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G = C23×Dic15order 480 = 25·3·5

Direct product of C23 and Dic15

direct product, metabelian, supersoluble, monomial, A-group, 2-hyperelementary

Aliases: C23×Dic15, C24.3D15, C30.67C24, C23.41D30, C1511(C23×C4), (C23×C6).3D5, C32(C23×Dic5), C53(C23×Dic3), (C22×C30)⋊13C4, C3011(C22×C4), (C23×C10).5S3, (C23×C30).3C2, (C22×C6)⋊5Dic5, C62(C22×Dic5), C6.67(C23×D5), C2.2(C23×D15), C10.67(S3×C23), C103(C22×Dic3), (C2×C30).325C23, (C22×C10)⋊11Dic3, (C22×C6).128D10, (C22×C10).146D6, C22.33(C22×D15), (C22×C30).151C22, (C2×C30)⋊41(C2×C4), (C2×C6)⋊9(C2×Dic5), (C2×C10)⋊16(C2×Dic3), (C2×C6).321(C22×D5), (C2×C10).321(C22×S3), SmallGroup(480,1178)

Series: Derived Chief Lower central Upper central

C1C15 — C23×Dic15
C1C5C15C30Dic15C2×Dic15C22×Dic15 — C23×Dic15
C15 — C23×Dic15
C1C24

Generators and relations for C23×Dic15
 G = < a,b,c,d,e | a2=b2=c2=d30=1, e2=d15, ab=ba, ac=ca, ad=da, ae=ea, bc=cb, bd=db, be=eb, cd=dc, ce=ec, ede-1=d-1 >

Subgroups: 1492 in 472 conjugacy classes, 319 normal (13 characteristic)
C1, C2, C2 [×14], C3, C4 [×8], C22 [×35], C5, C6, C6 [×14], C2×C4 [×28], C23 [×15], C10, C10 [×14], Dic3 [×8], C2×C6 [×35], C15, C22×C4 [×14], C24, Dic5 [×8], C2×C10 [×35], C2×Dic3 [×28], C22×C6 [×15], C30, C30 [×14], C23×C4, C2×Dic5 [×28], C22×C10 [×15], C22×Dic3 [×14], C23×C6, Dic15 [×8], C2×C30 [×35], C22×Dic5 [×14], C23×C10, C23×Dic3, C2×Dic15 [×28], C22×C30 [×15], C23×Dic5, C22×Dic15 [×14], C23×C30, C23×Dic15
Quotients: C1, C2 [×15], C4 [×8], C22 [×35], S3, C2×C4 [×28], C23 [×15], D5, Dic3 [×8], D6 [×7], C22×C4 [×14], C24, Dic5 [×8], D10 [×7], C2×Dic3 [×28], C22×S3 [×7], D15, C23×C4, C2×Dic5 [×28], C22×D5 [×7], C22×Dic3 [×14], S3×C23, Dic15 [×8], D30 [×7], C22×Dic5 [×14], C23×D5, C23×Dic3, C2×Dic15 [×28], C22×D15 [×7], C23×Dic5, C22×Dic15 [×14], C23×D15, C23×Dic15

Smallest permutation representation of C23×Dic15
Regular action on 480 points
Generators in S480
(1 142)(2 143)(3 144)(4 145)(5 146)(6 147)(7 148)(8 149)(9 150)(10 121)(11 122)(12 123)(13 124)(14 125)(15 126)(16 127)(17 128)(18 129)(19 130)(20 131)(21 132)(22 133)(23 134)(24 135)(25 136)(26 137)(27 138)(28 139)(29 140)(30 141)(31 153)(32 154)(33 155)(34 156)(35 157)(36 158)(37 159)(38 160)(39 161)(40 162)(41 163)(42 164)(43 165)(44 166)(45 167)(46 168)(47 169)(48 170)(49 171)(50 172)(51 173)(52 174)(53 175)(54 176)(55 177)(56 178)(57 179)(58 180)(59 151)(60 152)(61 181)(62 182)(63 183)(64 184)(65 185)(66 186)(67 187)(68 188)(69 189)(70 190)(71 191)(72 192)(73 193)(74 194)(75 195)(76 196)(77 197)(78 198)(79 199)(80 200)(81 201)(82 202)(83 203)(84 204)(85 205)(86 206)(87 207)(88 208)(89 209)(90 210)(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)(106 226)(107 227)(108 228)(109 229)(110 230)(111 231)(112 232)(113 233)(114 234)(115 235)(116 236)(117 237)(118 238)(119 239)(120 240)(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)(256 376)(257 377)(258 378)(259 379)(260 380)(261 381)(262 382)(263 383)(264 384)(265 385)(266 386)(267 387)(268 388)(269 389)(270 390)(271 396)(272 397)(273 398)(274 399)(275 400)(276 401)(277 402)(278 403)(279 404)(280 405)(281 406)(282 407)(283 408)(284 409)(285 410)(286 411)(287 412)(288 413)(289 414)(290 415)(291 416)(292 417)(293 418)(294 419)(295 420)(296 391)(297 392)(298 393)(299 394)(300 395)(301 441)(302 442)(303 443)(304 444)(305 445)(306 446)(307 447)(308 448)(309 449)(310 450)(311 421)(312 422)(313 423)(314 424)(315 425)(316 426)(317 427)(318 428)(319 429)(320 430)(321 431)(322 432)(323 433)(324 434)(325 435)(326 436)(327 437)(328 438)(329 439)(330 440)(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)(346 466)(347 467)(348 468)(349 469)(350 470)(351 471)(352 472)(353 473)(354 474)(355 475)(356 476)(357 477)(358 478)(359 479)(360 480)
(1 98)(2 99)(3 100)(4 101)(5 102)(6 103)(7 104)(8 105)(9 106)(10 107)(11 108)(12 109)(13 110)(14 111)(15 112)(16 113)(17 114)(18 115)(19 116)(20 117)(21 118)(22 119)(23 120)(24 91)(25 92)(26 93)(27 94)(28 95)(29 96)(30 97)(31 62)(32 63)(33 64)(34 65)(35 66)(36 67)(37 68)(38 69)(39 70)(40 71)(41 72)(42 73)(43 74)(44 75)(45 76)(46 77)(47 78)(48 79)(49 80)(50 81)(51 82)(52 83)(53 84)(54 85)(55 86)(56 87)(57 88)(58 89)(59 90)(60 61)(121 227)(122 228)(123 229)(124 230)(125 231)(126 232)(127 233)(128 234)(129 235)(130 236)(131 237)(132 238)(133 239)(134 240)(135 211)(136 212)(137 213)(138 214)(139 215)(140 216)(141 217)(142 218)(143 219)(144 220)(145 221)(146 222)(147 223)(148 224)(149 225)(150 226)(151 210)(152 181)(153 182)(154 183)(155 184)(156 185)(157 186)(158 187)(159 188)(160 189)(161 190)(162 191)(163 192)(164 193)(165 194)(166 195)(167 196)(168 197)(169 198)(170 199)(171 200)(172 201)(173 202)(174 203)(175 204)(176 205)(177 206)(178 207)(179 208)(180 209)(241 351)(242 352)(243 353)(244 354)(245 355)(246 356)(247 357)(248 358)(249 359)(250 360)(251 331)(252 332)(253 333)(254 334)(255 335)(256 336)(257 337)(258 338)(259 339)(260 340)(261 341)(262 342)(263 343)(264 344)(265 345)(266 346)(267 347)(268 348)(269 349)(270 350)(271 301)(272 302)(273 303)(274 304)(275 305)(276 306)(277 307)(278 308)(279 309)(280 310)(281 311)(282 312)(283 313)(284 314)(285 315)(286 316)(287 317)(288 318)(289 319)(290 320)(291 321)(292 322)(293 323)(294 324)(295 325)(296 326)(297 327)(298 328)(299 329)(300 330)(361 471)(362 472)(363 473)(364 474)(365 475)(366 476)(367 477)(368 478)(369 479)(370 480)(371 451)(372 452)(373 453)(374 454)(375 455)(376 456)(377 457)(378 458)(379 459)(380 460)(381 461)(382 462)(383 463)(384 464)(385 465)(386 466)(387 467)(388 468)(389 469)(390 470)(391 436)(392 437)(393 438)(394 439)(395 440)(396 441)(397 442)(398 443)(399 444)(400 445)(401 446)(402 447)(403 448)(404 449)(405 450)(406 421)(407 422)(408 423)(409 424)(410 425)(411 426)(412 427)(413 428)(414 429)(415 430)(416 431)(417 432)(418 433)(419 434)(420 435)
(1 59)(2 60)(3 31)(4 32)(5 33)(6 34)(7 35)(8 36)(9 37)(10 38)(11 39)(12 40)(13 41)(14 42)(15 43)(16 44)(17 45)(18 46)(19 47)(20 48)(21 49)(22 50)(23 51)(24 52)(25 53)(26 54)(27 55)(28 56)(29 57)(30 58)(61 99)(62 100)(63 101)(64 102)(65 103)(66 104)(67 105)(68 106)(69 107)(70 108)(71 109)(72 110)(73 111)(74 112)(75 113)(76 114)(77 115)(78 116)(79 117)(80 118)(81 119)(82 120)(83 91)(84 92)(85 93)(86 94)(87 95)(88 96)(89 97)(90 98)(121 160)(122 161)(123 162)(124 163)(125 164)(126 165)(127 166)(128 167)(129 168)(130 169)(131 170)(132 171)(133 172)(134 173)(135 174)(136 175)(137 176)(138 177)(139 178)(140 179)(141 180)(142 151)(143 152)(144 153)(145 154)(146 155)(147 156)(148 157)(149 158)(150 159)(181 219)(182 220)(183 221)(184 222)(185 223)(186 224)(187 225)(188 226)(189 227)(190 228)(191 229)(192 230)(193 231)(194 232)(195 233)(196 234)(197 235)(198 236)(199 237)(200 238)(201 239)(202 240)(203 211)(204 212)(205 213)(206 214)(207 215)(208 216)(209 217)(210 218)(241 286)(242 287)(243 288)(244 289)(245 290)(246 291)(247 292)(248 293)(249 294)(250 295)(251 296)(252 297)(253 298)(254 299)(255 300)(256 271)(257 272)(258 273)(259 274)(260 275)(261 276)(262 277)(263 278)(264 279)(265 280)(266 281)(267 282)(268 283)(269 284)(270 285)(301 336)(302 337)(303 338)(304 339)(305 340)(306 341)(307 342)(308 343)(309 344)(310 345)(311 346)(312 347)(313 348)(314 349)(315 350)(316 351)(317 352)(318 353)(319 354)(320 355)(321 356)(322 357)(323 358)(324 359)(325 360)(326 331)(327 332)(328 333)(329 334)(330 335)(361 411)(362 412)(363 413)(364 414)(365 415)(366 416)(367 417)(368 418)(369 419)(370 420)(371 391)(372 392)(373 393)(374 394)(375 395)(376 396)(377 397)(378 398)(379 399)(380 400)(381 401)(382 402)(383 403)(384 404)(385 405)(386 406)(387 407)(388 408)(389 409)(390 410)(421 466)(422 467)(423 468)(424 469)(425 470)(426 471)(427 472)(428 473)(429 474)(430 475)(431 476)(432 477)(433 478)(434 479)(435 480)(436 451)(437 452)(438 453)(439 454)(440 455)(441 456)(442 457)(443 458)(444 459)(445 460)(446 461)(447 462)(448 463)(449 464)(450 465)
(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)
(1 436 16 421)(2 435 17 450)(3 434 18 449)(4 433 19 448)(5 432 20 447)(6 431 21 446)(7 430 22 445)(8 429 23 444)(9 428 24 443)(10 427 25 442)(11 426 26 441)(12 425 27 440)(13 424 28 439)(14 423 29 438)(15 422 30 437)(31 479 46 464)(32 478 47 463)(33 477 48 462)(34 476 49 461)(35 475 50 460)(36 474 51 459)(37 473 52 458)(38 472 53 457)(39 471 54 456)(40 470 55 455)(41 469 56 454)(42 468 57 453)(43 467 58 452)(44 466 59 451)(45 465 60 480)(61 370 76 385)(62 369 77 384)(63 368 78 383)(64 367 79 382)(65 366 80 381)(66 365 81 380)(67 364 82 379)(68 363 83 378)(69 362 84 377)(70 361 85 376)(71 390 86 375)(72 389 87 374)(73 388 88 373)(74 387 89 372)(75 386 90 371)(91 398 106 413)(92 397 107 412)(93 396 108 411)(94 395 109 410)(95 394 110 409)(96 393 111 408)(97 392 112 407)(98 391 113 406)(99 420 114 405)(100 419 115 404)(101 418 116 403)(102 417 117 402)(103 416 118 401)(104 415 119 400)(105 414 120 399)(121 317 136 302)(122 316 137 301)(123 315 138 330)(124 314 139 329)(125 313 140 328)(126 312 141 327)(127 311 142 326)(128 310 143 325)(129 309 144 324)(130 308 145 323)(131 307 146 322)(132 306 147 321)(133 305 148 320)(134 304 149 319)(135 303 150 318)(151 331 166 346)(152 360 167 345)(153 359 168 344)(154 358 169 343)(155 357 170 342)(156 356 171 341)(157 355 172 340)(158 354 173 339)(159 353 174 338)(160 352 175 337)(161 351 176 336)(162 350 177 335)(163 349 178 334)(164 348 179 333)(165 347 180 332)(181 250 196 265)(182 249 197 264)(183 248 198 263)(184 247 199 262)(185 246 200 261)(186 245 201 260)(187 244 202 259)(188 243 203 258)(189 242 204 257)(190 241 205 256)(191 270 206 255)(192 269 207 254)(193 268 208 253)(194 267 209 252)(195 266 210 251)(211 273 226 288)(212 272 227 287)(213 271 228 286)(214 300 229 285)(215 299 230 284)(216 298 231 283)(217 297 232 282)(218 296 233 281)(219 295 234 280)(220 294 235 279)(221 293 236 278)(222 292 237 277)(223 291 238 276)(224 290 239 275)(225 289 240 274)

G:=sub<Sym(480)| (1,142)(2,143)(3,144)(4,145)(5,146)(6,147)(7,148)(8,149)(9,150)(10,121)(11,122)(12,123)(13,124)(14,125)(15,126)(16,127)(17,128)(18,129)(19,130)(20,131)(21,132)(22,133)(23,134)(24,135)(25,136)(26,137)(27,138)(28,139)(29,140)(30,141)(31,153)(32,154)(33,155)(34,156)(35,157)(36,158)(37,159)(38,160)(39,161)(40,162)(41,163)(42,164)(43,165)(44,166)(45,167)(46,168)(47,169)(48,170)(49,171)(50,172)(51,173)(52,174)(53,175)(54,176)(55,177)(56,178)(57,179)(58,180)(59,151)(60,152)(61,181)(62,182)(63,183)(64,184)(65,185)(66,186)(67,187)(68,188)(69,189)(70,190)(71,191)(72,192)(73,193)(74,194)(75,195)(76,196)(77,197)(78,198)(79,199)(80,200)(81,201)(82,202)(83,203)(84,204)(85,205)(86,206)(87,207)(88,208)(89,209)(90,210)(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)(106,226)(107,227)(108,228)(109,229)(110,230)(111,231)(112,232)(113,233)(114,234)(115,235)(116,236)(117,237)(118,238)(119,239)(120,240)(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)(256,376)(257,377)(258,378)(259,379)(260,380)(261,381)(262,382)(263,383)(264,384)(265,385)(266,386)(267,387)(268,388)(269,389)(270,390)(271,396)(272,397)(273,398)(274,399)(275,400)(276,401)(277,402)(278,403)(279,404)(280,405)(281,406)(282,407)(283,408)(284,409)(285,410)(286,411)(287,412)(288,413)(289,414)(290,415)(291,416)(292,417)(293,418)(294,419)(295,420)(296,391)(297,392)(298,393)(299,394)(300,395)(301,441)(302,442)(303,443)(304,444)(305,445)(306,446)(307,447)(308,448)(309,449)(310,450)(311,421)(312,422)(313,423)(314,424)(315,425)(316,426)(317,427)(318,428)(319,429)(320,430)(321,431)(322,432)(323,433)(324,434)(325,435)(326,436)(327,437)(328,438)(329,439)(330,440)(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)(346,466)(347,467)(348,468)(349,469)(350,470)(351,471)(352,472)(353,473)(354,474)(355,475)(356,476)(357,477)(358,478)(359,479)(360,480), (1,98)(2,99)(3,100)(4,101)(5,102)(6,103)(7,104)(8,105)(9,106)(10,107)(11,108)(12,109)(13,110)(14,111)(15,112)(16,113)(17,114)(18,115)(19,116)(20,117)(21,118)(22,119)(23,120)(24,91)(25,92)(26,93)(27,94)(28,95)(29,96)(30,97)(31,62)(32,63)(33,64)(34,65)(35,66)(36,67)(37,68)(38,69)(39,70)(40,71)(41,72)(42,73)(43,74)(44,75)(45,76)(46,77)(47,78)(48,79)(49,80)(50,81)(51,82)(52,83)(53,84)(54,85)(55,86)(56,87)(57,88)(58,89)(59,90)(60,61)(121,227)(122,228)(123,229)(124,230)(125,231)(126,232)(127,233)(128,234)(129,235)(130,236)(131,237)(132,238)(133,239)(134,240)(135,211)(136,212)(137,213)(138,214)(139,215)(140,216)(141,217)(142,218)(143,219)(144,220)(145,221)(146,222)(147,223)(148,224)(149,225)(150,226)(151,210)(152,181)(153,182)(154,183)(155,184)(156,185)(157,186)(158,187)(159,188)(160,189)(161,190)(162,191)(163,192)(164,193)(165,194)(166,195)(167,196)(168,197)(169,198)(170,199)(171,200)(172,201)(173,202)(174,203)(175,204)(176,205)(177,206)(178,207)(179,208)(180,209)(241,351)(242,352)(243,353)(244,354)(245,355)(246,356)(247,357)(248,358)(249,359)(250,360)(251,331)(252,332)(253,333)(254,334)(255,335)(256,336)(257,337)(258,338)(259,339)(260,340)(261,341)(262,342)(263,343)(264,344)(265,345)(266,346)(267,347)(268,348)(269,349)(270,350)(271,301)(272,302)(273,303)(274,304)(275,305)(276,306)(277,307)(278,308)(279,309)(280,310)(281,311)(282,312)(283,313)(284,314)(285,315)(286,316)(287,317)(288,318)(289,319)(290,320)(291,321)(292,322)(293,323)(294,324)(295,325)(296,326)(297,327)(298,328)(299,329)(300,330)(361,471)(362,472)(363,473)(364,474)(365,475)(366,476)(367,477)(368,478)(369,479)(370,480)(371,451)(372,452)(373,453)(374,454)(375,455)(376,456)(377,457)(378,458)(379,459)(380,460)(381,461)(382,462)(383,463)(384,464)(385,465)(386,466)(387,467)(388,468)(389,469)(390,470)(391,436)(392,437)(393,438)(394,439)(395,440)(396,441)(397,442)(398,443)(399,444)(400,445)(401,446)(402,447)(403,448)(404,449)(405,450)(406,421)(407,422)(408,423)(409,424)(410,425)(411,426)(412,427)(413,428)(414,429)(415,430)(416,431)(417,432)(418,433)(419,434)(420,435), (1,59)(2,60)(3,31)(4,32)(5,33)(6,34)(7,35)(8,36)(9,37)(10,38)(11,39)(12,40)(13,41)(14,42)(15,43)(16,44)(17,45)(18,46)(19,47)(20,48)(21,49)(22,50)(23,51)(24,52)(25,53)(26,54)(27,55)(28,56)(29,57)(30,58)(61,99)(62,100)(63,101)(64,102)(65,103)(66,104)(67,105)(68,106)(69,107)(70,108)(71,109)(72,110)(73,111)(74,112)(75,113)(76,114)(77,115)(78,116)(79,117)(80,118)(81,119)(82,120)(83,91)(84,92)(85,93)(86,94)(87,95)(88,96)(89,97)(90,98)(121,160)(122,161)(123,162)(124,163)(125,164)(126,165)(127,166)(128,167)(129,168)(130,169)(131,170)(132,171)(133,172)(134,173)(135,174)(136,175)(137,176)(138,177)(139,178)(140,179)(141,180)(142,151)(143,152)(144,153)(145,154)(146,155)(147,156)(148,157)(149,158)(150,159)(181,219)(182,220)(183,221)(184,222)(185,223)(186,224)(187,225)(188,226)(189,227)(190,228)(191,229)(192,230)(193,231)(194,232)(195,233)(196,234)(197,235)(198,236)(199,237)(200,238)(201,239)(202,240)(203,211)(204,212)(205,213)(206,214)(207,215)(208,216)(209,217)(210,218)(241,286)(242,287)(243,288)(244,289)(245,290)(246,291)(247,292)(248,293)(249,294)(250,295)(251,296)(252,297)(253,298)(254,299)(255,300)(256,271)(257,272)(258,273)(259,274)(260,275)(261,276)(262,277)(263,278)(264,279)(265,280)(266,281)(267,282)(268,283)(269,284)(270,285)(301,336)(302,337)(303,338)(304,339)(305,340)(306,341)(307,342)(308,343)(309,344)(310,345)(311,346)(312,347)(313,348)(314,349)(315,350)(316,351)(317,352)(318,353)(319,354)(320,355)(321,356)(322,357)(323,358)(324,359)(325,360)(326,331)(327,332)(328,333)(329,334)(330,335)(361,411)(362,412)(363,413)(364,414)(365,415)(366,416)(367,417)(368,418)(369,419)(370,420)(371,391)(372,392)(373,393)(374,394)(375,395)(376,396)(377,397)(378,398)(379,399)(380,400)(381,401)(382,402)(383,403)(384,404)(385,405)(386,406)(387,407)(388,408)(389,409)(390,410)(421,466)(422,467)(423,468)(424,469)(425,470)(426,471)(427,472)(428,473)(429,474)(430,475)(431,476)(432,477)(433,478)(434,479)(435,480)(436,451)(437,452)(438,453)(439,454)(440,455)(441,456)(442,457)(443,458)(444,459)(445,460)(446,461)(447,462)(448,463)(449,464)(450,465), 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G:=Group( 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(1,59)(2,60)(3,31)(4,32)(5,33)(6,34)(7,35)(8,36)(9,37)(10,38)(11,39)(12,40)(13,41)(14,42)(15,43)(16,44)(17,45)(18,46)(19,47)(20,48)(21,49)(22,50)(23,51)(24,52)(25,53)(26,54)(27,55)(28,56)(29,57)(30,58)(61,99)(62,100)(63,101)(64,102)(65,103)(66,104)(67,105)(68,106)(69,107)(70,108)(71,109)(72,110)(73,111)(74,112)(75,113)(76,114)(77,115)(78,116)(79,117)(80,118)(81,119)(82,120)(83,91)(84,92)(85,93)(86,94)(87,95)(88,96)(89,97)(90,98)(121,160)(122,161)(123,162)(124,163)(125,164)(126,165)(127,166)(128,167)(129,168)(130,169)(131,170)(132,171)(133,172)(134,173)(135,174)(136,175)(137,176)(138,177)(139,178)(140,179)(141,180)(142,151)(143,152)(144,153)(145,154)(146,155)(147,156)(148,157)(149,158)(150,159)(181,219)(182,220)(183,221)(184,222)(185,223)(186,224)(187,225)(188,226)(189,227)(190,228)(191,229)(192,230)(193,231)(194,232)(195,233)(196,234)(197,235)(198,236)(199,237)(200,238)(201,239)(202,240)(203,211)(204,212)(205,213)(206,214)(207,215)(208,216)(209,217)(210,218)(241,286)(242,287)(243,288)(244,289)(245,290)(246,291)(247,292)(248,293)(249,294)(250,295)(251,296)(252,297)(253,298)(254,299)(255,300)(256,271)(257,272)(258,273)(259,274)(260,275)(261,276)(262,277)(263,278)(264,279)(265,280)(266,281)(267,282)(268,283)(269,284)(270,285)(301,336)(302,337)(303,338)(304,339)(305,340)(306,341)(307,342)(308,343)(309,344)(310,345)(311,346)(312,347)(313,348)(314,349)(315,350)(316,351)(317,352)(318,353)(319,354)(320,355)(321,356)(322,357)(323,358)(324,359)(325,360)(326,331)(327,332)(328,333)(329,334)(330,335)(361,411)(362,412)(363,413)(364,414)(365,415)(366,416)(367,417)(368,418)(369,419)(370,420)(371,391)(372,392)(373,393)(374,394)(375,395)(376,396)(377,397)(378,398)(379,399)(380,400)(381,401)(382,402)(383,403)(384,404)(385,405)(386,406)(387,407)(388,408)(389,409)(390,410)(421,466)(422,467)(423,468)(424,469)(425,470)(426,471)(427,472)(428,473)(429,474)(430,475)(431,476)(432,477)(433,478)(434,479)(435,480)(436,451)(437,452)(438,453)(439,454)(440,455)(441,456)(442,457)(443,458)(444,459)(445,460)(446,461)(447,462)(448,463)(449,464)(450,465), (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), (1,436,16,421)(2,435,17,450)(3,434,18,449)(4,433,19,448)(5,432,20,447)(6,431,21,446)(7,430,22,445)(8,429,23,444)(9,428,24,443)(10,427,25,442)(11,426,26,441)(12,425,27,440)(13,424,28,439)(14,423,29,438)(15,422,30,437)(31,479,46,464)(32,478,47,463)(33,477,48,462)(34,476,49,461)(35,475,50,460)(36,474,51,459)(37,473,52,458)(38,472,53,457)(39,471,54,456)(40,470,55,455)(41,469,56,454)(42,468,57,453)(43,467,58,452)(44,466,59,451)(45,465,60,480)(61,370,76,385)(62,369,77,384)(63,368,78,383)(64,367,79,382)(65,366,80,381)(66,365,81,380)(67,364,82,379)(68,363,83,378)(69,362,84,377)(70,361,85,376)(71,390,86,375)(72,389,87,374)(73,388,88,373)(74,387,89,372)(75,386,90,371)(91,398,106,413)(92,397,107,412)(93,396,108,411)(94,395,109,410)(95,394,110,409)(96,393,111,408)(97,392,112,407)(98,391,113,406)(99,420,114,405)(100,419,115,404)(101,418,116,403)(102,417,117,402)(103,416,118,401)(104,415,119,400)(105,414,120,399)(121,317,136,302)(122,316,137,301)(123,315,138,330)(124,314,139,329)(125,313,140,328)(126,312,141,327)(127,311,142,326)(128,310,143,325)(129,309,144,324)(130,308,145,323)(131,307,146,322)(132,306,147,321)(133,305,148,320)(134,304,149,319)(135,303,150,318)(151,331,166,346)(152,360,167,345)(153,359,168,344)(154,358,169,343)(155,357,170,342)(156,356,171,341)(157,355,172,340)(158,354,173,339)(159,353,174,338)(160,352,175,337)(161,351,176,336)(162,350,177,335)(163,349,178,334)(164,348,179,333)(165,347,180,332)(181,250,196,265)(182,249,197,264)(183,248,198,263)(184,247,199,262)(185,246,200,261)(186,245,201,260)(187,244,202,259)(188,243,203,258)(189,242,204,257)(190,241,205,256)(191,270,206,255)(192,269,207,254)(193,268,208,253)(194,267,209,252)(195,266,210,251)(211,273,226,288)(212,272,227,287)(213,271,228,286)(214,300,229,285)(215,299,230,284)(216,298,231,283)(217,297,232,282)(218,296,233,281)(219,295,234,280)(220,294,235,279)(221,293,236,278)(222,292,237,277)(223,291,238,276)(224,290,239,275)(225,289,240,274) );

G=PermutationGroup([(1,142),(2,143),(3,144),(4,145),(5,146),(6,147),(7,148),(8,149),(9,150),(10,121),(11,122),(12,123),(13,124),(14,125),(15,126),(16,127),(17,128),(18,129),(19,130),(20,131),(21,132),(22,133),(23,134),(24,135),(25,136),(26,137),(27,138),(28,139),(29,140),(30,141),(31,153),(32,154),(33,155),(34,156),(35,157),(36,158),(37,159),(38,160),(39,161),(40,162),(41,163),(42,164),(43,165),(44,166),(45,167),(46,168),(47,169),(48,170),(49,171),(50,172),(51,173),(52,174),(53,175),(54,176),(55,177),(56,178),(57,179),(58,180),(59,151),(60,152),(61,181),(62,182),(63,183),(64,184),(65,185),(66,186),(67,187),(68,188),(69,189),(70,190),(71,191),(72,192),(73,193),(74,194),(75,195),(76,196),(77,197),(78,198),(79,199),(80,200),(81,201),(82,202),(83,203),(84,204),(85,205),(86,206),(87,207),(88,208),(89,209),(90,210),(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),(106,226),(107,227),(108,228),(109,229),(110,230),(111,231),(112,232),(113,233),(114,234),(115,235),(116,236),(117,237),(118,238),(119,239),(120,240),(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),(256,376),(257,377),(258,378),(259,379),(260,380),(261,381),(262,382),(263,383),(264,384),(265,385),(266,386),(267,387),(268,388),(269,389),(270,390),(271,396),(272,397),(273,398),(274,399),(275,400),(276,401),(277,402),(278,403),(279,404),(280,405),(281,406),(282,407),(283,408),(284,409),(285,410),(286,411),(287,412),(288,413),(289,414),(290,415),(291,416),(292,417),(293,418),(294,419),(295,420),(296,391),(297,392),(298,393),(299,394),(300,395),(301,441),(302,442),(303,443),(304,444),(305,445),(306,446),(307,447),(308,448),(309,449),(310,450),(311,421),(312,422),(313,423),(314,424),(315,425),(316,426),(317,427),(318,428),(319,429),(320,430),(321,431),(322,432),(323,433),(324,434),(325,435),(326,436),(327,437),(328,438),(329,439),(330,440),(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),(346,466),(347,467),(348,468),(349,469),(350,470),(351,471),(352,472),(353,473),(354,474),(355,475),(356,476),(357,477),(358,478),(359,479),(360,480)], [(1,98),(2,99),(3,100),(4,101),(5,102),(6,103),(7,104),(8,105),(9,106),(10,107),(11,108),(12,109),(13,110),(14,111),(15,112),(16,113),(17,114),(18,115),(19,116),(20,117),(21,118),(22,119),(23,120),(24,91),(25,92),(26,93),(27,94),(28,95),(29,96),(30,97),(31,62),(32,63),(33,64),(34,65),(35,66),(36,67),(37,68),(38,69),(39,70),(40,71),(41,72),(42,73),(43,74),(44,75),(45,76),(46,77),(47,78),(48,79),(49,80),(50,81),(51,82),(52,83),(53,84),(54,85),(55,86),(56,87),(57,88),(58,89),(59,90),(60,61),(121,227),(122,228),(123,229),(124,230),(125,231),(126,232),(127,233),(128,234),(129,235),(130,236),(131,237),(132,238),(133,239),(134,240),(135,211),(136,212),(137,213),(138,214),(139,215),(140,216),(141,217),(142,218),(143,219),(144,220),(145,221),(146,222),(147,223),(148,224),(149,225),(150,226),(151,210),(152,181),(153,182),(154,183),(155,184),(156,185),(157,186),(158,187),(159,188),(160,189),(161,190),(162,191),(163,192),(164,193),(165,194),(166,195),(167,196),(168,197),(169,198),(170,199),(171,200),(172,201),(173,202),(174,203),(175,204),(176,205),(177,206),(178,207),(179,208),(180,209),(241,351),(242,352),(243,353),(244,354),(245,355),(246,356),(247,357),(248,358),(249,359),(250,360),(251,331),(252,332),(253,333),(254,334),(255,335),(256,336),(257,337),(258,338),(259,339),(260,340),(261,341),(262,342),(263,343),(264,344),(265,345),(266,346),(267,347),(268,348),(269,349),(270,350),(271,301),(272,302),(273,303),(274,304),(275,305),(276,306),(277,307),(278,308),(279,309),(280,310),(281,311),(282,312),(283,313),(284,314),(285,315),(286,316),(287,317),(288,318),(289,319),(290,320),(291,321),(292,322),(293,323),(294,324),(295,325),(296,326),(297,327),(298,328),(299,329),(300,330),(361,471),(362,472),(363,473),(364,474),(365,475),(366,476),(367,477),(368,478),(369,479),(370,480),(371,451),(372,452),(373,453),(374,454),(375,455),(376,456),(377,457),(378,458),(379,459),(380,460),(381,461),(382,462),(383,463),(384,464),(385,465),(386,466),(387,467),(388,468),(389,469),(390,470),(391,436),(392,437),(393,438),(394,439),(395,440),(396,441),(397,442),(398,443),(399,444),(400,445),(401,446),(402,447),(403,448),(404,449),(405,450),(406,421),(407,422),(408,423),(409,424),(410,425),(411,426),(412,427),(413,428),(414,429),(415,430),(416,431),(417,432),(418,433),(419,434),(420,435)], [(1,59),(2,60),(3,31),(4,32),(5,33),(6,34),(7,35),(8,36),(9,37),(10,38),(11,39),(12,40),(13,41),(14,42),(15,43),(16,44),(17,45),(18,46),(19,47),(20,48),(21,49),(22,50),(23,51),(24,52),(25,53),(26,54),(27,55),(28,56),(29,57),(30,58),(61,99),(62,100),(63,101),(64,102),(65,103),(66,104),(67,105),(68,106),(69,107),(70,108),(71,109),(72,110),(73,111),(74,112),(75,113),(76,114),(77,115),(78,116),(79,117),(80,118),(81,119),(82,120),(83,91),(84,92),(85,93),(86,94),(87,95),(88,96),(89,97),(90,98),(121,160),(122,161),(123,162),(124,163),(125,164),(126,165),(127,166),(128,167),(129,168),(130,169),(131,170),(132,171),(133,172),(134,173),(135,174),(136,175),(137,176),(138,177),(139,178),(140,179),(141,180),(142,151),(143,152),(144,153),(145,154),(146,155),(147,156),(148,157),(149,158),(150,159),(181,219),(182,220),(183,221),(184,222),(185,223),(186,224),(187,225),(188,226),(189,227),(190,228),(191,229),(192,230),(193,231),(194,232),(195,233),(196,234),(197,235),(198,236),(199,237),(200,238),(201,239),(202,240),(203,211),(204,212),(205,213),(206,214),(207,215),(208,216),(209,217),(210,218),(241,286),(242,287),(243,288),(244,289),(245,290),(246,291),(247,292),(248,293),(249,294),(250,295),(251,296),(252,297),(253,298),(254,299),(255,300),(256,271),(257,272),(258,273),(259,274),(260,275),(261,276),(262,277),(263,278),(264,279),(265,280),(266,281),(267,282),(268,283),(269,284),(270,285),(301,336),(302,337),(303,338),(304,339),(305,340),(306,341),(307,342),(308,343),(309,344),(310,345),(311,346),(312,347),(313,348),(314,349),(315,350),(316,351),(317,352),(318,353),(319,354),(320,355),(321,356),(322,357),(323,358),(324,359),(325,360),(326,331),(327,332),(328,333),(329,334),(330,335),(361,411),(362,412),(363,413),(364,414),(365,415),(366,416),(367,417),(368,418),(369,419),(370,420),(371,391),(372,392),(373,393),(374,394),(375,395),(376,396),(377,397),(378,398),(379,399),(380,400),(381,401),(382,402),(383,403),(384,404),(385,405),(386,406),(387,407),(388,408),(389,409),(390,410),(421,466),(422,467),(423,468),(424,469),(425,470),(426,471),(427,472),(428,473),(429,474),(430,475),(431,476),(432,477),(433,478),(434,479),(435,480),(436,451),(437,452),(438,453),(439,454),(440,455),(441,456),(442,457),(443,458),(444,459),(445,460),(446,461),(447,462),(448,463),(449,464),(450,465)], [(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)], [(1,436,16,421),(2,435,17,450),(3,434,18,449),(4,433,19,448),(5,432,20,447),(6,431,21,446),(7,430,22,445),(8,429,23,444),(9,428,24,443),(10,427,25,442),(11,426,26,441),(12,425,27,440),(13,424,28,439),(14,423,29,438),(15,422,30,437),(31,479,46,464),(32,478,47,463),(33,477,48,462),(34,476,49,461),(35,475,50,460),(36,474,51,459),(37,473,52,458),(38,472,53,457),(39,471,54,456),(40,470,55,455),(41,469,56,454),(42,468,57,453),(43,467,58,452),(44,466,59,451),(45,465,60,480),(61,370,76,385),(62,369,77,384),(63,368,78,383),(64,367,79,382),(65,366,80,381),(66,365,81,380),(67,364,82,379),(68,363,83,378),(69,362,84,377),(70,361,85,376),(71,390,86,375),(72,389,87,374),(73,388,88,373),(74,387,89,372),(75,386,90,371),(91,398,106,413),(92,397,107,412),(93,396,108,411),(94,395,109,410),(95,394,110,409),(96,393,111,408),(97,392,112,407),(98,391,113,406),(99,420,114,405),(100,419,115,404),(101,418,116,403),(102,417,117,402),(103,416,118,401),(104,415,119,400),(105,414,120,399),(121,317,136,302),(122,316,137,301),(123,315,138,330),(124,314,139,329),(125,313,140,328),(126,312,141,327),(127,311,142,326),(128,310,143,325),(129,309,144,324),(130,308,145,323),(131,307,146,322),(132,306,147,321),(133,305,148,320),(134,304,149,319),(135,303,150,318),(151,331,166,346),(152,360,167,345),(153,359,168,344),(154,358,169,343),(155,357,170,342),(156,356,171,341),(157,355,172,340),(158,354,173,339),(159,353,174,338),(160,352,175,337),(161,351,176,336),(162,350,177,335),(163,349,178,334),(164,348,179,333),(165,347,180,332),(181,250,196,265),(182,249,197,264),(183,248,198,263),(184,247,199,262),(185,246,200,261),(186,245,201,260),(187,244,202,259),(188,243,203,258),(189,242,204,257),(190,241,205,256),(191,270,206,255),(192,269,207,254),(193,268,208,253),(194,267,209,252),(195,266,210,251),(211,273,226,288),(212,272,227,287),(213,271,228,286),(214,300,229,285),(215,299,230,284),(216,298,231,283),(217,297,232,282),(218,296,233,281),(219,295,234,280),(220,294,235,279),(221,293,236,278),(222,292,237,277),(223,291,238,276),(224,290,239,275),(225,289,240,274)])

144 conjugacy classes

class 1 2A···2O 3 4A···4P5A5B6A···6O10A···10AD15A15B15C15D30A···30BH
order12···234···4556···610···101515151530···30
size11···1215···15222···22···222222···2

144 irreducible representations

dim1111222222222
type+++++-+-++-+
imageC1C2C2C4S3D5Dic3D6Dic5D10D15Dic15D30
kernelC23×Dic15C22×Dic15C23×C30C22×C30C23×C10C23×C6C22×C10C22×C10C22×C6C22×C6C24C23C23
# reps1141161287161443228

Matrix representation of C23×Dic15 in GL7(𝔽61)

1000000
06000000
00600000
0001000
0000100
0000010
0000001
,
60000000
06000000
00600000
00060000
00006000
0000010
0000001
,
60000000
06000000
00600000
00060000
00006000
00000600
00000060
,
1000000
0010000
060170000
00027000
00025200
0000050
000005049
,
60000000
049550000
034120000
000554700
0007600
000001213
000001749

G:=sub<GL(7,GF(61))| [1,0,0,0,0,0,0,0,60,0,0,0,0,0,0,0,60,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1],[60,0,0,0,0,0,0,0,60,0,0,0,0,0,0,0,60,0,0,0,0,0,0,0,60,0,0,0,0,0,0,0,60,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1],[60,0,0,0,0,0,0,0,60,0,0,0,0,0,0,0,60,0,0,0,0,0,0,0,60,0,0,0,0,0,0,0,60,0,0,0,0,0,0,0,60,0,0,0,0,0,0,0,60],[1,0,0,0,0,0,0,0,0,60,0,0,0,0,0,1,17,0,0,0,0,0,0,0,27,2,0,0,0,0,0,0,52,0,0,0,0,0,0,0,5,50,0,0,0,0,0,0,49],[60,0,0,0,0,0,0,0,49,34,0,0,0,0,0,55,12,0,0,0,0,0,0,0,55,7,0,0,0,0,0,47,6,0,0,0,0,0,0,0,12,17,0,0,0,0,0,13,49] >;

C23×Dic15 in GAP, Magma, Sage, TeX

C_2^3\times {\rm Dic}_{15}
% in TeX

G:=Group("C2^3xDic15");
// GroupNames label

G:=SmallGroup(480,1178);
// by ID

G=gap.SmallGroup(480,1178);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,112,2693,18822]);
// Polycyclic

G:=Group<a,b,c,d,e|a^2=b^2=c^2=d^30=1,e^2=d^15,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,b*c=c*b,b*d=d*b,b*e=e*b,c*d=d*c,c*e=e*c,e*d*e^-1=d^-1>;
// generators/relations

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