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## G = C4×Dic29order 464 = 24·29

### Direct product of C4 and Dic29

Aliases: C4×Dic29, C1164C4, C292C42, C22.3D58, C2.2(C4×D29), (C2×C4).6D29, C58.10(C2×C4), (C2×C116).7C2, (C2×C58).3C22, C2.2(C2×Dic29), (C2×Dic29).6C2, SmallGroup(464,11)

Series: Derived Chief Lower central Upper central

 Derived series C1 — C29 — C4×Dic29
 Chief series C1 — C29 — C58 — C2×C58 — C2×Dic29 — C4×Dic29
 Lower central C29 — C4×Dic29
 Upper central C1 — C2×C4

Generators and relations for C4×Dic29
G = < a,b,c | a4=b58=1, c2=b29, ab=ba, ac=ca, cbc-1=b-1 >

Smallest permutation representation of C4×Dic29
Regular action on 464 points
Generators in S464
(1 434 350 264)(2 435 351 265)(3 436 352 266)(4 437 353 267)(5 438 354 268)(6 439 355 269)(7 440 356 270)(8 441 357 271)(9 442 358 272)(10 443 359 273)(11 444 360 274)(12 445 361 275)(13 446 362 276)(14 447 363 277)(15 448 364 278)(16 449 365 279)(17 450 366 280)(18 451 367 281)(19 452 368 282)(20 453 369 283)(21 454 370 284)(22 455 371 285)(23 456 372 286)(24 457 373 287)(25 458 374 288)(26 459 375 289)(27 460 376 290)(28 461 377 233)(29 462 378 234)(30 463 379 235)(31 464 380 236)(32 407 381 237)(33 408 382 238)(34 409 383 239)(35 410 384 240)(36 411 385 241)(37 412 386 242)(38 413 387 243)(39 414 388 244)(40 415 389 245)(41 416 390 246)(42 417 391 247)(43 418 392 248)(44 419 393 249)(45 420 394 250)(46 421 395 251)(47 422 396 252)(48 423 397 253)(49 424 398 254)(50 425 399 255)(51 426 400 256)(52 427 401 257)(53 428 402 258)(54 429 403 259)(55 430 404 260)(56 431 405 261)(57 432 406 262)(58 433 349 263)(59 345 227 124)(60 346 228 125)(61 347 229 126)(62 348 230 127)(63 291 231 128)(64 292 232 129)(65 293 175 130)(66 294 176 131)(67 295 177 132)(68 296 178 133)(69 297 179 134)(70 298 180 135)(71 299 181 136)(72 300 182 137)(73 301 183 138)(74 302 184 139)(75 303 185 140)(76 304 186 141)(77 305 187 142)(78 306 188 143)(79 307 189 144)(80 308 190 145)(81 309 191 146)(82 310 192 147)(83 311 193 148)(84 312 194 149)(85 313 195 150)(86 314 196 151)(87 315 197 152)(88 316 198 153)(89 317 199 154)(90 318 200 155)(91 319 201 156)(92 320 202 157)(93 321 203 158)(94 322 204 159)(95 323 205 160)(96 324 206 161)(97 325 207 162)(98 326 208 163)(99 327 209 164)(100 328 210 165)(101 329 211 166)(102 330 212 167)(103 331 213 168)(104 332 214 169)(105 333 215 170)(106 334 216 171)(107 335 217 172)(108 336 218 173)(109 337 219 174)(110 338 220 117)(111 339 221 118)(112 340 222 119)(113 341 223 120)(114 342 224 121)(115 343 225 122)(116 344 226 123)
(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)
(1 196 30 225)(2 195 31 224)(3 194 32 223)(4 193 33 222)(5 192 34 221)(6 191 35 220)(7 190 36 219)(8 189 37 218)(9 188 38 217)(10 187 39 216)(11 186 40 215)(12 185 41 214)(13 184 42 213)(14 183 43 212)(15 182 44 211)(16 181 45 210)(17 180 46 209)(18 179 47 208)(19 178 48 207)(20 177 49 206)(21 176 50 205)(22 175 51 204)(23 232 52 203)(24 231 53 202)(25 230 54 201)(26 229 55 200)(27 228 56 199)(28 227 57 198)(29 226 58 197)(59 406 88 377)(60 405 89 376)(61 404 90 375)(62 403 91 374)(63 402 92 373)(64 401 93 372)(65 400 94 371)(66 399 95 370)(67 398 96 369)(68 397 97 368)(69 396 98 367)(70 395 99 366)(71 394 100 365)(72 393 101 364)(73 392 102 363)(74 391 103 362)(75 390 104 361)(76 389 105 360)(77 388 106 359)(78 387 107 358)(79 386 108 357)(80 385 109 356)(81 384 110 355)(82 383 111 354)(83 382 112 353)(84 381 113 352)(85 380 114 351)(86 379 115 350)(87 378 116 349)(117 439 146 410)(118 438 147 409)(119 437 148 408)(120 436 149 407)(121 435 150 464)(122 434 151 463)(123 433 152 462)(124 432 153 461)(125 431 154 460)(126 430 155 459)(127 429 156 458)(128 428 157 457)(129 427 158 456)(130 426 159 455)(131 425 160 454)(132 424 161 453)(133 423 162 452)(134 422 163 451)(135 421 164 450)(136 420 165 449)(137 419 166 448)(138 418 167 447)(139 417 168 446)(140 416 169 445)(141 415 170 444)(142 414 171 443)(143 413 172 442)(144 412 173 441)(145 411 174 440)(233 345 262 316)(234 344 263 315)(235 343 264 314)(236 342 265 313)(237 341 266 312)(238 340 267 311)(239 339 268 310)(240 338 269 309)(241 337 270 308)(242 336 271 307)(243 335 272 306)(244 334 273 305)(245 333 274 304)(246 332 275 303)(247 331 276 302)(248 330 277 301)(249 329 278 300)(250 328 279 299)(251 327 280 298)(252 326 281 297)(253 325 282 296)(254 324 283 295)(255 323 284 294)(256 322 285 293)(257 321 286 292)(258 320 287 291)(259 319 288 348)(260 318 289 347)(261 317 290 346)

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

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

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

128 conjugacy classes

 class 1 2A 2B 2C 4A 4B 4C 4D 4E ··· 4L 29A ··· 29N 58A ··· 58AP 116A ··· 116BD order 1 2 2 2 4 4 4 4 4 ··· 4 29 ··· 29 58 ··· 58 116 ··· 116 size 1 1 1 1 1 1 1 1 29 ··· 29 2 ··· 2 2 ··· 2 2 ··· 2

128 irreducible representations

 dim 1 1 1 1 1 2 2 2 2 type + + + + - + image C1 C2 C2 C4 C4 D29 Dic29 D58 C4×D29 kernel C4×Dic29 C2×Dic29 C2×C116 Dic29 C116 C2×C4 C4 C22 C2 # reps 1 2 1 8 4 14 28 14 56

Matrix representation of C4×Dic29 in GL4(𝔽233) generated by

 89 0 0 0 0 144 0 0 0 0 1 0 0 0 0 1
,
 1 0 0 0 0 232 0 0 0 0 0 1 0 0 232 206
,
 232 0 0 0 0 89 0 0 0 0 207 145 0 0 148 26
G:=sub<GL(4,GF(233))| [89,0,0,0,0,144,0,0,0,0,1,0,0,0,0,1],[1,0,0,0,0,232,0,0,0,0,0,232,0,0,1,206],[232,0,0,0,0,89,0,0,0,0,207,148,0,0,145,26] >;

C4×Dic29 in GAP, Magma, Sage, TeX

C_4\times {\rm Dic}_{29}
% in TeX

G:=Group("C4xDic29");
// GroupNames label

G:=SmallGroup(464,11);
// by ID

G=gap.SmallGroup(464,11);
# by ID

G:=PCGroup([5,-2,-2,-2,-2,-29,20,46,11204]);
// Polycyclic

G:=Group<a,b,c|a^4=b^58=1,c^2=b^29,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations

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