direct product, abelian, monomial, 2-elementary
Aliases: C22×C116, SmallGroup(464,45)
Series: Derived ►Chief ►Lower central ►Upper central
| C1 — C22×C116 |
| C1 — C22×C116 |
| C1 — C22×C116 |
Generators and relations for C22×C116
G = < a,b,c | a2=b2=c116=1, ab=ba, ac=ca, bc=cb >
Subgroups: 54, all normal (8 characteristic)
C1, C2, C2, C4, C22, C2×C4, C23, C22×C4, C29, C58, C58, C116, C2×C58, C2×C116, C22×C58, C22×C116
Quotients: C1, C2, C4, C22, C2×C4, C23, C22×C4, C29, C58, C116, C2×C58, C2×C116, C22×C58, C22×C116
►Regular action on 464 points
Generators in S464
(1 401)(2 402)(3 403)(4 404)(5 405)(6 406)(7 407)(8 408)(9 409)(10 410)(11 411)(12 412)(13 413)(14 414)(15 415)(16 416)(17 417)(18 418)(19 419)(20 420)(21 421)(22 422)(23 423)(24 424)(25 425)(26 426)(27 427)(28 428)(29 429)(30 430)(31 431)(32 432)(33 433)(34 434)(35 435)(36 436)(37 437)(38 438)(39 439)(40 440)(41 441)(42 442)(43 443)(44 444)(45 445)(46 446)(47 447)(48 448)(49 449)(50 450)(51 451)(52 452)(53 453)(54 454)(55 455)(56 456)(57 457)(58 458)(59 459)(60 460)(61 461)(62 462)(63 463)(64 464)(65 349)(66 350)(67 351)(68 352)(69 353)(70 354)(71 355)(72 356)(73 357)(74 358)(75 359)(76 360)(77 361)(78 362)(79 363)(80 364)(81 365)(82 366)(83 367)(84 368)(85 369)(86 370)(87 371)(88 372)(89 373)(90 374)(91 375)(92 376)(93 377)(94 378)(95 379)(96 380)(97 381)(98 382)(99 383)(100 384)(101 385)(102 386)(103 387)(104 388)(105 389)(106 390)(107 391)(108 392)(109 393)(110 394)(111 395)(112 396)(113 397)(114 398)(115 399)(116 400)(117 284)(118 285)(119 286)(120 287)(121 288)(122 289)(123 290)(124 291)(125 292)(126 293)(127 294)(128 295)(129 296)(130 297)(131 298)(132 299)(133 300)(134 301)(135 302)(136 303)(137 304)(138 305)(139 306)(140 307)(141 308)(142 309)(143 310)(144 311)(145 312)(146 313)(147 314)(148 315)(149 316)(150 317)(151 318)(152 319)(153 320)(154 321)(155 322)(156 323)(157 324)(158 325)(159 326)(160 327)(161 328)(162 329)(163 330)(164 331)(165 332)(166 333)(167 334)(168 335)(169 336)(170 337)(171 338)(172 339)(173 340)(174 341)(175 342)(176 343)(177 344)(178 345)(179 346)(180 347)(181 348)(182 233)(183 234)(184 235)(185 236)(186 237)(187 238)(188 239)(189 240)(190 241)(191 242)(192 243)(193 244)(194 245)(195 246)(196 247)(197 248)(198 249)(199 250)(200 251)(201 252)(202 253)(203 254)(204 255)(205 256)(206 257)(207 258)(208 259)(209 260)(210 261)(211 262)(212 263)(213 264)(214 265)(215 266)(216 267)(217 268)(218 269)(219 270)(220 271)(221 272)(222 273)(223 274)(224 275)(225 276)(226 277)(227 278)(228 279)(229 280)(230 281)(231 282)(232 283)
(1 173)(2 174)(3 175)(4 176)(5 177)(6 178)(7 179)(8 180)(9 181)(10 182)(11 183)(12 184)(13 185)(14 186)(15 187)(16 188)(17 189)(18 190)(19 191)(20 192)(21 193)(22 194)(23 195)(24 196)(25 197)(26 198)(27 199)(28 200)(29 201)(30 202)(31 203)(32 204)(33 205)(34 206)(35 207)(36 208)(37 209)(38 210)(39 211)(40 212)(41 213)(42 214)(43 215)(44 216)(45 217)(46 218)(47 219)(48 220)(49 221)(50 222)(51 223)(52 224)(53 225)(54 226)(55 227)(56 228)(57 229)(58 230)(59 231)(60 232)(61 117)(62 118)(63 119)(64 120)(65 121)(66 122)(67 123)(68 124)(69 125)(70 126)(71 127)(72 128)(73 129)(74 130)(75 131)(76 132)(77 133)(78 134)(79 135)(80 136)(81 137)(82 138)(83 139)(84 140)(85 141)(86 142)(87 143)(88 144)(89 145)(90 146)(91 147)(92 148)(93 149)(94 150)(95 151)(96 152)(97 153)(98 154)(99 155)(100 156)(101 157)(102 158)(103 159)(104 160)(105 161)(106 162)(107 163)(108 164)(109 165)(110 166)(111 167)(112 168)(113 169)(114 170)(115 171)(116 172)(233 410)(234 411)(235 412)(236 413)(237 414)(238 415)(239 416)(240 417)(241 418)(242 419)(243 420)(244 421)(245 422)(246 423)(247 424)(248 425)(249 426)(250 427)(251 428)(252 429)(253 430)(254 431)(255 432)(256 433)(257 434)(258 435)(259 436)(260 437)(261 438)(262 439)(263 440)(264 441)(265 442)(266 443)(267 444)(268 445)(269 446)(270 447)(271 448)(272 449)(273 450)(274 451)(275 452)(276 453)(277 454)(278 455)(279 456)(280 457)(281 458)(282 459)(283 460)(284 461)(285 462)(286 463)(287 464)(288 349)(289 350)(290 351)(291 352)(292 353)(293 354)(294 355)(295 356)(296 357)(297 358)(298 359)(299 360)(300 361)(301 362)(302 363)(303 364)(304 365)(305 366)(306 367)(307 368)(308 369)(309 370)(310 371)(311 372)(312 373)(313 374)(314 375)(315 376)(316 377)(317 378)(318 379)(319 380)(320 381)(321 382)(322 383)(323 384)(324 385)(325 386)(326 387)(327 388)(328 389)(329 390)(330 391)(331 392)(332 393)(333 394)(334 395)(335 396)(336 397)(337 398)(338 399)(339 400)(340 401)(341 402)(342 403)(343 404)(344 405)(345 406)(346 407)(347 408)(348 409)
(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)
G:=sub<Sym(464)| (1,401)(2,402)(3,403)(4,404)(5,405)(6,406)(7,407)(8,408)(9,409)(10,410)(11,411)(12,412)(13,413)(14,414)(15,415)(16,416)(17,417)(18,418)(19,419)(20,420)(21,421)(22,422)(23,423)(24,424)(25,425)(26,426)(27,427)(28,428)(29,429)(30,430)(31,431)(32,432)(33,433)(34,434)(35,435)(36,436)(37,437)(38,438)(39,439)(40,440)(41,441)(42,442)(43,443)(44,444)(45,445)(46,446)(47,447)(48,448)(49,449)(50,450)(51,451)(52,452)(53,453)(54,454)(55,455)(56,456)(57,457)(58,458)(59,459)(60,460)(61,461)(62,462)(63,463)(64,464)(65,349)(66,350)(67,351)(68,352)(69,353)(70,354)(71,355)(72,356)(73,357)(74,358)(75,359)(76,360)(77,361)(78,362)(79,363)(80,364)(81,365)(82,366)(83,367)(84,368)(85,369)(86,370)(87,371)(88,372)(89,373)(90,374)(91,375)(92,376)(93,377)(94,378)(95,379)(96,380)(97,381)(98,382)(99,383)(100,384)(101,385)(102,386)(103,387)(104,388)(105,389)(106,390)(107,391)(108,392)(109,393)(110,394)(111,395)(112,396)(113,397)(114,398)(115,399)(116,400)(117,284)(118,285)(119,286)(120,287)(121,288)(122,289)(123,290)(124,291)(125,292)(126,293)(127,294)(128,295)(129,296)(130,297)(131,298)(132,299)(133,300)(134,301)(135,302)(136,303)(137,304)(138,305)(139,306)(140,307)(141,308)(142,309)(143,310)(144,311)(145,312)(146,313)(147,314)(148,315)(149,316)(150,317)(151,318)(152,319)(153,320)(154,321)(155,322)(156,323)(157,324)(158,325)(159,326)(160,327)(161,328)(162,329)(163,330)(164,331)(165,332)(166,333)(167,334)(168,335)(169,336)(170,337)(171,338)(172,339)(173,340)(174,341)(175,342)(176,343)(177,344)(178,345)(179,346)(180,347)(181,348)(182,233)(183,234)(184,235)(185,236)(186,237)(187,238)(188,239)(189,240)(190,241)(191,242)(192,243)(193,244)(194,245)(195,246)(196,247)(197,248)(198,249)(199,250)(200,251)(201,252)(202,253)(203,254)(204,255)(205,256)(206,257)(207,258)(208,259)(209,260)(210,261)(211,262)(212,263)(213,264)(214,265)(215,266)(216,267)(217,268)(218,269)(219,270)(220,271)(221,272)(222,273)(223,274)(224,275)(225,276)(226,277)(227,278)(228,279)(229,280)(230,281)(231,282)(232,283), (1,173)(2,174)(3,175)(4,176)(5,177)(6,178)(7,179)(8,180)(9,181)(10,182)(11,183)(12,184)(13,185)(14,186)(15,187)(16,188)(17,189)(18,190)(19,191)(20,192)(21,193)(22,194)(23,195)(24,196)(25,197)(26,198)(27,199)(28,200)(29,201)(30,202)(31,203)(32,204)(33,205)(34,206)(35,207)(36,208)(37,209)(38,210)(39,211)(40,212)(41,213)(42,214)(43,215)(44,216)(45,217)(46,218)(47,219)(48,220)(49,221)(50,222)(51,223)(52,224)(53,225)(54,226)(55,227)(56,228)(57,229)(58,230)(59,231)(60,232)(61,117)(62,118)(63,119)(64,120)(65,121)(66,122)(67,123)(68,124)(69,125)(70,126)(71,127)(72,128)(73,129)(74,130)(75,131)(76,132)(77,133)(78,134)(79,135)(80,136)(81,137)(82,138)(83,139)(84,140)(85,141)(86,142)(87,143)(88,144)(89,145)(90,146)(91,147)(92,148)(93,149)(94,150)(95,151)(96,152)(97,153)(98,154)(99,155)(100,156)(101,157)(102,158)(103,159)(104,160)(105,161)(106,162)(107,163)(108,164)(109,165)(110,166)(111,167)(112,168)(113,169)(114,170)(115,171)(116,172)(233,410)(234,411)(235,412)(236,413)(237,414)(238,415)(239,416)(240,417)(241,418)(242,419)(243,420)(244,421)(245,422)(246,423)(247,424)(248,425)(249,426)(250,427)(251,428)(252,429)(253,430)(254,431)(255,432)(256,433)(257,434)(258,435)(259,436)(260,437)(261,438)(262,439)(263,440)(264,441)(265,442)(266,443)(267,444)(268,445)(269,446)(270,447)(271,448)(272,449)(273,450)(274,451)(275,452)(276,453)(277,454)(278,455)(279,456)(280,457)(281,458)(282,459)(283,460)(284,461)(285,462)(286,463)(287,464)(288,349)(289,350)(290,351)(291,352)(292,353)(293,354)(294,355)(295,356)(296,357)(297,358)(298,359)(299,360)(300,361)(301,362)(302,363)(303,364)(304,365)(305,366)(306,367)(307,368)(308,369)(309,370)(310,371)(311,372)(312,373)(313,374)(314,375)(315,376)(316,377)(317,378)(318,379)(319,380)(320,381)(321,382)(322,383)(323,384)(324,385)(325,386)(326,387)(327,388)(328,389)(329,390)(330,391)(331,392)(332,393)(333,394)(334,395)(335,396)(336,397)(337,398)(338,399)(339,400)(340,401)(341,402)(342,403)(343,404)(344,405)(345,406)(346,407)(347,408)(348,409), (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)>;
G:=Group( (1,401)(2,402)(3,403)(4,404)(5,405)(6,406)(7,407)(8,408)(9,409)(10,410)(11,411)(12,412)(13,413)(14,414)(15,415)(16,416)(17,417)(18,418)(19,419)(20,420)(21,421)(22,422)(23,423)(24,424)(25,425)(26,426)(27,427)(28,428)(29,429)(30,430)(31,431)(32,432)(33,433)(34,434)(35,435)(36,436)(37,437)(38,438)(39,439)(40,440)(41,441)(42,442)(43,443)(44,444)(45,445)(46,446)(47,447)(48,448)(49,449)(50,450)(51,451)(52,452)(53,453)(54,454)(55,455)(56,456)(57,457)(58,458)(59,459)(60,460)(61,461)(62,462)(63,463)(64,464)(65,349)(66,350)(67,351)(68,352)(69,353)(70,354)(71,355)(72,356)(73,357)(74,358)(75,359)(76,360)(77,361)(78,362)(79,363)(80,364)(81,365)(82,366)(83,367)(84,368)(85,369)(86,370)(87,371)(88,372)(89,373)(90,374)(91,375)(92,376)(93,377)(94,378)(95,379)(96,380)(97,381)(98,382)(99,383)(100,384)(101,385)(102,386)(103,387)(104,388)(105,389)(106,390)(107,391)(108,392)(109,393)(110,394)(111,395)(112,396)(113,397)(114,398)(115,399)(116,400)(117,284)(118,285)(119,286)(120,287)(121,288)(122,289)(123,290)(124,291)(125,292)(126,293)(127,294)(128,295)(129,296)(130,297)(131,298)(132,299)(133,300)(134,301)(135,302)(136,303)(137,304)(138,305)(139,306)(140,307)(141,308)(142,309)(143,310)(144,311)(145,312)(146,313)(147,314)(148,315)(149,316)(150,317)(151,318)(152,319)(153,320)(154,321)(155,322)(156,323)(157,324)(158,325)(159,326)(160,327)(161,328)(162,329)(163,330)(164,331)(165,332)(166,333)(167,334)(168,335)(169,336)(170,337)(171,338)(172,339)(173,340)(174,341)(175,342)(176,343)(177,344)(178,345)(179,346)(180,347)(181,348)(182,233)(183,234)(184,235)(185,236)(186,237)(187,238)(188,239)(189,240)(190,241)(191,242)(192,243)(193,244)(194,245)(195,246)(196,247)(197,248)(198,249)(199,250)(200,251)(201,252)(202,253)(203,254)(204,255)(205,256)(206,257)(207,258)(208,259)(209,260)(210,261)(211,262)(212,263)(213,264)(214,265)(215,266)(216,267)(217,268)(218,269)(219,270)(220,271)(221,272)(222,273)(223,274)(224,275)(225,276)(226,277)(227,278)(228,279)(229,280)(230,281)(231,282)(232,283), (1,173)(2,174)(3,175)(4,176)(5,177)(6,178)(7,179)(8,180)(9,181)(10,182)(11,183)(12,184)(13,185)(14,186)(15,187)(16,188)(17,189)(18,190)(19,191)(20,192)(21,193)(22,194)(23,195)(24,196)(25,197)(26,198)(27,199)(28,200)(29,201)(30,202)(31,203)(32,204)(33,205)(34,206)(35,207)(36,208)(37,209)(38,210)(39,211)(40,212)(41,213)(42,214)(43,215)(44,216)(45,217)(46,218)(47,219)(48,220)(49,221)(50,222)(51,223)(52,224)(53,225)(54,226)(55,227)(56,228)(57,229)(58,230)(59,231)(60,232)(61,117)(62,118)(63,119)(64,120)(65,121)(66,122)(67,123)(68,124)(69,125)(70,126)(71,127)(72,128)(73,129)(74,130)(75,131)(76,132)(77,133)(78,134)(79,135)(80,136)(81,137)(82,138)(83,139)(84,140)(85,141)(86,142)(87,143)(88,144)(89,145)(90,146)(91,147)(92,148)(93,149)(94,150)(95,151)(96,152)(97,153)(98,154)(99,155)(100,156)(101,157)(102,158)(103,159)(104,160)(105,161)(106,162)(107,163)(108,164)(109,165)(110,166)(111,167)(112,168)(113,169)(114,170)(115,171)(116,172)(233,410)(234,411)(235,412)(236,413)(237,414)(238,415)(239,416)(240,417)(241,418)(242,419)(243,420)(244,421)(245,422)(246,423)(247,424)(248,425)(249,426)(250,427)(251,428)(252,429)(253,430)(254,431)(255,432)(256,433)(257,434)(258,435)(259,436)(260,437)(261,438)(262,439)(263,440)(264,441)(265,442)(266,443)(267,444)(268,445)(269,446)(270,447)(271,448)(272,449)(273,450)(274,451)(275,452)(276,453)(277,454)(278,455)(279,456)(280,457)(281,458)(282,459)(283,460)(284,461)(285,462)(286,463)(287,464)(288,349)(289,350)(290,351)(291,352)(292,353)(293,354)(294,355)(295,356)(296,357)(297,358)(298,359)(299,360)(300,361)(301,362)(302,363)(303,364)(304,365)(305,366)(306,367)(307,368)(308,369)(309,370)(310,371)(311,372)(312,373)(313,374)(314,375)(315,376)(316,377)(317,378)(318,379)(319,380)(320,381)(321,382)(322,383)(323,384)(324,385)(325,386)(326,387)(327,388)(328,389)(329,390)(330,391)(331,392)(332,393)(333,394)(334,395)(335,396)(336,397)(337,398)(338,399)(339,400)(340,401)(341,402)(342,403)(343,404)(344,405)(345,406)(346,407)(347,408)(348,409), (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) );
G=PermutationGroup([[(1,401),(2,402),(3,403),(4,404),(5,405),(6,406),(7,407),(8,408),(9,409),(10,410),(11,411),(12,412),(13,413),(14,414),(15,415),(16,416),(17,417),(18,418),(19,419),(20,420),(21,421),(22,422),(23,423),(24,424),(25,425),(26,426),(27,427),(28,428),(29,429),(30,430),(31,431),(32,432),(33,433),(34,434),(35,435),(36,436),(37,437),(38,438),(39,439),(40,440),(41,441),(42,442),(43,443),(44,444),(45,445),(46,446),(47,447),(48,448),(49,449),(50,450),(51,451),(52,452),(53,453),(54,454),(55,455),(56,456),(57,457),(58,458),(59,459),(60,460),(61,461),(62,462),(63,463),(64,464),(65,349),(66,350),(67,351),(68,352),(69,353),(70,354),(71,355),(72,356),(73,357),(74,358),(75,359),(76,360),(77,361),(78,362),(79,363),(80,364),(81,365),(82,366),(83,367),(84,368),(85,369),(86,370),(87,371),(88,372),(89,373),(90,374),(91,375),(92,376),(93,377),(94,378),(95,379),(96,380),(97,381),(98,382),(99,383),(100,384),(101,385),(102,386),(103,387),(104,388),(105,389),(106,390),(107,391),(108,392),(109,393),(110,394),(111,395),(112,396),(113,397),(114,398),(115,399),(116,400),(117,284),(118,285),(119,286),(120,287),(121,288),(122,289),(123,290),(124,291),(125,292),(126,293),(127,294),(128,295),(129,296),(130,297),(131,298),(132,299),(133,300),(134,301),(135,302),(136,303),(137,304),(138,305),(139,306),(140,307),(141,308),(142,309),(143,310),(144,311),(145,312),(146,313),(147,314),(148,315),(149,316),(150,317),(151,318),(152,319),(153,320),(154,321),(155,322),(156,323),(157,324),(158,325),(159,326),(160,327),(161,328),(162,329),(163,330),(164,331),(165,332),(166,333),(167,334),(168,335),(169,336),(170,337),(171,338),(172,339),(173,340),(174,341),(175,342),(176,343),(177,344),(178,345),(179,346),(180,347),(181,348),(182,233),(183,234),(184,235),(185,236),(186,237),(187,238),(188,239),(189,240),(190,241),(191,242),(192,243),(193,244),(194,245),(195,246),(196,247),(197,248),(198,249),(199,250),(200,251),(201,252),(202,253),(203,254),(204,255),(205,256),(206,257),(207,258),(208,259),(209,260),(210,261),(211,262),(212,263),(213,264),(214,265),(215,266),(216,267),(217,268),(218,269),(219,270),(220,271),(221,272),(222,273),(223,274),(224,275),(225,276),(226,277),(227,278),(228,279),(229,280),(230,281),(231,282),(232,283)], [(1,173),(2,174),(3,175),(4,176),(5,177),(6,178),(7,179),(8,180),(9,181),(10,182),(11,183),(12,184),(13,185),(14,186),(15,187),(16,188),(17,189),(18,190),(19,191),(20,192),(21,193),(22,194),(23,195),(24,196),(25,197),(26,198),(27,199),(28,200),(29,201),(30,202),(31,203),(32,204),(33,205),(34,206),(35,207),(36,208),(37,209),(38,210),(39,211),(40,212),(41,213),(42,214),(43,215),(44,216),(45,217),(46,218),(47,219),(48,220),(49,221),(50,222),(51,223),(52,224),(53,225),(54,226),(55,227),(56,228),(57,229),(58,230),(59,231),(60,232),(61,117),(62,118),(63,119),(64,120),(65,121),(66,122),(67,123),(68,124),(69,125),(70,126),(71,127),(72,128),(73,129),(74,130),(75,131),(76,132),(77,133),(78,134),(79,135),(80,136),(81,137),(82,138),(83,139),(84,140),(85,141),(86,142),(87,143),(88,144),(89,145),(90,146),(91,147),(92,148),(93,149),(94,150),(95,151),(96,152),(97,153),(98,154),(99,155),(100,156),(101,157),(102,158),(103,159),(104,160),(105,161),(106,162),(107,163),(108,164),(109,165),(110,166),(111,167),(112,168),(113,169),(114,170),(115,171),(116,172),(233,410),(234,411),(235,412),(236,413),(237,414),(238,415),(239,416),(240,417),(241,418),(242,419),(243,420),(244,421),(245,422),(246,423),(247,424),(248,425),(249,426),(250,427),(251,428),(252,429),(253,430),(254,431),(255,432),(256,433),(257,434),(258,435),(259,436),(260,437),(261,438),(262,439),(263,440),(264,441),(265,442),(266,443),(267,444),(268,445),(269,446),(270,447),(271,448),(272,449),(273,450),(274,451),(275,452),(276,453),(277,454),(278,455),(279,456),(280,457),(281,458),(282,459),(283,460),(284,461),(285,462),(286,463),(287,464),(288,349),(289,350),(290,351),(291,352),(292,353),(293,354),(294,355),(295,356),(296,357),(297,358),(298,359),(299,360),(300,361),(301,362),(302,363),(303,364),(304,365),(305,366),(306,367),(307,368),(308,369),(309,370),(310,371),(311,372),(312,373),(313,374),(314,375),(315,376),(316,377),(317,378),(318,379),(319,380),(320,381),(321,382),(322,383),(323,384),(324,385),(325,386),(326,387),(327,388),(328,389),(329,390),(330,391),(331,392),(332,393),(333,394),(334,395),(335,396),(336,397),(337,398),(338,399),(339,400),(340,401),(341,402),(342,403),(343,404),(344,405),(345,406),(346,407),(347,408),(348,409)], [(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)]])
464 conjugacy classes
| class | 1 | 2A | ··· | 2G | 4A | ··· | 4H | 29A | ··· | 29AB | 58A | ··· | 58GN | 116A | ··· | 116HP |
| order | 1 | 2 | ··· | 2 | 4 | ··· | 4 | 29 | ··· | 29 | 58 | ··· | 58 | 116 | ··· | 116 |
| size | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 1 | ··· | 1 |
464 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| type | + | + | + | |||||
| image | C1 | C2 | C2 | C4 | C29 | C58 | C58 | C116 |
| kernel | C22×C116 | C2×C116 | C22×C58 | C2×C58 | C22×C4 | C2×C4 | C23 | C22 |
| # reps | 1 | 6 | 1 | 8 | 28 | 168 | 28 | 224 |
Matrix representation of C22×C116 ►in GL3(𝔽233) generated by
| 1 | 0 | 0 |
| 0 | 1 | 0 |
| 0 | 0 | 232 |
| 232 | 0 | 0 |
| 0 | 1 | 0 |
| 0 | 0 | 232 |
| 217 | 0 | 0 |
| 0 | 120 | 0 |
| 0 | 0 | 133 |
G:=sub<GL(3,GF(233))| [1,0,0,0,1,0,0,0,232],[232,0,0,0,1,0,0,0,232],[217,0,0,0,120,0,0,0,133] >;
C22×C116 in GAP, Magma, Sage, TeX
C_2^2\times C_{116} % in TeX
G:=Group("C2^2xC116"); // GroupNames label
G:=SmallGroup(464,45);
// by ID
G=gap.SmallGroup(464,45);
# by ID
G:=PCGroup([5,-2,-2,-2,-29,-2,1160]);
// Polycyclic
G:=Group<a,b,c|a^2=b^2=c^116=1,a*b=b*a,a*c=c*a,b*c=c*b>;
// generators/relations