)(345,465)(346,472)(347,473)(348,474)(349,475)(350,476)(351,477)(352,478)(353,479)(354,480)(355,466)(356,467)(357,468)(358,469)(359,470)(360,471), (1,86)(2,87)(3,88)(4,89)(5,90)(6,76)(7,77)(8,78)(9,79)(10,80)(11,81)(12,82)(13,83)(14,84)(15,85)(16,62)(17,63)(18,64)(19,65)(20,66)(21,67)(22,68)(23,69)(24,70)(25,71)(26,72)(27,73)(28,74)(29,75)(30,61)(31,106)(32,107)(33,108)(34,109)(35,110)(36,111)(37,112)(38,113)(39,114)(40,115)(41,116)(42,117)(43,118)(44,119)(45,120)(46,98)(47,99)(48,100)(49,101)(50,102)(51,103)(52,104)(53,105)(54,91)(55,92)(56,93)(57,94)(58,95)(59,96)(60,97)(121,197)(122,198)(123,199)(124,200)(125,201)(126,202)(127,203)(128,204)(129,205)(130,206)(131,207)(132,208)(133,209)(134,210)(135,196)(136,186)(137,187)(138,188)(139,189)(140,190)(141,191)(142,192)(143,193)(144,194)(145,195)(146,181)(147,182)(148,183)(149,184)(150,185)(151,231)(152,232)(153,233)(154,234)(155,235)(156,236)(157,237)(158,238)(159,239)(160,240)(161,226)(162,227)(163,228)(164,229)(165,230)(166,219)(167,220)(168,221)(169,222)(170,223)(171,224)(172,225)(173,211)(174,212)(175,213)(176,214)(177,215)(178,216)(179,217)(180,218)(241,321)(242,322)(243,323)(244,324)(245,325)(246,326)(247,327)(248,328)(249,329)(250,330)(251,316)(252,317)(253,318)(254,319)(255,320)(256,301)(257,302)(258,303)(259,304)(260,305)(261,306)(262,307)(263,308)(264,309)(265,310)(266,311)(267,312)(268,313)(269,314)(270,315)(271,354)(272,355)(273,356)(274,357)(275,358)(276,359)(277,360)(278,346)(279,347)(280,348)(281,349)(282,350)(283,351)(284,352)(285,353)(286,332)(287,333)(288,334)(289,335)(290,336)(291,337)(292,338)(293,339)(294,340)(295,341)(296,342)(297,343)(298,344)(299,345)(300,331)(361,441)(362,442)(363,443)(364,444)(365,445)(366,446)(367,447)(368,448)(369,449)(370,450)(371,436)(372,437)(373,438)(374,439)(375,440)(376,426)(377,427)(378,428)(379,429)(380,430)(381,431)(382,432)(383,433)(384,434)(385,435)(386,421)(387,422)(388,423)(389,424)(390,425)(391,466)(392,467)(393,468)(394,469)(395,470)(396,471)(397,472)(398,473)(399,474)(400,475)(401,476)(402,477)(403,478)(404,479)(405,480)(406,451)(407,452)(408,453)(409,454)(410,455)(411,456)(412,457)(413,458)(414,459)(415,460)(416,461)(417,462)(418,463)(419,464)(420,465), (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)(316,317,318,319,320,321,322,323,324,325,326,327,328,329,330)(331,332,333,334,335,336,337,338,339,340,341,342,343,344,345)(346,347,348,349,350,351,352,353,354,355,356,357,358,359,360)(361,362,363,364,365,366,367,368,369,370,371,372,373,374,375)(376,377,378,379,380,381,382,383,384,385,386,387,388,389,390)(391,392,393,394,395,396,397,398,399,400,401,402,403,404,405)(406,407,408,409,410,411,412,413,414,415,416,417,418,419,420)(421,422,423,424,425,426,427,428,429,430,431,432,433,434,435)(436,437,438,439,440,441,442,443,444,445,446,447,448,449,450)(451,452,453,454,455,456,457,458,459,460,461,462,463,464,465)(466,467,468,469,470,471,472,473,474,475,476,477,478,479,480), (1,413,57,381,28,404,32,371)(2,406,46,383,29,397,36,373)(3,414,50,385,30,405,40,375)(4,407,54,387,16,398,44,362)(5,415,58,389,17,391,33,364)(6,408,47,376,18,399,37,366)(7,416,51,378,19,392,41,368)(8,409,55,380,20,400,45,370)(9,417,59,382,21,393,34,372)(10,410,48,384,22,401,38,374)(11,418,52,386,23,394,42,361)(12,411,56,388,24,402,31,363)(13,419,60,390,25,395,35,365)(14,412,49,377,26,403,39,367)(15,420,53,379,27,396,43,369)(61,480,115,440,88,459,102,435)(62,473,119,442,89,452,91,422)(63,466,108,444,90,460,95,424)(64,474,112,446,76,453,99,426)(65,467,116,448,77,461,103,428)(66,475,120,450,78,454,92,430)(67,468,109,437,79,462,96,432)(68,476,113,439,80,455,100,434)(69,469,117,441,81,463,104,421)(70,477,106,443,82,456,93,423)(71,470,110,445,83,464,97,425)(72,478,114,447,84,457,101,427)(73,471,118,449,85,465,105,429)(74,479,107,436,86,458,94,431)(75,472,111,438,87,451,98,433)(121,293,169,260,141,271,159,255)(122,286,173,262,142,279,163,242)(123,294,177,264,143,272,152,244)(124,287,166,266,144,280,156,246)(125,295,170,268,145,273,160,248)(126,288,174,270,146,281,164,250)(127,296,178,257,147,274,153,252)(128,289,167,259,148,282,157,254)(129,297,171,261,149,275,161,241)(130,290,175,263,150,283,165,243)(131,298,179,265,136,276,154,245)(132,291,168,267,137,284,158,247)(133,299,172,269,138,277,162,249)(134,292,176,256,139,285,151,251)(135,300,180,258,140,278,155,253)(181,349,229,330,202,334,212,315)(182,357,233,317,203,342,216,302)(183,350,237,319,204,335,220,304)(184,358,226,321,205,343,224,306)(185,351,230,323,206,336,213,308)(186,359,234,325,207,344,217,310)(187,352,238,327,208,337,221,312)(188,360,227,329,209,345,225,314)(189,353,231,316,210,338,214,301)(190,346,235,318,196,331,218,303)(191,354,239,320,197,339,222,305)(192,347,228,322,198,332,211,307)(193,355,232,324,199,340,215,309)(194,348,236,326,200,333,219,311)(195,356,240,328,201,341,223,313)>;
G:=Group( (1,134)(2,135)(3,121)(4,122)(5,123)(6,124)(7,125)(8,126)(9,127)(10,128)(11,129)(12,130)(13,131)(14,132)(15,133)(16,142)(17,143)(18,144)(19,145)(20,146)(21,147)(22,148)(23,149)(24,150)(25,136)(26,137)(27,138)(28,139)(29,140)(30,141)(31,165)(32,151)(33,152)(34,153)(35,154)(36,155)(37,156)(38,157)(39,158)(40,159)(41,160)(42,161)(43,162)(44,163)(45,164)(46,180)(47,166)(48,167)(49,168)(50,169)(51,170)(52,171)(53,172)(54,173)(55,174)(56,175)(57,176)(58,177)(59,178)(60,179)(61,191)(62,192)(63,193)(64,194)(65,195)(66,181)(67,182)(68,183)(69,184)(70,185)(71,186)(72,187)(73,188)(74,189)(75,190)(76,200)(77,201)(78,202)(79,203)(80,204)(81,205)(82,206)(83,207)(84,208)(85,209)(86,210)(87,196)(88,197)(89,198)(90,199)(91,211)(92,212)(93,213)(94,214)(95,215)(96,216)(97,217)(98,218)(99,219)(100,220)(101,221)(102,222)(103,223)(104,224)(105,225)(106,230)(107,231)(108,232)(109,233)(110,234)(111,235)(112,236)(113,237)(114,238)(115,239)(116,240)(117,226)(118,227)(119,228)(120,229)(241,361)(242,362)(243,363)(244,364)(245,365)(246,366)(247,367)(248,368)(249,369)(250,370)(251,371)(252,372)(253,373)(254,374)(255,375)(256,381)(257,382)(258,383)(259,384)(260,385)(261,386)(262,387)(263,388)(264,389)(265,390)(266,376)(267,377)(268,378)(269,379)(270,380)(271,405)(272,391)(273,392)(274,393)(275,394)(276,395)(277,396)(278,397)(279,398)(280,399)(281,400)(282,401)(283,402)(284,403)(285,404)(286,407)(287,408)(288,409)(289,410)(290,411)(291,412)(292,413)(293,414)(294,415)(295,416)(296,417)(297,418)(298,419)(299,420)(300,406)(301,431)(302,432)(303,433)(304,434)(305,435)(306,421)(307,422)(308,423)(309,424)(310,425)(311,426)(312,427)(313,428)(314,429)(315,430)(316,436)(317,437)(318,438)(319,439)(320,440)(321,441)(322,442)(323,443)(324,444)(325,445)(326,446)(327,447)(328,448)(329,449)(330,450)(331,451)(332,452)(333,453)(334,454)(335,455)(336,456)(337,457)(338,458)(339,459)(340,460)(341,461)(342,462)(343,463)(344,464)(345,465)(346,472)(347,473)(348,474)(349,475)(350,476)(351,477)(352,478)(353,479)(354,480)(355,466)(356,467)(357,468)(358,469)(359,470)(360,471), (1,86)(2,87)(3,88)(4,89)(5,90)(6,76)(7,77)(8,78)(9,79)(10,80)(11,81)(12,82)(13,83)(14,84)(15,85)(16,62)(17,63)(18,64)(19,65)(20,66)(21,67)(22,68)(23,69)(24,70)(25,71)(26,72)(27,73)(28,74)(29,75)(30,61)(31,106)(32,107)(33,108)(34,109)(35,110)(36,111)(37,112)(38,113)(39,114)(40,115)(41,116)(42,117)(43,118)(44,119)(45,120)(46,98)(47,99)(48,100)(49,101)(50,102)(51,103)(52,104)(53,105)(54,91)(55,92)(56,93)(57,94)(58,95)(59,96)(60,97)(121,197)(122,198)(123,199)(124,200)(125,201)(126,202)(127,203)(128,204)(129,205)(130,206)(131,207)(132,208)(133,209)(134,210)(135,196)(136,186)(137,187)(138,188)(139,189)(140,190)(141,191)(142,192)(143,193)(144,194)(145,195)(146,181)(147,182)(148,183)(149,184)(150,185)(151,231)(152,232)(153,233)(154,234)(155,235)(156,236)(157,237)(158,238)(159,239)(160,240)(161,226)(162,227)(163,228)(164,229)(165,230)(166,219)(167,220)(168,221)(169,222)(170,223)(171,224)(172,225)(173,211)(174,212)(175,213)(176,214)(177,215)(178,216)(179,217)(180,218)(241,321)(242,322)(243,323)(244,324)(245,325)(246,326)(247,327)(248,328)(249,329)(250,330)(251,316)(252,317)(253,318)(254,319)(255,320)(256,301)(257,302)(258,303)(259,304)(260,305)(261,306)(262,307)(263,308)(264,309)(265,310)(266,311)(267,312)(268,313)(269,314)(270,315)(271,354)(272,355)(273,356)(274,357)(275,358)(276,359)(277,360)(278,346)(279,347)(280,348)(281,349)(282,350)(283,351)(284,352)(285,353)(286,332)(287,333)(288,334)(289,335)(290,336)(291,337)(292,338)(293,339)(294,340)(295,341)(296,342)(297,343)(298,344)(299,345)(300,331)(361,441)(362,442)(363,443)(364,444)(365,445)(366,446)(367,447)(368,448)(369,449)(370,450)(371,436)(372,437)(373,438)(374,439)(375,440)(376,426)(377,427)(378,428)(379,429)(380,430)(381,431)(382,432)(383,433)(384,434)(385,435)(386,421)(387,422)(388,423)(389,424)(390,425)(391,466)(392,467)(393,468)(394,469)(395,470)(396,471)(397,472)(398,473)(399,474)(400,475)(401,476)(402,477)(403,478)(404,479)(405,480)(406,451)(407,452)(408,453)(409,454)(410,455)(411,456)(412,457)(413,458)(414,459)(415,460)(416,461)(417,462)(418,463)(419,464)(420,465), (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)(316,317,318,319,320,321,322,323,324,325,326,327,328,329,330)(331,332,333,334,335,336,337,338,339,340,341,342,343,344,345)(346,347,348,349,350,351,352,353,354,355,356,357,358,359,360)(361,362,363,364,365,366,367,368,369,370,371,372,373,374,375)(376,377,378,379,380,381,382,383,384,385,386,387,388,389,390)(391,392,393,394,395,396,397,398,399,400,401,402,403,404,405)(406,407,408,409,410,411,412,413,414,415,416,417,418,419,420)(421,422,423,424,425,426,427,428,429,430,431,432,433,434,435)(436,437,438,439,440,441,442,443,444,445,446,447,448,449,450)(451,452,453,454,455,456,457,458,459,460,461,462,463,464,465)(466,467,468,469,470,471,472,473,474,475,476,477,478,479,480), (1,413,57,381,28,404,32,371)(2,406,46,383,29,397,36,373)(3,414,50,385,30,405,40,375)(4,407,54,387,16,398,44,362)(5,415,58,389,17,391,33,364)(6,408,47,376,18,399,37,366)(7,416,51,378,19,392,41,368)(8,409,55,380,20,400,45,370)(9,417,59,382,21,393,34,372)(10,410,48,384,22,401,38,374)(11,418,52,386,23,394,42,361)(12,411,56,388,24,402,31,363)(13,419,60,390,25,395,35,365)(14,412,49,377,26,403,39,367)(15,420,53,379,27,396,43,369)(61,480,115,440,88,459,102,435)(62,473,119,442,89,452,91,422)(63,466,108,444,90,460,95,424)(64,474,112,446,76,453,99,426)(65,467,116,448,77,461,103,428)(66,475,120,450,78,454,92,430)(67,468,109,437,79,462,96,432)(68,476,113,439,80,455,100,434)(69,469,117,441,81,463,104,421)(70,477,106,443,82,456,93,423)(71,470,110,445,83,464,97,425)(72,478,114,447,84,457,101,427)(73,471,118,449,85,465,105,429)(74,479,107,436,86,458,94,431)(75,472,111,438,87,451,98,433)(121,293,169,260,141,271,159,255)(122,286,173,262,142,279,163,242)(123,294,177,264,143,272,152,244)(124,287,166,266,144,280,156,246)(125,295,170,268,145,273,160,248)(126,288,174,270,146,281,164,250)(127,296,178,257,147,274,153,252)(128,289,167,259,148,282,157,254)(129,297,171,261,149,275,161,241)(130,290,175,263,150,283,165,243)(131,298,179,265,136,276,154,245)(132,291,168,267,137,284,158,247)(133,299,172,269,138,277,162,249)(134,292,176,256,139,285,151,251)(135,300,180,258,140,278,155,253)(181,349,229,330,202,334,212,315)(182,357,233,317,203,342,216,302)(183,350,237,319,204,335,220,304)(184,358,226,321,205,343,224,306)(185,351,230,323,206,336,213,308)(186,359,234,325,207,344,217,310)(187,352,238,327,208,337,221,312)(188,360,227,329,209,345,225,314)(189,353,231,316,210,338,214,301)(190,346,235,318,196,331,218,303)(191,354,239,320,197,339,222,305)(192,347,228,322,198,332,211,307)(193,355,232,324,199,340,215,309)(194,348,236,326,200,333,219,311)(195,356,240,328,201,341,223,313) );
G=PermutationGroup([(1,134),(2,135),(3,121),(4,122),(5,123),(6,124),(7,125),(8,126),(9,127),(10,128),(11,129),(12,130),(13,131),(14,132),(15,133),(16,142),(17,143),(18,144),(19,145),(20,146),(21,147),(22,148),(23,149),(24,150),(25,136),(26,137),(27,138),(28,139),(29,140),(30,141),(31,165),(32,151),(33,152),(34,153),(35,154),(36,155),(37,156),(38,157),(39,158),(40,159),(41,160),(42,161),(43,162),(44,163),(45,164),(46,180),(47,166),(48,167),(49,168),(50,169),(51,170),(52,171),(53,172),(54,173),(55,174),(56,175),(57,176),(58,177),(59,178),(60,179),(61,191),(62,192),(63,193),(64,194),(65,195),(66,181),(67,182),(68,183),(69,184),(70,185),(71,186),(72,187),(73,188),(74,189),(75,190),(76,200),(77,201),(78,202),(79,203),(80,204),(81,205),(82,206),(83,207),(84,208),(85,209),(86,210),(87,196),(88,197),(89,198),(90,199),(91,211),(92,212),(93,213),(94,214),(95,215),(96,216),(97,217),(98,218),(99,219),(100,220),(101,221),(102,222),(103,223),(104,224),(105,225),(106,230),(107,231),(108,232),(109,233),(110,234),(111,235),(112,236),(113,237),(114,238),(115,239),(116,240),(117,226),(118,227),(119,228),(120,229),(241,361),(242,362),(243,363),(244,364),(245,365),(246,366),(247,367),(248,368),(249,369),(250,370),(251,371),(252,372),(253,373),(254,374),(255,375),(256,381),(257,382),(258,383),(259,384),(260,385),(261,386),(262,387),(263,388),(264,389),(265,390),(266,376),(267,377),(268,378),(269,379),(270,380),(271,405),(272,391),(273,392),(274,393),(275,394),(276,395),(277,396),(278,397),(279,398),(280,399),(281,400),(282,401),(283,402),(284,403),(285,404),(286,407),(287,408),(288,409),(289,410),(290,411),(291,412),(292,413),(293,414),(294,415),(295,416),(296,417),(297,418),(298,419),(299,420),(300,406),(301,431),(302,432),(303,433),(304,434),(305,435),(306,421),(307,422),(308,423),(309,424),(310,425),(311,426),(312,427),(313,428),(314,429),(315,430),(316,436),(317,437),(318,438),(319,439),(320,440),(321,441),(322,442),(323,443),(324,444),(325,445),(326,446),(327,447),(328,448),(329,449),(330,450),(331,451),(332,452),(333,453),(334,454),(335,455),(336,456),(337,457),(338,458),(339,459),(340,460),(341,461),(342,462),(343,463),(344,464),(345,465),(346,472),(347,473),(348,474),(349,475),(350,476),(351,477),(352,478),(353,479),(354,480),(355,466),(356,467),(357,468),(358,469),(359,470),(360,471)], [(1,86),(2,87),(3,88),(4,89),(5,90),(6,76),(7,77),(8,78),(9,79),(10,80),(11,81),(12,82),(13,83),(14,84),(15,85),(16,62),(17,63),(18,64),(19,65),(20,66),(21,67),(22,68),(23,69),(24,70),(25,71),(26,72),(27,73),(28,74),(29,75),(30,61),(31,106),(32,107),(33,108),(34,109),(35,110),(36,111),(37,112),(38,113),(39,114),(40,115),(41,116),(42,117),(43,118),(44,119),(45,120),(46,98),(47,99),(48,100),(49,101),(50,102),(51,103),(52,104),(53,105),(54,91),(55,92),(56,93),(57,94),(58,95),(59,96),(60,97),(121,197),(122,198),(123,199),(124,200),(125,201),(126,202),(127,203),(128,204),(129,205),(130,206),(131,207),(132,208),(133,209),(134,210),(135,196),(136,186),(137,187),(138,188),(139,189),(140,190),(141,191),(142,192),(143,193),(144,194),(145,195),(146,181),(147,182),(148,183),(149,184),(150,185),(151,231),(152,232),(153,233),(154,234),(155,235),(156,236),(157,237),(158,238),(159,239),(160,240),(161,226),(162,227),(163,228),(164,229),(165,230),(166,219),(167,220),(168,221),(169,222),(170,223),(171,224),(172,225),(173,211),(174,212),(175,213),(176,214),(177,215),(178,216),(179,217),(180,218),(241,321),(242,322),(243,323),(244,324),(245,325),(246,326),(247,327),(248,328),(249,329),(250,330),(251,316),(252,317),(253,318),(254,319),(255,320),(256,301),(257,302),(258,303),(259,304),(260,305),(261,306),(262,307),(263,308),(264,309),(265,310),(266,311),(267,312),(268,313),(269,314),(270,315),(271,354),(272,355),(273,356),(274,357),(275,358),(276,359),(277,360),(278,346),(279,347),(280,348),(281,349),(282,350),(283,351),(284,352),(285,353),(286,332),(287,333),(288,334),(289,335),(290,336),(291,337),(292,338),(293,339),(294,340),(295,341),(296,342),(297,343),(298,344),(299,345),(300,331),(361,441),(362,442),(363,443),(364,444),(365,445),(366,446),(367,447),(368,448),(369,449),(370,450),(371,436),(372,437),(373,438),(374,439),(375,440),(376,426),(377,427),(378,428),(379,429),(380,430),(381,431),(382,432),(383,433),(384,434),(385,435),(386,421),(387,422),(388,423),(389,424),(390,425),(391,466),(392,467),(393,468),(394,469),(395,470),(396,471),(397,472),(398,473),(399,474),(400,475),(401,476),(402,477),(403,478),(404,479),(405,480),(406,451),(407,452),(408,453),(409,454),(410,455),(411,456),(412,457),(413,458),(414,459),(415,460),(416,461),(417,462),(418,463),(419,464),(420,465)], [(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),(316,317,318,319,320,321,322,323,324,325,326,327,328,329,330),(331,332,333,334,335,336,337,338,339,340,341,342,343,344,345),(346,347,348,349,350,351,352,353,354,355,356,357,358,359,360),(361,362,363,364,365,366,367,368,369,370,371,372,373,374,375),(376,377,378,379,380,381,382,383,384,385,386,387,388,389,390),(391,392,393,394,395,396,397,398,399,400,401,402,403,404,405),(406,407,408,409,410,411,412,413,414,415,416,417,418,419,420),(421,422,423,424,425,426,427,428,429,430,431,432,433,434,435),(436,437,438,439,440,441,442,443,444,445,446,447,448,449,450),(451,452,453,454,455,456,457,458,459,460,461,462,463,464,465),(466,467,468,469,470,471,472,473,474,475,476,477,478,479,480)], [(1,413,57,381,28,404,32,371),(2,406,46,383,29,397,36,373),(3,414,50,385,30,405,40,375),(4,407,54,387,16,398,44,362),(5,415,58,389,17,391,33,364),(6,408,47,376,18,399,37,366),(7,416,51,378,19,392,41,368),(8,409,55,380,20,400,45,370),(9,417,59,382,21,393,34,372),(10,410,48,384,22,401,38,374),(11,418,52,386,23,394,42,361),(12,411,56,388,24,402,31,363),(13,419,60,390,25,395,35,365),(14,412,49,377,26,403,39,367),(15,420,53,379,27,396,43,369),(61,480,115,440,88,459,102,435),(62,473,119,442,89,452,91,422),(63,466,108,444,90,460,95,424),(64,474,112,446,76,453,99,426),(65,467,116,448,77,461,103,428),(66,475,120,450,78,454,92,430),(67,468,109,437,79,462,96,432),(68,476,113,439,80,455,100,434),(69,469,117,441,81,463,104,421),(70,477,106,443,82,456,93,423),(71,470,110,445,83,464,97,425),(72,478,114,447,84,457,101,427),(73,471,118,449,85,465,105,429),(74,479,107,436,86,458,94,431),(75,472,111,438,87,451,98,433),(121,293,169,260,141,271,159,255),(122,286,173,262,142,279,163,242),(123,294,177,264,143,272,152,244),(124,287,166,266,144,280,156,246),(125,295,170,268,145,273,160,248),(126,288,174,270,146,281,164,250),(127,296,178,257,147,274,153,252),(128,289,167,259,148,282,157,254),(129,297,171,261,149,275,161,241),(130,290,175,263,150,283,165,243),(131,298,179,265,136,276,154,245),(132,291,168,267,137,284,158,247),(133,299,172,269,138,277,162,249),(134,292,176,256,139,285,151,251),(135,300,180,258,140,278,155,253),(181,349,229,330,202,334,212,315),(182,357,233,317,203,342,216,302),(183,350,237,319,204,335,220,304),(184,358,226,321,205,343,224,306),(185,351,230,323,206,336,213,308),(186,359,234,325,207,344,217,310),(187,352,238,327,208,337,221,312),(188,360,227,329,209,345,225,314),(189,353,231,316,210,338,214,301),(190,346,235,318,196,331,218,303),(191,354,239,320,197,339,222,305),(192,347,228,322,198,332,211,307),(193,355,232,324,199,340,215,309),(194,348,236,326,200,333,219,311),(195,356,240,328,201,341,223,313)])
Matrix representation ►G ⊆ GL8(𝔽241)
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 240 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 240 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 240 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 240 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 240 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 240 |
| 0 | 240 | 0 | 0 | 0 | 0 | 0 | 0 |
| 1 | 240 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 240 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 240 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 240 | 240 | 240 | 240 |
| 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |
| 236 | 183 | 0 | 0 | 0 | 0 | 0 | 0 |
| 178 | 5 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 20 | 93 | 0 | 0 | 0 | 0 |
| 0 | 0 | 113 | 221 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 74 | 4 | 181 | 217 |
| 0 | 0 | 0 | 0 | 36 | 60 | 134 | 64 |
| 0 | 0 | 0 | 0 | 171 | 107 | 143 | 167 |
| 0 | 0 | 0 | 0 | 24 | 98 | 28 | 205 |
G:=sub<GL(8,GF(241))| [1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,240,0,0,0,0,0,0,0,0,240,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,240,0,0,0,0,0,0,0,0,240,0,0,0,0,0,0,0,0,240,0,0,0,0,0,0,0,0,240],[0,1,0,0,0,0,0,0,240,240,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,240,240,0,0,0,0,0,0,0,0,0,240,1,0,0,0,0,0,0,240,0,1,0,0,0,0,0,240,0,0,0,0,0,0,1,240,0,0],[236,178,0,0,0,0,0,0,183,5,0,0,0,0,0,0,0,0,20,113,0,0,0,0,0,0,93,221,0,0,0,0,0,0,0,0,74,36,171,24,0,0,0,0,4,60,107,98,0,0,0,0,181,134,143,28,0,0,0,0,217,64,167,205] >;
72 conjugacy classes
| class | 1 | 2A | ··· | 2G | 3 | 4A | ··· | 4H | 5 | 6A | ··· | 6G | 8A | ··· | 8P | 10A | ··· | 10G | 12A | ··· | 12H | 15A | 15B | 30A | ··· | 30N |
| order | 1 | 2 | ··· | 2 | 3 | 4 | ··· | 4 | 5 | 6 | ··· | 6 | 8 | ··· | 8 | 10 | ··· | 10 | 12 | ··· | 12 | 15 | 15 | 30 | ··· | 30 |
| size | 1 | 1 | ··· | 1 | 2 | 5 | ··· | 5 | 4 | 2 | ··· | 2 | 15 | ··· | 15 | 4 | ··· | 4 | 10 | ··· | 10 | 4 | 4 | 4 | ··· | 4 |
72 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | - | + | - | + | - | + | |||||||
| image | C1 | C2 | C2 | C4 | C4 | C8 | S3 | Dic3 | D6 | Dic3 | C3⋊C8 | F5 | C5⋊C8 | C2×F5 | C3⋊F5 | C15⋊C8 | C2×C3⋊F5 |
| kernel | C22×C15⋊C8 | C2×C15⋊C8 | C2×C6×Dic5 | C6×Dic5 | C22×C30 | C2×C30 | C22×Dic5 | C2×Dic5 | C2×Dic5 | C22×C10 | C2×C10 | C22×C6 | C2×C6 | C2×C6 | C23 | C22 | C22 |
| # reps | 1 | 6 | 1 | 6 | 2 | 16 | 1 | 3 | 3 | 1 | 8 | 1 | 4 | 3 | 2 | 8 | 6 |
In GAP, Magma, Sage, TeX
C_2^2\times C_{15}\rtimes C_8 % in TeX
G:=Group("C2^2xC15:C8"); // GroupNames label
G:=SmallGroup(480,1070);
// by ID
G=gap.SmallGroup(480,1070);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,56,80,2693,14118,2379]);
// Polycyclic
G:=Group<a,b,c,d|a^2=b^2=c^15=d^8=1,a*b=b*a,a*c=c*a,a*d=d*a,b*c=c*b,b*d=d*b,d*c*d^-1=c^2>;
// generators/relations
×
⋊
ℤ
𝔽
○
≀