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G = C22×Dic29  order 464 = 24·29

Direct product of C22 and Dic29

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

Aliases: C22×Dic29, C58.9C23, C23.2D29, C22.11D58, (C2×C58)⋊5C4, C58⋊3(C2×C4), C29⋊3(C22×C4), (C22×C58).3C2, C2.2(C22×D29), (C2×C58).12C22, SmallGroup(464,43)

Series: Derived ►Chief ►Lower central ►Upper central

Derived series
C1 — C29 — C22×Dic29
Chief series
C1 — C29 — C58 — Dic29 — C2×Dic29 — C22×Dic29
Lower central
C29 — C22×Dic29
Upper central
C1 — C23

Generators and relations for C22×Dic29
 G = < a,b,c,d | a2=b2=c58=1, d2=c29, ab=ba, ac=ca, ad=da, bc=cb, bd=db, dcd-1=c-1 >

Subgroups: 362 in 54 conjugacy classes, 43 normal (7 characteristic)
C1, C2, C2, C4, C22, C2×C4, C23, C22×C4, C29, C58, C58, Dic29, C2×C58, C2×Dic29, C22×C58, C22×Dic29
Quotients: C1, C2, C4, C22, C2×C4, C23, C22×C4, D29, Dic29, D58, C2×Dic29, C22×D29, C22×Dic29

Smallest permutation representation of C22×Dic29
►Regular action on 464 points
Generators in S464
(1 136)(2 137)(3 138)(4 139)(5 140)(6 141)(7 142)(8 143)(9 144)(10 145)(11 146)(12 147)(13 148)(14 149)(15 150)(16 151)(17 152)(18 153)(19 154)(20 155)(21 156)(22 157)(23 158)(24 159)(25 160)(26 161)(27 162)(28 163)(29 164)(30 165)(31 166)(32 167)(33 168)(34 169)(35 170)(36 171)(37 172)(38 173)(39 174)(40 117)(41 118)(42 119)(43 120)(44 121)(45 122)(46 123)(47 124)(48 125)(49 126)(50 127)(51 128)(52 129)(53 130)(54 131)(55 132)(56 133)(57 134)(58 135)(59 215)(60 216)(61 217)(62 218)(63 219)(64 220)(65 221)(66 222)(67 223)(68 224)(69 225)(70 226)(71 227)(72 228)(73 229)(74 230)(75 231)(76 232)(77 175)(78 176)(79 177)(80 178)(81 179)(82 180)(83 181)(84 182)(85 183)(86 184)(87 185)(88 186)(89 187)(90 188)(91 189)(92 190)(93 191)(94 192)(95 193)(96 194)(97 195)(98 196)(99 197)(100 198)(101 199)(102 200)(103 201)(104 202)(105 203)(106 204)(107 205)(108 206)(109 207)(110 208)(111 209)(112 210)(113 211)(114 212)(115 213)(116 214)(233 349)(234 350)(235 351)(236 352)(237 353)(238 354)(239 355)(240 356)(241 357)(242 358)(243 359)(244 360)(245 361)(246 362)(247 363)(248 364)(249 365)(250 366)(251 367)(252 368)(253 369)(254 370)(255 371)(256 372)(257 373)(258 374)(259 375)(260 376)(261 377)(262 378)(263 379)(264 380)(265 381)(266 382)(267 383)(268 384)(269 385)(270 386)(271 387)(272 388)(273 389)(274 390)(275 391)(276 392)(277 393)(278 394)(279 395)(280 396)(281 397)(282 398)(283 399)(284 400)(285 401)(286 402)(287 403)(288 404)(289 405)(290 406)(291 436)(292 437)(293 438)(294 439)(295 440)(296 441)(297 442)(298 443)(299 444)(300 445)(301 446)(302 447)(303 448)(304 449)(305 450)(306 451)(307 452)(308 453)(309 454)(310 455)(311 456)(312 457)(313 458)(314 459)(315 460)(316 461)(317 462)(318 463)(319 464)(320 407)(321 408)(322 409)(323 410)(324 411)(325 412)(326 413)(327 414)(328 415)(329 416)(330 417)(331 418)(332 419)(333 420)(334 421)(335 422)(336 423)(337 424)(338 425)(339 426)(340 427)(341 428)(342 429)(343 430)(344 431)(345 432)(346 433)(347 434)(348 435)

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

(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)

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

128 conjugacy classes

class 1 2A···2G4A···4H29A···29N58A···58CT
order12···24···429···2958···58
size11···129···292···22···2

128 irreducible representations

dim1111222
type++++-+
imageC1C2C2C4D29Dic29D58
kernelC22×Dic29C2×Dic29C22×C58C2×C58C23C22C22
# reps1618145642

Matrix representation of C22×Dic29 ►in GL4(𝔽233) generated by

232000
023200
002320
000232
,
1000
0100
002320
000232
,
232000
0100
0001
00232118
,
144000
023200
00198126
0019035
G:=sub<GL(4,GF(233))| [232,0,0,0,0,232,0,0,0,0,232,0,0,0,0,232],[1,0,0,0,0,1,0,0,0,0,232,0,0,0,0,232],[232,0,0,0,0,1,0,0,0,0,0,232,0,0,1,118],[144,0,0,0,0,232,0,0,0,0,198,190,0,0,126,35] >;
 

C22×Dic29 in GAP, Magma, Sage, TeX 

C_2^2\times {\rm Dic}_{29}
 
% in TeX
 
G:=Group("C2^2xDic29");
 
// GroupNames label
 
G:=SmallGroup(464,43);
 
// by ID
 
G=gap.SmallGroup(464,43);
 
# by ID
 
G:=PCGroup([5,-2,-2,-2,-2,-29,40,11204]);
 
// Polycyclic
 
G:=Group<a,b,c,d|a^2=b^2=c^58=1,d^2=c^29,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^-1>;
 
// generators/relations
 

׿
×
⋊
ℤ
𝔽
○
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