metacyclic, supersoluble, monomial, 2-hyperelementary
Aliases: C4⋊Dic29, C116⋊3C4, C58.4D4, C58.2Q8, C2.1D116, C2.2Dic58, C22.5D58, C29⋊3(C4⋊C4), (C2×C4).3D29, C58.15(C2×C4), (C2×C116).3C2, (C2×C58).5C22, C2.4(C2×Dic29), (C2×Dic29).2C2, SmallGroup(464,13)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C4⋊Dic29
G = < a,b,c | a4=b58=1, c2=b29, ab=ba, cac-1=a-1, cbc-1=b-1 >
Smallest permutation representation of C4⋊Dic29
►Regular action on 464 points
Generators in S464
(1 125 253 427)(2 126 254 428)(3 127 255 429)(4 128 256 430)(5 129 257 431)(6 130 258 432)(7 131 259 433)(8 132 260 434)(9 133 261 435)(10 134 262 436)(11 135 263 437)(12 136 264 438)(13 137 265 439)(14 138 266 440)(15 139 267 441)(16 140 268 442)(17 141 269 443)(18 142 270 444)(19 143 271 445)(20 144 272 446)(21 145 273 447)(22 146 274 448)(23 147 275 449)(24 148 276 450)(25 149 277 451)(26 150 278 452)(27 151 279 453)(28 152 280 454)(29 153 281 455)(30 154 282 456)(31 155 283 457)(32 156 284 458)(33 157 285 459)(34 158 286 460)(35 159 287 461)(36 160 288 462)(37 161 289 463)(38 162 290 464)(39 163 233 407)(40 164 234 408)(41 165 235 409)(42 166 236 410)(43 167 237 411)(44 168 238 412)(45 169 239 413)(46 170 240 414)(47 171 241 415)(48 172 242 416)(49 173 243 417)(50 174 244 418)(51 117 245 419)(52 118 246 420)(53 119 247 421)(54 120 248 422)(55 121 249 423)(56 122 250 424)(57 123 251 425)(58 124 252 426)(59 337 352 189)(60 338 353 190)(61 339 354 191)(62 340 355 192)(63 341 356 193)(64 342 357 194)(65 343 358 195)(66 344 359 196)(67 345 360 197)(68 346 361 198)(69 347 362 199)(70 348 363 200)(71 291 364 201)(72 292 365 202)(73 293 366 203)(74 294 367 204)(75 295 368 205)(76 296 369 206)(77 297 370 207)(78 298 371 208)(79 299 372 209)(80 300 373 210)(81 301 374 211)(82 302 375 212)(83 303 376 213)(84 304 377 214)(85 305 378 215)(86 306 379 216)(87 307 380 217)(88 308 381 218)(89 309 382 219)(90 310 383 220)(91 311 384 221)(92 312 385 222)(93 313 386 223)(94 314 387 224)(95 315 388 225)(96 316 389 226)(97 317 390 227)(98 318 391 228)(99 319 392 229)(100 320 393 230)(101 321 394 231)(102 322 395 232)(103 323 396 175)(104 324 397 176)(105 325 398 177)(106 326 399 178)(107 327 400 179)(108 328 401 180)(109 329 402 181)(110 330 403 182)(111 331 404 183)(112 332 405 184)(113 333 406 185)(114 334 349 186)(115 335 350 187)(116 336 351 188)
(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)
(1 304 30 333)(2 303 31 332)(3 302 32 331)(4 301 33 330)(5 300 34 329)(6 299 35 328)(7 298 36 327)(8 297 37 326)(9 296 38 325)(10 295 39 324)(11 294 40 323)(12 293 41 322)(13 292 42 321)(14 291 43 320)(15 348 44 319)(16 347 45 318)(17 346 46 317)(18 345 47 316)(19 344 48 315)(20 343 49 314)(21 342 50 313)(22 341 51 312)(23 340 52 311)(24 339 53 310)(25 338 54 309)(26 337 55 308)(27 336 56 307)(28 335 57 306)(29 334 58 305)(59 121 88 150)(60 120 89 149)(61 119 90 148)(62 118 91 147)(63 117 92 146)(64 174 93 145)(65 173 94 144)(66 172 95 143)(67 171 96 142)(68 170 97 141)(69 169 98 140)(70 168 99 139)(71 167 100 138)(72 166 101 137)(73 165 102 136)(74 164 103 135)(75 163 104 134)(76 162 105 133)(77 161 106 132)(78 160 107 131)(79 159 108 130)(80 158 109 129)(81 157 110 128)(82 156 111 127)(83 155 112 126)(84 154 113 125)(85 153 114 124)(86 152 115 123)(87 151 116 122)(175 263 204 234)(176 262 205 233)(177 261 206 290)(178 260 207 289)(179 259 208 288)(180 258 209 287)(181 257 210 286)(182 256 211 285)(183 255 212 284)(184 254 213 283)(185 253 214 282)(186 252 215 281)(187 251 216 280)(188 250 217 279)(189 249 218 278)(190 248 219 277)(191 247 220 276)(192 246 221 275)(193 245 222 274)(194 244 223 273)(195 243 224 272)(196 242 225 271)(197 241 226 270)(198 240 227 269)(199 239 228 268)(200 238 229 267)(201 237 230 266)(202 236 231 265)(203 235 232 264)(349 426 378 455)(350 425 379 454)(351 424 380 453)(352 423 381 452)(353 422 382 451)(354 421 383 450)(355 420 384 449)(356 419 385 448)(357 418 386 447)(358 417 387 446)(359 416 388 445)(360 415 389 444)(361 414 390 443)(362 413 391 442)(363 412 392 441)(364 411 393 440)(365 410 394 439)(366 409 395 438)(367 408 396 437)(368 407 397 436)(369 464 398 435)(370 463 399 434)(371 462 400 433)(372 461 401 432)(373 460 402 431)(374 459 403 430)(375 458 404 429)(376 457 405 428)(377 456 406 427)
G:=sub<Sym(464)| (1,125,253,427)(2,126,254,428)(3,127,255,429)(4,128,256,430)(5,129,257,431)(6,130,258,432)(7,131,259,433)(8,132,260,434)(9,133,261,435)(10,134,262,436)(11,135,263,437)(12,136,264,438)(13,137,265,439)(14,138,266,440)(15,139,267,441)(16,140,268,442)(17,141,269,443)(18,142,270,444)(19,143,271,445)(20,144,272,446)(21,145,273,447)(22,146,274,448)(23,147,275,449)(24,148,276,450)(25,149,277,451)(26,150,278,452)(27,151,279,453)(28,152,280,454)(29,153,281,455)(30,154,282,456)(31,155,283,457)(32,156,284,458)(33,157,285,459)(34,158,286,460)(35,159,287,461)(36,160,288,462)(37,161,289,463)(38,162,290,464)(39,163,233,407)(40,164,234,408)(41,165,235,409)(42,166,236,410)(43,167,237,411)(44,168,238,412)(45,169,239,413)(46,170,240,414)(47,171,241,415)(48,172,242,416)(49,173,243,417)(50,174,244,418)(51,117,245,419)(52,118,246,420)(53,119,247,421)(54,120,248,422)(55,121,249,423)(56,122,250,424)(57,123,251,425)(58,124,252,426)(59,337,352,189)(60,338,353,190)(61,339,354,191)(62,340,355,192)(63,341,356,193)(64,342,357,194)(65,343,358,195)(66,344,359,196)(67,345,360,197)(68,346,361,198)(69,347,362,199)(70,348,363,200)(71,291,364,201)(72,292,365,202)(73,293,366,203)(74,294,367,204)(75,295,368,205)(76,296,369,206)(77,297,370,207)(78,298,371,208)(79,299,372,209)(80,300,373,210)(81,301,374,211)(82,302,375,212)(83,303,376,213)(84,304,377,214)(85,305,378,215)(86,306,379,216)(87,307,380,217)(88,308,381,218)(89,309,382,219)(90,310,383,220)(91,311,384,221)(92,312,385,222)(93,313,386,223)(94,314,387,224)(95,315,388,225)(96,316,389,226)(97,317,390,227)(98,318,391,228)(99,319,392,229)(100,320,393,230)(101,321,394,231)(102,322,395,232)(103,323,396,175)(104,324,397,176)(105,325,398,177)(106,326,399,178)(107,327,400,179)(108,328,401,180)(109,329,402,181)(110,330,403,182)(111,331,404,183)(112,332,405,184)(113,333,406,185)(114,334,349,186)(115,335,350,187)(116,336,351,188), (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), (1,304,30,333)(2,303,31,332)(3,302,32,331)(4,301,33,330)(5,300,34,329)(6,299,35,328)(7,298,36,327)(8,297,37,326)(9,296,38,325)(10,295,39,324)(11,294,40,323)(12,293,41,322)(13,292,42,321)(14,291,43,320)(15,348,44,319)(16,347,45,318)(17,346,46,317)(18,345,47,316)(19,344,48,315)(20,343,49,314)(21,342,50,313)(22,341,51,312)(23,340,52,311)(24,339,53,310)(25,338,54,309)(26,337,55,308)(27,336,56,307)(28,335,57,306)(29,334,58,305)(59,121,88,150)(60,120,89,149)(61,119,90,148)(62,118,91,147)(63,117,92,146)(64,174,93,145)(65,173,94,144)(66,172,95,143)(67,171,96,142)(68,170,97,141)(69,169,98,140)(70,168,99,139)(71,167,100,138)(72,166,101,137)(73,165,102,136)(74,164,103,135)(75,163,104,134)(76,162,105,133)(77,161,106,132)(78,160,107,131)(79,159,108,130)(80,158,109,129)(81,157,110,128)(82,156,111,127)(83,155,112,126)(84,154,113,125)(85,153,114,124)(86,152,115,123)(87,151,116,122)(175,263,204,234)(176,262,205,233)(177,261,206,290)(178,260,207,289)(179,259,208,288)(180,258,209,287)(181,257,210,286)(182,256,211,285)(183,255,212,284)(184,254,213,283)(185,253,214,282)(186,252,215,281)(187,251,216,280)(188,250,217,279)(189,249,218,278)(190,248,219,277)(191,247,220,276)(192,246,221,275)(193,245,222,274)(194,244,223,273)(195,243,224,272)(196,242,225,271)(197,241,226,270)(198,240,227,269)(199,239,228,268)(200,238,229,267)(201,237,230,266)(202,236,231,265)(203,235,232,264)(349,426,378,455)(350,425,379,454)(351,424,380,453)(352,423,381,452)(353,422,382,451)(354,421,383,450)(355,420,384,449)(356,419,385,448)(357,418,386,447)(358,417,387,446)(359,416,388,445)(360,415,389,444)(361,414,390,443)(362,413,391,442)(363,412,392,441)(364,411,393,440)(365,410,394,439)(366,409,395,438)(367,408,396,437)(368,407,397,436)(369,464,398,435)(370,463,399,434)(371,462,400,433)(372,461,401,432)(373,460,402,431)(374,459,403,430)(375,458,404,429)(376,457,405,428)(377,456,406,427)>;
G:=Group( (1,125,253,427)(2,126,254,428)(3,127,255,429)(4,128,256,430)(5,129,257,431)(6,130,258,432)(7,131,259,433)(8,132,260,434)(9,133,261,435)(10,134,262,436)(11,135,263,437)(12,136,264,438)(13,137,265,439)(14,138,266,440)(15,139,267,441)(16,140,268,442)(17,141,269,443)(18,142,270,444)(19,143,271,445)(20,144,272,446)(21,145,273,447)(22,146,274,448)(23,147,275,449)(24,148,276,450)(25,149,277,451)(26,150,278,452)(27,151,279,453)(28,152,280,454)(29,153,281,455)(30,154,282,456)(31,155,283,457)(32,156,284,458)(33,157,285,459)(34,158,286,460)(35,159,287,461)(36,160,288,462)(37,161,289,463)(38,162,290,464)(39,163,233,407)(40,164,234,408)(41,165,235,409)(42,166,236,410)(43,167,237,411)(44,168,238,412)(45,169,239,413)(46,170,240,414)(47,171,241,415)(48,172,242,416)(49,173,243,417)(50,174,244,418)(51,117,245,419)(52,118,246,420)(53,119,247,421)(54,120,248,422)(55,121,249,423)(56,122,250,424)(57,123,251,425)(58,124,252,426)(59,337,352,189)(60,338,353,190)(61,339,354,191)(62,340,355,192)(63,341,356,193)(64,342,357,194)(65,343,358,195)(66,344,359,196)(67,345,360,197)(68,346,361,198)(69,347,362,199)(70,348,363,200)(71,291,364,201)(72,292,365,202)(73,293,366,203)(74,294,367,204)(75,295,368,205)(76,296,369,206)(77,297,370,207)(78,298,371,208)(79,299,372,209)(80,300,373,210)(81,301,374,211)(82,302,375,212)(83,303,376,213)(84,304,377,214)(85,305,378,215)(86,306,379,216)(87,307,380,217)(88,308,381,218)(89,309,382,219)(90,310,383,220)(91,311,384,221)(92,312,385,222)(93,313,386,223)(94,314,387,224)(95,315,388,225)(96,316,389,226)(97,317,390,227)(98,318,391,228)(99,319,392,229)(100,320,393,230)(101,321,394,231)(102,322,395,232)(103,323,396,175)(104,324,397,176)(105,325,398,177)(106,326,399,178)(107,327,400,179)(108,328,401,180)(109,329,402,181)(110,330,403,182)(111,331,404,183)(112,332,405,184)(113,333,406,185)(114,334,349,186)(115,335,350,187)(116,336,351,188), (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), (1,304,30,333)(2,303,31,332)(3,302,32,331)(4,301,33,330)(5,300,34,329)(6,299,35,328)(7,298,36,327)(8,297,37,326)(9,296,38,325)(10,295,39,324)(11,294,40,323)(12,293,41,322)(13,292,42,321)(14,291,43,320)(15,348,44,319)(16,347,45,318)(17,346,46,317)(18,345,47,316)(19,344,48,315)(20,343,49,314)(21,342,50,313)(22,341,51,312)(23,340,52,311)(24,339,53,310)(25,338,54,309)(26,337,55,308)(27,336,56,307)(28,335,57,306)(29,334,58,305)(59,121,88,150)(60,120,89,149)(61,119,90,148)(62,118,91,147)(63,117,92,146)(64,174,93,145)(65,173,94,144)(66,172,95,143)(67,171,96,142)(68,170,97,141)(69,169,98,140)(70,168,99,139)(71,167,100,138)(72,166,101,137)(73,165,102,136)(74,164,103,135)(75,163,104,134)(76,162,105,133)(77,161,106,132)(78,160,107,131)(79,159,108,130)(80,158,109,129)(81,157,110,128)(82,156,111,127)(83,155,112,126)(84,154,113,125)(85,153,114,124)(86,152,115,123)(87,151,116,122)(175,263,204,234)(176,262,205,233)(177,261,206,290)(178,260,207,289)(179,259,208,288)(180,258,209,287)(181,257,210,286)(182,256,211,285)(183,255,212,284)(184,254,213,283)(185,253,214,282)(186,252,215,281)(187,251,216,280)(188,250,217,279)(189,249,218,278)(190,248,219,277)(191,247,220,276)(192,246,221,275)(193,245,222,274)(194,244,223,273)(195,243,224,272)(196,242,225,271)(197,241,226,270)(198,240,227,269)(199,239,228,268)(200,238,229,267)(201,237,230,266)(202,236,231,265)(203,235,232,264)(349,426,378,455)(350,425,379,454)(351,424,380,453)(352,423,381,452)(353,422,382,451)(354,421,383,450)(355,420,384,449)(356,419,385,448)(357,418,386,447)(358,417,387,446)(359,416,388,445)(360,415,389,444)(361,414,390,443)(362,413,391,442)(363,412,392,441)(364,411,393,440)(365,410,394,439)(366,409,395,438)(367,408,396,437)(368,407,397,436)(369,464,398,435)(370,463,399,434)(371,462,400,433)(372,461,401,432)(373,460,402,431)(374,459,403,430)(375,458,404,429)(376,457,405,428)(377,456,406,427) );
G=PermutationGroup([[(1,125,253,427),(2,126,254,428),(3,127,255,429),(4,128,256,430),(5,129,257,431),(6,130,258,432),(7,131,259,433),(8,132,260,434),(9,133,261,435),(10,134,262,436),(11,135,263,437),(12,136,264,438),(13,137,265,439),(14,138,266,440),(15,139,267,441),(16,140,268,442),(17,141,269,443),(18,142,270,444),(19,143,271,445),(20,144,272,446),(21,145,273,447),(22,146,274,448),(23,147,275,449),(24,148,276,450),(25,149,277,451),(26,150,278,452),(27,151,279,453),(28,152,280,454),(29,153,281,455),(30,154,282,456),(31,155,283,457),(32,156,284,458),(33,157,285,459),(34,158,286,460),(35,159,287,461),(36,160,288,462),(37,161,289,463),(38,162,290,464),(39,163,233,407),(40,164,234,408),(41,165,235,409),(42,166,236,410),(43,167,237,411),(44,168,238,412),(45,169,239,413),(46,170,240,414),(47,171,241,415),(48,172,242,416),(49,173,243,417),(50,174,244,418),(51,117,245,419),(52,118,246,420),(53,119,247,421),(54,120,248,422),(55,121,249,423),(56,122,250,424),(57,123,251,425),(58,124,252,426),(59,337,352,189),(60,338,353,190),(61,339,354,191),(62,340,355,192),(63,341,356,193),(64,342,357,194),(65,343,358,195),(66,344,359,196),(67,345,360,197),(68,346,361,198),(69,347,362,199),(70,348,363,200),(71,291,364,201),(72,292,365,202),(73,293,366,203),(74,294,367,204),(75,295,368,205),(76,296,369,206),(77,297,370,207),(78,298,371,208),(79,299,372,209),(80,300,373,210),(81,301,374,211),(82,302,375,212),(83,303,376,213),(84,304,377,214),(85,305,378,215),(86,306,379,216),(87,307,380,217),(88,308,381,218),(89,309,382,219),(90,310,383,220),(91,311,384,221),(92,312,385,222),(93,313,386,223),(94,314,387,224),(95,315,388,225),(96,316,389,226),(97,317,390,227),(98,318,391,228),(99,319,392,229),(100,320,393,230),(101,321,394,231),(102,322,395,232),(103,323,396,175),(104,324,397,176),(105,325,398,177),(106,326,399,178),(107,327,400,179),(108,328,401,180),(109,329,402,181),(110,330,403,182),(111,331,404,183),(112,332,405,184),(113,333,406,185),(114,334,349,186),(115,335,350,187),(116,336,351,188)], [(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)], [(1,304,30,333),(2,303,31,332),(3,302,32,331),(4,301,33,330),(5,300,34,329),(6,299,35,328),(7,298,36,327),(8,297,37,326),(9,296,38,325),(10,295,39,324),(11,294,40,323),(12,293,41,322),(13,292,42,321),(14,291,43,320),(15,348,44,319),(16,347,45,318),(17,346,46,317),(18,345,47,316),(19,344,48,315),(20,343,49,314),(21,342,50,313),(22,341,51,312),(23,340,52,311),(24,339,53,310),(25,338,54,309),(26,337,55,308),(27,336,56,307),(28,335,57,306),(29,334,58,305),(59,121,88,150),(60,120,89,149),(61,119,90,148),(62,118,91,147),(63,117,92,146),(64,174,93,145),(65,173,94,144),(66,172,95,143),(67,171,96,142),(68,170,97,141),(69,169,98,140),(70,168,99,139),(71,167,100,138),(72,166,101,137),(73,165,102,136),(74,164,103,135),(75,163,104,134),(76,162,105,133),(77,161,106,132),(78,160,107,131),(79,159,108,130),(80,158,109,129),(81,157,110,128),(82,156,111,127),(83,155,112,126),(84,154,113,125),(85,153,114,124),(86,152,115,123),(87,151,116,122),(175,263,204,234),(176,262,205,233),(177,261,206,290),(178,260,207,289),(179,259,208,288),(180,258,209,287),(181,257,210,286),(182,256,211,285),(183,255,212,284),(184,254,213,283),(185,253,214,282),(186,252,215,281),(187,251,216,280),(188,250,217,279),(189,249,218,278),(190,248,219,277),(191,247,220,276),(192,246,221,275),(193,245,222,274),(194,244,223,273),(195,243,224,272),(196,242,225,271),(197,241,226,270),(198,240,227,269),(199,239,228,268),(200,238,229,267),(201,237,230,266),(202,236,231,265),(203,235,232,264),(349,426,378,455),(350,425,379,454),(351,424,380,453),(352,423,381,452),(353,422,382,451),(354,421,383,450),(355,420,384,449),(356,419,385,448),(357,418,386,447),(358,417,387,446),(359,416,388,445),(360,415,389,444),(361,414,390,443),(362,413,391,442),(363,412,392,441),(364,411,393,440),(365,410,394,439),(366,409,395,438),(367,408,396,437),(368,407,397,436),(369,464,398,435),(370,463,399,434),(371,462,400,433),(372,461,401,432),(373,460,402,431),(374,459,403,430),(375,458,404,429),(376,457,405,428),(377,456,406,427)]])
122 conjugacy classes
| class | 1 | 2A | 2B | 2C | 4A | 4B | 4C | 4D | 4E | 4F | 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 | 2 | 2 | 58 | 58 | 58 | 58 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
122 irreducible representations
| dim | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | - | + | - | + | - | + | |
| image | C1 | C2 | C2 | C4 | D4 | Q8 | D29 | Dic29 | D58 | Dic58 | D116 |
| kernel | C4⋊Dic29 | C2×Dic29 | C2×C116 | C116 | C58 | C58 | C2×C4 | C4 | C22 | C2 | C2 |
| # reps | 1 | 2 | 1 | 4 | 1 | 1 | 14 | 28 | 14 | 28 | 28 |
Matrix representation of C4⋊Dic29 ►in GL4(𝔽233) generated by
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 163 | 170 |
| 0 | 0 | 63 | 70 |
| 0 | 232 | 0 | 0 |
| 1 | 54 | 0 | 0 |
| 0 | 0 | 0 | 1 |
| 0 | 0 | 232 | 179 |
| 89 | 146 | 0 | 0 |
| 0 | 144 | 0 | 0 |
| 0 | 0 | 87 | 15 |
| 0 | 0 | 210 | 146 |
G:=sub<GL(4,GF(233))| [1,0,0,0,0,1,0,0,0,0,163,63,0,0,170,70],[0,1,0,0,232,54,0,0,0,0,0,232,0,0,1,179],[89,0,0,0,146,144,0,0,0,0,87,210,0,0,15,146] >;
C4⋊Dic29 in GAP, Magma, Sage, TeX
C_4\rtimes {\rm Dic}_{29} % in TeX
G:=Group("C4:Dic29"); // GroupNames label
G:=SmallGroup(464,13);
// by ID
G=gap.SmallGroup(464,13);
# by ID
G:=PCGroup([5,-2,-2,-2,-2,-29,20,101,46,11204]);
// Polycyclic
G:=Group<a,b,c|a^4=b^58=1,c^2=b^29,a*b=b*a,c*a*c^-1=a^-1,c*b*c^-1=b^-1>;
// generators/relations
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