direct product, metacyclic, supersoluble, monomial, A-group, 2-hyperelementary
Aliases: C2×Dic61, C122⋊2C4, C22.D61, C2.2D122, C122.4C22, C61⋊3(C2×C4), (C2×C122).C2, SmallGroup(488,7)
Series: Derived ►Chief ►Lower central ►Upper central
| C61 — C2×Dic61 |
Generators and relations for C2×Dic61
G = < a,b,c | a2=b122=1, c2=b61, ab=ba, ac=ca, cbc-1=b-1 >
Smallest permutation representation of C2×Dic61
►Regular action on 488 points
Generators in S488
(1 164)(2 165)(3 166)(4 167)(5 168)(6 169)(7 170)(8 171)(9 172)(10 173)(11 174)(12 175)(13 176)(14 177)(15 178)(16 179)(17 180)(18 181)(19 182)(20 183)(21 184)(22 185)(23 186)(24 187)(25 188)(26 189)(27 190)(28 191)(29 192)(30 193)(31 194)(32 195)(33 196)(34 197)(35 198)(36 199)(37 200)(38 201)(39 202)(40 203)(41 204)(42 205)(43 206)(44 207)(45 208)(46 209)(47 210)(48 211)(49 212)(50 213)(51 214)(52 215)(53 216)(54 217)(55 218)(56 219)(57 220)(58 221)(59 222)(60 223)(61 224)(62 225)(63 226)(64 227)(65 228)(66 229)(67 230)(68 231)(69 232)(70 233)(71 234)(72 235)(73 236)(74 237)(75 238)(76 239)(77 240)(78 241)(79 242)(80 243)(81 244)(82 123)(83 124)(84 125)(85 126)(86 127)(87 128)(88 129)(89 130)(90 131)(91 132)(92 133)(93 134)(94 135)(95 136)(96 137)(97 138)(98 139)(99 140)(100 141)(101 142)(102 143)(103 144)(104 145)(105 146)(106 147)(107 148)(108 149)(109 150)(110 151)(111 152)(112 153)(113 154)(114 155)(115 156)(116 157)(117 158)(118 159)(119 160)(120 161)(121 162)(122 163)(245 367)(246 368)(247 369)(248 370)(249 371)(250 372)(251 373)(252 374)(253 375)(254 376)(255 377)(256 378)(257 379)(258 380)(259 381)(260 382)(261 383)(262 384)(263 385)(264 386)(265 387)(266 388)(267 389)(268 390)(269 391)(270 392)(271 393)(272 394)(273 395)(274 396)(275 397)(276 398)(277 399)(278 400)(279 401)(280 402)(281 403)(282 404)(283 405)(284 406)(285 407)(286 408)(287 409)(288 410)(289 411)(290 412)(291 413)(292 414)(293 415)(294 416)(295 417)(296 418)(297 419)(298 420)(299 421)(300 422)(301 423)(302 424)(303 425)(304 426)(305 427)(306 428)(307 429)(308 430)(309 431)(310 432)(311 433)(312 434)(313 435)(314 436)(315 437)(316 438)(317 439)(318 440)(319 441)(320 442)(321 443)(322 444)(323 445)(324 446)(325 447)(326 448)(327 449)(328 450)(329 451)(330 452)(331 453)(332 454)(333 455)(334 456)(335 457)(336 458)(337 459)(338 460)(339 461)(340 462)(341 463)(342 464)(343 465)(344 466)(345 467)(346 468)(347 469)(348 470)(349 471)(350 472)(351 473)(352 474)(353 475)(354 476)(355 477)(356 478)(357 479)(358 480)(359 481)(360 482)(361 483)(362 484)(363 485)(364 486)(365 487)(366 488)
(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)(367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488)
(1 306 62 245)(2 305 63 366)(3 304 64 365)(4 303 65 364)(5 302 66 363)(6 301 67 362)(7 300 68 361)(8 299 69 360)(9 298 70 359)(10 297 71 358)(11 296 72 357)(12 295 73 356)(13 294 74 355)(14 293 75 354)(15 292 76 353)(16 291 77 352)(17 290 78 351)(18 289 79 350)(19 288 80 349)(20 287 81 348)(21 286 82 347)(22 285 83 346)(23 284 84 345)(24 283 85 344)(25 282 86 343)(26 281 87 342)(27 280 88 341)(28 279 89 340)(29 278 90 339)(30 277 91 338)(31 276 92 337)(32 275 93 336)(33 274 94 335)(34 273 95 334)(35 272 96 333)(36 271 97 332)(37 270 98 331)(38 269 99 330)(39 268 100 329)(40 267 101 328)(41 266 102 327)(42 265 103 326)(43 264 104 325)(44 263 105 324)(45 262 106 323)(46 261 107 322)(47 260 108 321)(48 259 109 320)(49 258 110 319)(50 257 111 318)(51 256 112 317)(52 255 113 316)(53 254 114 315)(54 253 115 314)(55 252 116 313)(56 251 117 312)(57 250 118 311)(58 249 119 310)(59 248 120 309)(60 247 121 308)(61 246 122 307)(123 469 184 408)(124 468 185 407)(125 467 186 406)(126 466 187 405)(127 465 188 404)(128 464 189 403)(129 463 190 402)(130 462 191 401)(131 461 192 400)(132 460 193 399)(133 459 194 398)(134 458 195 397)(135 457 196 396)(136 456 197 395)(137 455 198 394)(138 454 199 393)(139 453 200 392)(140 452 201 391)(141 451 202 390)(142 450 203 389)(143 449 204 388)(144 448 205 387)(145 447 206 386)(146 446 207 385)(147 445 208 384)(148 444 209 383)(149 443 210 382)(150 442 211 381)(151 441 212 380)(152 440 213 379)(153 439 214 378)(154 438 215 377)(155 437 216 376)(156 436 217 375)(157 435 218 374)(158 434 219 373)(159 433 220 372)(160 432 221 371)(161 431 222 370)(162 430 223 369)(163 429 224 368)(164 428 225 367)(165 427 226 488)(166 426 227 487)(167 425 228 486)(168 424 229 485)(169 423 230 484)(170 422 231 483)(171 421 232 482)(172 420 233 481)(173 419 234 480)(174 418 235 479)(175 417 236 478)(176 416 237 477)(177 415 238 476)(178 414 239 475)(179 413 240 474)(180 412 241 473)(181 411 242 472)(182 410 243 471)(183 409 244 470)
G:=sub<Sym(488)| (1,164)(2,165)(3,166)(4,167)(5,168)(6,169)(7,170)(8,171)(9,172)(10,173)(11,174)(12,175)(13,176)(14,177)(15,178)(16,179)(17,180)(18,181)(19,182)(20,183)(21,184)(22,185)(23,186)(24,187)(25,188)(26,189)(27,190)(28,191)(29,192)(30,193)(31,194)(32,195)(33,196)(34,197)(35,198)(36,199)(37,200)(38,201)(39,202)(40,203)(41,204)(42,205)(43,206)(44,207)(45,208)(46,209)(47,210)(48,211)(49,212)(50,213)(51,214)(52,215)(53,216)(54,217)(55,218)(56,219)(57,220)(58,221)(59,222)(60,223)(61,224)(62,225)(63,226)(64,227)(65,228)(66,229)(67,230)(68,231)(69,232)(70,233)(71,234)(72,235)(73,236)(74,237)(75,238)(76,239)(77,240)(78,241)(79,242)(80,243)(81,244)(82,123)(83,124)(84,125)(85,126)(86,127)(87,128)(88,129)(89,130)(90,131)(91,132)(92,133)(93,134)(94,135)(95,136)(96,137)(97,138)(98,139)(99,140)(100,141)(101,142)(102,143)(103,144)(104,145)(105,146)(106,147)(107,148)(108,149)(109,150)(110,151)(111,152)(112,153)(113,154)(114,155)(115,156)(116,157)(117,158)(118,159)(119,160)(120,161)(121,162)(122,163)(245,367)(246,368)(247,369)(248,370)(249,371)(250,372)(251,373)(252,374)(253,375)(254,376)(255,377)(256,378)(257,379)(258,380)(259,381)(260,382)(261,383)(262,384)(263,385)(264,386)(265,387)(266,388)(267,389)(268,390)(269,391)(270,392)(271,393)(272,394)(273,395)(274,396)(275,397)(276,398)(277,399)(278,400)(279,401)(280,402)(281,403)(282,404)(283,405)(284,406)(285,407)(286,408)(287,409)(288,410)(289,411)(290,412)(291,413)(292,414)(293,415)(294,416)(295,417)(296,418)(297,419)(298,420)(299,421)(300,422)(301,423)(302,424)(303,425)(304,426)(305,427)(306,428)(307,429)(308,430)(309,431)(310,432)(311,433)(312,434)(313,435)(314,436)(315,437)(316,438)(317,439)(318,440)(319,441)(320,442)(321,443)(322,444)(323,445)(324,446)(325,447)(326,448)(327,449)(328,450)(329,451)(330,452)(331,453)(332,454)(333,455)(334,456)(335,457)(336,458)(337,459)(338,460)(339,461)(340,462)(341,463)(342,464)(343,465)(344,466)(345,467)(346,468)(347,469)(348,470)(349,471)(350,472)(351,473)(352,474)(353,475)(354,476)(355,477)(356,478)(357,479)(358,480)(359,481)(360,482)(361,483)(362,484)(363,485)(364,486)(365,487)(366,488), (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)(367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488), (1,306,62,245)(2,305,63,366)(3,304,64,365)(4,303,65,364)(5,302,66,363)(6,301,67,362)(7,300,68,361)(8,299,69,360)(9,298,70,359)(10,297,71,358)(11,296,72,357)(12,295,73,356)(13,294,74,355)(14,293,75,354)(15,292,76,353)(16,291,77,352)(17,290,78,351)(18,289,79,350)(19,288,80,349)(20,287,81,348)(21,286,82,347)(22,285,83,346)(23,284,84,345)(24,283,85,344)(25,282,86,343)(26,281,87,342)(27,280,88,341)(28,279,89,340)(29,278,90,339)(30,277,91,338)(31,276,92,337)(32,275,93,336)(33,274,94,335)(34,273,95,334)(35,272,96,333)(36,271,97,332)(37,270,98,331)(38,269,99,330)(39,268,100,329)(40,267,101,328)(41,266,102,327)(42,265,103,326)(43,264,104,325)(44,263,105,324)(45,262,106,323)(46,261,107,322)(47,260,108,321)(48,259,109,320)(49,258,110,319)(50,257,111,318)(51,256,112,317)(52,255,113,316)(53,254,114,315)(54,253,115,314)(55,252,116,313)(56,251,117,312)(57,250,118,311)(58,249,119,310)(59,248,120,309)(60,247,121,308)(61,246,122,307)(123,469,184,408)(124,468,185,407)(125,467,186,406)(126,466,187,405)(127,465,188,404)(128,464,189,403)(129,463,190,402)(130,462,191,401)(131,461,192,400)(132,460,193,399)(133,459,194,398)(134,458,195,397)(135,457,196,396)(136,456,197,395)(137,455,198,394)(138,454,199,393)(139,453,200,392)(140,452,201,391)(141,451,202,390)(142,450,203,389)(143,449,204,388)(144,448,205,387)(145,447,206,386)(146,446,207,385)(147,445,208,384)(148,444,209,383)(149,443,210,382)(150,442,211,381)(151,441,212,380)(152,440,213,379)(153,439,214,378)(154,438,215,377)(155,437,216,376)(156,436,217,375)(157,435,218,374)(158,434,219,373)(159,433,220,372)(160,432,221,371)(161,431,222,370)(162,430,223,369)(163,429,224,368)(164,428,225,367)(165,427,226,488)(166,426,227,487)(167,425,228,486)(168,424,229,485)(169,423,230,484)(170,422,231,483)(171,421,232,482)(172,420,233,481)(173,419,234,480)(174,418,235,479)(175,417,236,478)(176,416,237,477)(177,415,238,476)(178,414,239,475)(179,413,240,474)(180,412,241,473)(181,411,242,472)(182,410,243,471)(183,409,244,470)>;
G:=Group( (1,164)(2,165)(3,166)(4,167)(5,168)(6,169)(7,170)(8,171)(9,172)(10,173)(11,174)(12,175)(13,176)(14,177)(15,178)(16,179)(17,180)(18,181)(19,182)(20,183)(21,184)(22,185)(23,186)(24,187)(25,188)(26,189)(27,190)(28,191)(29,192)(30,193)(31,194)(32,195)(33,196)(34,197)(35,198)(36,199)(37,200)(38,201)(39,202)(40,203)(41,204)(42,205)(43,206)(44,207)(45,208)(46,209)(47,210)(48,211)(49,212)(50,213)(51,214)(52,215)(53,216)(54,217)(55,218)(56,219)(57,220)(58,221)(59,222)(60,223)(61,224)(62,225)(63,226)(64,227)(65,228)(66,229)(67,230)(68,231)(69,232)(70,233)(71,234)(72,235)(73,236)(74,237)(75,238)(76,239)(77,240)(78,241)(79,242)(80,243)(81,244)(82,123)(83,124)(84,125)(85,126)(86,127)(87,128)(88,129)(89,130)(90,131)(91,132)(92,133)(93,134)(94,135)(95,136)(96,137)(97,138)(98,139)(99,140)(100,141)(101,142)(102,143)(103,144)(104,145)(105,146)(106,147)(107,148)(108,149)(109,150)(110,151)(111,152)(112,153)(113,154)(114,155)(115,156)(116,157)(117,158)(118,159)(119,160)(120,161)(121,162)(122,163)(245,367)(246,368)(247,369)(248,370)(249,371)(250,372)(251,373)(252,374)(253,375)(254,376)(255,377)(256,378)(257,379)(258,380)(259,381)(260,382)(261,383)(262,384)(263,385)(264,386)(265,387)(266,388)(267,389)(268,390)(269,391)(270,392)(271,393)(272,394)(273,395)(274,396)(275,397)(276,398)(277,399)(278,400)(279,401)(280,402)(281,403)(282,404)(283,405)(284,406)(285,407)(286,408)(287,409)(288,410)(289,411)(290,412)(291,413)(292,414)(293,415)(294,416)(295,417)(296,418)(297,419)(298,420)(299,421)(300,422)(301,423)(302,424)(303,425)(304,426)(305,427)(306,428)(307,429)(308,430)(309,431)(310,432)(311,433)(312,434)(313,435)(314,436)(315,437)(316,438)(317,439)(318,440)(319,441)(320,442)(321,443)(322,444)(323,445)(324,446)(325,447)(326,448)(327,449)(328,450)(329,451)(330,452)(331,453)(332,454)(333,455)(334,456)(335,457)(336,458)(337,459)(338,460)(339,461)(340,462)(341,463)(342,464)(343,465)(344,466)(345,467)(346,468)(347,469)(348,470)(349,471)(350,472)(351,473)(352,474)(353,475)(354,476)(355,477)(356,478)(357,479)(358,480)(359,481)(360,482)(361,483)(362,484)(363,485)(364,486)(365,487)(366,488), (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)(367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488), (1,306,62,245)(2,305,63,366)(3,304,64,365)(4,303,65,364)(5,302,66,363)(6,301,67,362)(7,300,68,361)(8,299,69,360)(9,298,70,359)(10,297,71,358)(11,296,72,357)(12,295,73,356)(13,294,74,355)(14,293,75,354)(15,292,76,353)(16,291,77,352)(17,290,78,351)(18,289,79,350)(19,288,80,349)(20,287,81,348)(21,286,82,347)(22,285,83,346)(23,284,84,345)(24,283,85,344)(25,282,86,343)(26,281,87,342)(27,280,88,341)(28,279,89,340)(29,278,90,339)(30,277,91,338)(31,276,92,337)(32,275,93,336)(33,274,94,335)(34,273,95,334)(35,272,96,333)(36,271,97,332)(37,270,98,331)(38,269,99,330)(39,268,100,329)(40,267,101,328)(41,266,102,327)(42,265,103,326)(43,264,104,325)(44,263,105,324)(45,262,106,323)(46,261,107,322)(47,260,108,321)(48,259,109,320)(49,258,110,319)(50,257,111,318)(51,256,112,317)(52,255,113,316)(53,254,114,315)(54,253,115,314)(55,252,116,313)(56,251,117,312)(57,250,118,311)(58,249,119,310)(59,248,120,309)(60,247,121,308)(61,246,122,307)(123,469,184,408)(124,468,185,407)(125,467,186,406)(126,466,187,405)(127,465,188,404)(128,464,189,403)(129,463,190,402)(130,462,191,401)(131,461,192,400)(132,460,193,399)(133,459,194,398)(134,458,195,397)(135,457,196,396)(136,456,197,395)(137,455,198,394)(138,454,199,393)(139,453,200,392)(140,452,201,391)(141,451,202,390)(142,450,203,389)(143,449,204,388)(144,448,205,387)(145,447,206,386)(146,446,207,385)(147,445,208,384)(148,444,209,383)(149,443,210,382)(150,442,211,381)(151,441,212,380)(152,440,213,379)(153,439,214,378)(154,438,215,377)(155,437,216,376)(156,436,217,375)(157,435,218,374)(158,434,219,373)(159,433,220,372)(160,432,221,371)(161,431,222,370)(162,430,223,369)(163,429,224,368)(164,428,225,367)(165,427,226,488)(166,426,227,487)(167,425,228,486)(168,424,229,485)(169,423,230,484)(170,422,231,483)(171,421,232,482)(172,420,233,481)(173,419,234,480)(174,418,235,479)(175,417,236,478)(176,416,237,477)(177,415,238,476)(178,414,239,475)(179,413,240,474)(180,412,241,473)(181,411,242,472)(182,410,243,471)(183,409,244,470) );
G=PermutationGroup([[(1,164),(2,165),(3,166),(4,167),(5,168),(6,169),(7,170),(8,171),(9,172),(10,173),(11,174),(12,175),(13,176),(14,177),(15,178),(16,179),(17,180),(18,181),(19,182),(20,183),(21,184),(22,185),(23,186),(24,187),(25,188),(26,189),(27,190),(28,191),(29,192),(30,193),(31,194),(32,195),(33,196),(34,197),(35,198),(36,199),(37,200),(38,201),(39,202),(40,203),(41,204),(42,205),(43,206),(44,207),(45,208),(46,209),(47,210),(48,211),(49,212),(50,213),(51,214),(52,215),(53,216),(54,217),(55,218),(56,219),(57,220),(58,221),(59,222),(60,223),(61,224),(62,225),(63,226),(64,227),(65,228),(66,229),(67,230),(68,231),(69,232),(70,233),(71,234),(72,235),(73,236),(74,237),(75,238),(76,239),(77,240),(78,241),(79,242),(80,243),(81,244),(82,123),(83,124),(84,125),(85,126),(86,127),(87,128),(88,129),(89,130),(90,131),(91,132),(92,133),(93,134),(94,135),(95,136),(96,137),(97,138),(98,139),(99,140),(100,141),(101,142),(102,143),(103,144),(104,145),(105,146),(106,147),(107,148),(108,149),(109,150),(110,151),(111,152),(112,153),(113,154),(114,155),(115,156),(116,157),(117,158),(118,159),(119,160),(120,161),(121,162),(122,163),(245,367),(246,368),(247,369),(248,370),(249,371),(250,372),(251,373),(252,374),(253,375),(254,376),(255,377),(256,378),(257,379),(258,380),(259,381),(260,382),(261,383),(262,384),(263,385),(264,386),(265,387),(266,388),(267,389),(268,390),(269,391),(270,392),(271,393),(272,394),(273,395),(274,396),(275,397),(276,398),(277,399),(278,400),(279,401),(280,402),(281,403),(282,404),(283,405),(284,406),(285,407),(286,408),(287,409),(288,410),(289,411),(290,412),(291,413),(292,414),(293,415),(294,416),(295,417),(296,418),(297,419),(298,420),(299,421),(300,422),(301,423),(302,424),(303,425),(304,426),(305,427),(306,428),(307,429),(308,430),(309,431),(310,432),(311,433),(312,434),(313,435),(314,436),(315,437),(316,438),(317,439),(318,440),(319,441),(320,442),(321,443),(322,444),(323,445),(324,446),(325,447),(326,448),(327,449),(328,450),(329,451),(330,452),(331,453),(332,454),(333,455),(334,456),(335,457),(336,458),(337,459),(338,460),(339,461),(340,462),(341,463),(342,464),(343,465),(344,466),(345,467),(346,468),(347,469),(348,470),(349,471),(350,472),(351,473),(352,474),(353,475),(354,476),(355,477),(356,478),(357,479),(358,480),(359,481),(360,482),(361,483),(362,484),(363,485),(364,486),(365,487),(366,488)], [(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),(367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488)], [(1,306,62,245),(2,305,63,366),(3,304,64,365),(4,303,65,364),(5,302,66,363),(6,301,67,362),(7,300,68,361),(8,299,69,360),(9,298,70,359),(10,297,71,358),(11,296,72,357),(12,295,73,356),(13,294,74,355),(14,293,75,354),(15,292,76,353),(16,291,77,352),(17,290,78,351),(18,289,79,350),(19,288,80,349),(20,287,81,348),(21,286,82,347),(22,285,83,346),(23,284,84,345),(24,283,85,344),(25,282,86,343),(26,281,87,342),(27,280,88,341),(28,279,89,340),(29,278,90,339),(30,277,91,338),(31,276,92,337),(32,275,93,336),(33,274,94,335),(34,273,95,334),(35,272,96,333),(36,271,97,332),(37,270,98,331),(38,269,99,330),(39,268,100,329),(40,267,101,328),(41,266,102,327),(42,265,103,326),(43,264,104,325),(44,263,105,324),(45,262,106,323),(46,261,107,322),(47,260,108,321),(48,259,109,320),(49,258,110,319),(50,257,111,318),(51,256,112,317),(52,255,113,316),(53,254,114,315),(54,253,115,314),(55,252,116,313),(56,251,117,312),(57,250,118,311),(58,249,119,310),(59,248,120,309),(60,247,121,308),(61,246,122,307),(123,469,184,408),(124,468,185,407),(125,467,186,406),(126,466,187,405),(127,465,188,404),(128,464,189,403),(129,463,190,402),(130,462,191,401),(131,461,192,400),(132,460,193,399),(133,459,194,398),(134,458,195,397),(135,457,196,396),(136,456,197,395),(137,455,198,394),(138,454,199,393),(139,453,200,392),(140,452,201,391),(141,451,202,390),(142,450,203,389),(143,449,204,388),(144,448,205,387),(145,447,206,386),(146,446,207,385),(147,445,208,384),(148,444,209,383),(149,443,210,382),(150,442,211,381),(151,441,212,380),(152,440,213,379),(153,439,214,378),(154,438,215,377),(155,437,216,376),(156,436,217,375),(157,435,218,374),(158,434,219,373),(159,433,220,372),(160,432,221,371),(161,431,222,370),(162,430,223,369),(163,429,224,368),(164,428,225,367),(165,427,226,488),(166,426,227,487),(167,425,228,486),(168,424,229,485),(169,423,230,484),(170,422,231,483),(171,421,232,482),(172,420,233,481),(173,419,234,480),(174,418,235,479),(175,417,236,478),(176,416,237,477),(177,415,238,476),(178,414,239,475),(179,413,240,474),(180,412,241,473),(181,411,242,472),(182,410,243,471),(183,409,244,470)]])
128 conjugacy classes
| class | 1 | 2A | 2B | 2C | 4A | 4B | 4C | 4D | 61A | ··· | 61AD | 122A | ··· | 122CL |
| order | 1 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 61 | ··· | 61 | 122 | ··· | 122 |
| size | 1 | 1 | 1 | 1 | 61 | 61 | 61 | 61 | 2 | ··· | 2 | 2 | ··· | 2 |
128 irreducible representations
| dim | 1 | 1 | 1 | 1 | 2 | 2 | 2 |
| type | + | + | + | + | - | + | |
| image | C1 | C2 | C2 | C4 | D61 | Dic61 | D122 |
| kernel | C2×Dic61 | Dic61 | C2×C122 | C122 | C22 | C2 | C2 |
| # reps | 1 | 2 | 1 | 4 | 30 | 60 | 30 |
Matrix representation of C2×Dic61 ►in GL3(𝔽733) generated by
| 732 | 0 | 0 |
| 0 | 732 | 0 |
| 0 | 0 | 732 |
| 1 | 0 | 0 |
| 0 | 0 | 732 |
| 0 | 1 | 562 |
| 732 | 0 | 0 |
| 0 | 361 | 594 |
| 0 | 20 | 372 |
G:=sub<GL(3,GF(733))| [732,0,0,0,732,0,0,0,732],[1,0,0,0,0,1,0,732,562],[732,0,0,0,361,20,0,594,372] >;
C2×Dic61 in GAP, Magma, Sage, TeX
C_2\times {\rm Dic}_{61} % in TeX
G:=Group("C2xDic61"); // GroupNames label
G:=SmallGroup(488,7);
// by ID
G=gap.SmallGroup(488,7);
# by ID
G:=PCGroup([4,-2,-2,-2,-61,16,7683]);
// Polycyclic
G:=Group<a,b,c|a^2=b^122=1,c^2=b^61,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations
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