direct product, metacyclic, supersoluble, monomial, Z-group, 2-hyperelementary
Aliases: C5×Dic23, C23⋊C20, C115⋊4C4, C46.C10, C230.2C2, C10.2D23, C2.(C5×D23), SmallGroup(460,2)
Series: Derived ►Chief ►Lower central ►Upper central
| C23 — C5×Dic23 |
Generators and relations for C5×Dic23
G = < a,b,c | a5=b46=1, c2=b23, ab=ba, ac=ca, cbc-1=b-1 >
Smallest permutation representation of C5×Dic23
►Regular action on 460 points
Generators in S460
(1 193 163 113 72)(2 194 164 114 73)(3 195 165 115 74)(4 196 166 116 75)(5 197 167 117 76)(6 198 168 118 77)(7 199 169 119 78)(8 200 170 120 79)(9 201 171 121 80)(10 202 172 122 81)(11 203 173 123 82)(12 204 174 124 83)(13 205 175 125 84)(14 206 176 126 85)(15 207 177 127 86)(16 208 178 128 87)(17 209 179 129 88)(18 210 180 130 89)(19 211 181 131 90)(20 212 182 132 91)(21 213 183 133 92)(22 214 184 134 47)(23 215 139 135 48)(24 216 140 136 49)(25 217 141 137 50)(26 218 142 138 51)(27 219 143 93 52)(28 220 144 94 53)(29 221 145 95 54)(30 222 146 96 55)(31 223 147 97 56)(32 224 148 98 57)(33 225 149 99 58)(34 226 150 100 59)(35 227 151 101 60)(36 228 152 102 61)(37 229 153 103 62)(38 230 154 104 63)(39 185 155 105 64)(40 186 156 106 65)(41 187 157 107 66)(42 188 158 108 67)(43 189 159 109 68)(44 190 160 110 69)(45 191 161 111 70)(46 192 162 112 71)(231 438 369 323 300)(232 439 370 324 301)(233 440 371 325 302)(234 441 372 326 303)(235 442 373 327 304)(236 443 374 328 305)(237 444 375 329 306)(238 445 376 330 307)(239 446 377 331 308)(240 447 378 332 309)(241 448 379 333 310)(242 449 380 334 311)(243 450 381 335 312)(244 451 382 336 313)(245 452 383 337 314)(246 453 384 338 315)(247 454 385 339 316)(248 455 386 340 317)(249 456 387 341 318)(250 457 388 342 319)(251 458 389 343 320)(252 459 390 344 321)(253 460 391 345 322)(254 415 392 346 277)(255 416 393 347 278)(256 417 394 348 279)(257 418 395 349 280)(258 419 396 350 281)(259 420 397 351 282)(260 421 398 352 283)(261 422 399 353 284)(262 423 400 354 285)(263 424 401 355 286)(264 425 402 356 287)(265 426 403 357 288)(266 427 404 358 289)(267 428 405 359 290)(268 429 406 360 291)(269 430 407 361 292)(270 431 408 362 293)(271 432 409 363 294)(272 433 410 364 295)(273 434 411 365 296)(274 435 412 366 297)(275 436 413 367 298)(276 437 414 368 299)
(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)
(1 231 24 254)(2 276 25 253)(3 275 26 252)(4 274 27 251)(5 273 28 250)(6 272 29 249)(7 271 30 248)(8 270 31 247)(9 269 32 246)(10 268 33 245)(11 267 34 244)(12 266 35 243)(13 265 36 242)(14 264 37 241)(15 263 38 240)(16 262 39 239)(17 261 40 238)(18 260 41 237)(19 259 42 236)(20 258 43 235)(21 257 44 234)(22 256 45 233)(23 255 46 232)(47 279 70 302)(48 278 71 301)(49 277 72 300)(50 322 73 299)(51 321 74 298)(52 320 75 297)(53 319 76 296)(54 318 77 295)(55 317 78 294)(56 316 79 293)(57 315 80 292)(58 314 81 291)(59 313 82 290)(60 312 83 289)(61 311 84 288)(62 310 85 287)(63 309 86 286)(64 308 87 285)(65 307 88 284)(66 306 89 283)(67 305 90 282)(68 304 91 281)(69 303 92 280)(93 343 116 366)(94 342 117 365)(95 341 118 364)(96 340 119 363)(97 339 120 362)(98 338 121 361)(99 337 122 360)(100 336 123 359)(101 335 124 358)(102 334 125 357)(103 333 126 356)(104 332 127 355)(105 331 128 354)(106 330 129 353)(107 329 130 352)(108 328 131 351)(109 327 132 350)(110 326 133 349)(111 325 134 348)(112 324 135 347)(113 323 136 346)(114 368 137 345)(115 367 138 344)(139 393 162 370)(140 392 163 369)(141 391 164 414)(142 390 165 413)(143 389 166 412)(144 388 167 411)(145 387 168 410)(146 386 169 409)(147 385 170 408)(148 384 171 407)(149 383 172 406)(150 382 173 405)(151 381 174 404)(152 380 175 403)(153 379 176 402)(154 378 177 401)(155 377 178 400)(156 376 179 399)(157 375 180 398)(158 374 181 397)(159 373 182 396)(160 372 183 395)(161 371 184 394)(185 446 208 423)(186 445 209 422)(187 444 210 421)(188 443 211 420)(189 442 212 419)(190 441 213 418)(191 440 214 417)(192 439 215 416)(193 438 216 415)(194 437 217 460)(195 436 218 459)(196 435 219 458)(197 434 220 457)(198 433 221 456)(199 432 222 455)(200 431 223 454)(201 430 224 453)(202 429 225 452)(203 428 226 451)(204 427 227 450)(205 426 228 449)(206 425 229 448)(207 424 230 447)
G:=sub<Sym(460)| (1,193,163,113,72)(2,194,164,114,73)(3,195,165,115,74)(4,196,166,116,75)(5,197,167,117,76)(6,198,168,118,77)(7,199,169,119,78)(8,200,170,120,79)(9,201,171,121,80)(10,202,172,122,81)(11,203,173,123,82)(12,204,174,124,83)(13,205,175,125,84)(14,206,176,126,85)(15,207,177,127,86)(16,208,178,128,87)(17,209,179,129,88)(18,210,180,130,89)(19,211,181,131,90)(20,212,182,132,91)(21,213,183,133,92)(22,214,184,134,47)(23,215,139,135,48)(24,216,140,136,49)(25,217,141,137,50)(26,218,142,138,51)(27,219,143,93,52)(28,220,144,94,53)(29,221,145,95,54)(30,222,146,96,55)(31,223,147,97,56)(32,224,148,98,57)(33,225,149,99,58)(34,226,150,100,59)(35,227,151,101,60)(36,228,152,102,61)(37,229,153,103,62)(38,230,154,104,63)(39,185,155,105,64)(40,186,156,106,65)(41,187,157,107,66)(42,188,158,108,67)(43,189,159,109,68)(44,190,160,110,69)(45,191,161,111,70)(46,192,162,112,71)(231,438,369,323,300)(232,439,370,324,301)(233,440,371,325,302)(234,441,372,326,303)(235,442,373,327,304)(236,443,374,328,305)(237,444,375,329,306)(238,445,376,330,307)(239,446,377,331,308)(240,447,378,332,309)(241,448,379,333,310)(242,449,380,334,311)(243,450,381,335,312)(244,451,382,336,313)(245,452,383,337,314)(246,453,384,338,315)(247,454,385,339,316)(248,455,386,340,317)(249,456,387,341,318)(250,457,388,342,319)(251,458,389,343,320)(252,459,390,344,321)(253,460,391,345,322)(254,415,392,346,277)(255,416,393,347,278)(256,417,394,348,279)(257,418,395,349,280)(258,419,396,350,281)(259,420,397,351,282)(260,421,398,352,283)(261,422,399,353,284)(262,423,400,354,285)(263,424,401,355,286)(264,425,402,356,287)(265,426,403,357,288)(266,427,404,358,289)(267,428,405,359,290)(268,429,406,360,291)(269,430,407,361,292)(270,431,408,362,293)(271,432,409,363,294)(272,433,410,364,295)(273,434,411,365,296)(274,435,412,366,297)(275,436,413,367,298)(276,437,414,368,299), (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), (1,231,24,254)(2,276,25,253)(3,275,26,252)(4,274,27,251)(5,273,28,250)(6,272,29,249)(7,271,30,248)(8,270,31,247)(9,269,32,246)(10,268,33,245)(11,267,34,244)(12,266,35,243)(13,265,36,242)(14,264,37,241)(15,263,38,240)(16,262,39,239)(17,261,40,238)(18,260,41,237)(19,259,42,236)(20,258,43,235)(21,257,44,234)(22,256,45,233)(23,255,46,232)(47,279,70,302)(48,278,71,301)(49,277,72,300)(50,322,73,299)(51,321,74,298)(52,320,75,297)(53,319,76,296)(54,318,77,295)(55,317,78,294)(56,316,79,293)(57,315,80,292)(58,314,81,291)(59,313,82,290)(60,312,83,289)(61,311,84,288)(62,310,85,287)(63,309,86,286)(64,308,87,285)(65,307,88,284)(66,306,89,283)(67,305,90,282)(68,304,91,281)(69,303,92,280)(93,343,116,366)(94,342,117,365)(95,341,118,364)(96,340,119,363)(97,339,120,362)(98,338,121,361)(99,337,122,360)(100,336,123,359)(101,335,124,358)(102,334,125,357)(103,333,126,356)(104,332,127,355)(105,331,128,354)(106,330,129,353)(107,329,130,352)(108,328,131,351)(109,327,132,350)(110,326,133,349)(111,325,134,348)(112,324,135,347)(113,323,136,346)(114,368,137,345)(115,367,138,344)(139,393,162,370)(140,392,163,369)(141,391,164,414)(142,390,165,413)(143,389,166,412)(144,388,167,411)(145,387,168,410)(146,386,169,409)(147,385,170,408)(148,384,171,407)(149,383,172,406)(150,382,173,405)(151,381,174,404)(152,380,175,403)(153,379,176,402)(154,378,177,401)(155,377,178,400)(156,376,179,399)(157,375,180,398)(158,374,181,397)(159,373,182,396)(160,372,183,395)(161,371,184,394)(185,446,208,423)(186,445,209,422)(187,444,210,421)(188,443,211,420)(189,442,212,419)(190,441,213,418)(191,440,214,417)(192,439,215,416)(193,438,216,415)(194,437,217,460)(195,436,218,459)(196,435,219,458)(197,434,220,457)(198,433,221,456)(199,432,222,455)(200,431,223,454)(201,430,224,453)(202,429,225,452)(203,428,226,451)(204,427,227,450)(205,426,228,449)(206,425,229,448)(207,424,230,447)>;
G:=Group( (1,193,163,113,72)(2,194,164,114,73)(3,195,165,115,74)(4,196,166,116,75)(5,197,167,117,76)(6,198,168,118,77)(7,199,169,119,78)(8,200,170,120,79)(9,201,171,121,80)(10,202,172,122,81)(11,203,173,123,82)(12,204,174,124,83)(13,205,175,125,84)(14,206,176,126,85)(15,207,177,127,86)(16,208,178,128,87)(17,209,179,129,88)(18,210,180,130,89)(19,211,181,131,90)(20,212,182,132,91)(21,213,183,133,92)(22,214,184,134,47)(23,215,139,135,48)(24,216,140,136,49)(25,217,141,137,50)(26,218,142,138,51)(27,219,143,93,52)(28,220,144,94,53)(29,221,145,95,54)(30,222,146,96,55)(31,223,147,97,56)(32,224,148,98,57)(33,225,149,99,58)(34,226,150,100,59)(35,227,151,101,60)(36,228,152,102,61)(37,229,153,103,62)(38,230,154,104,63)(39,185,155,105,64)(40,186,156,106,65)(41,187,157,107,66)(42,188,158,108,67)(43,189,159,109,68)(44,190,160,110,69)(45,191,161,111,70)(46,192,162,112,71)(231,438,369,323,300)(232,439,370,324,301)(233,440,371,325,302)(234,441,372,326,303)(235,442,373,327,304)(236,443,374,328,305)(237,444,375,329,306)(238,445,376,330,307)(239,446,377,331,308)(240,447,378,332,309)(241,448,379,333,310)(242,449,380,334,311)(243,450,381,335,312)(244,451,382,336,313)(245,452,383,337,314)(246,453,384,338,315)(247,454,385,339,316)(248,455,386,340,317)(249,456,387,341,318)(250,457,388,342,319)(251,458,389,343,320)(252,459,390,344,321)(253,460,391,345,322)(254,415,392,346,277)(255,416,393,347,278)(256,417,394,348,279)(257,418,395,349,280)(258,419,396,350,281)(259,420,397,351,282)(260,421,398,352,283)(261,422,399,353,284)(262,423,400,354,285)(263,424,401,355,286)(264,425,402,356,287)(265,426,403,357,288)(266,427,404,358,289)(267,428,405,359,290)(268,429,406,360,291)(269,430,407,361,292)(270,431,408,362,293)(271,432,409,363,294)(272,433,410,364,295)(273,434,411,365,296)(274,435,412,366,297)(275,436,413,367,298)(276,437,414,368,299), (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), (1,231,24,254)(2,276,25,253)(3,275,26,252)(4,274,27,251)(5,273,28,250)(6,272,29,249)(7,271,30,248)(8,270,31,247)(9,269,32,246)(10,268,33,245)(11,267,34,244)(12,266,35,243)(13,265,36,242)(14,264,37,241)(15,263,38,240)(16,262,39,239)(17,261,40,238)(18,260,41,237)(19,259,42,236)(20,258,43,235)(21,257,44,234)(22,256,45,233)(23,255,46,232)(47,279,70,302)(48,278,71,301)(49,277,72,300)(50,322,73,299)(51,321,74,298)(52,320,75,297)(53,319,76,296)(54,318,77,295)(55,317,78,294)(56,316,79,293)(57,315,80,292)(58,314,81,291)(59,313,82,290)(60,312,83,289)(61,311,84,288)(62,310,85,287)(63,309,86,286)(64,308,87,285)(65,307,88,284)(66,306,89,283)(67,305,90,282)(68,304,91,281)(69,303,92,280)(93,343,116,366)(94,342,117,365)(95,341,118,364)(96,340,119,363)(97,339,120,362)(98,338,121,361)(99,337,122,360)(100,336,123,359)(101,335,124,358)(102,334,125,357)(103,333,126,356)(104,332,127,355)(105,331,128,354)(106,330,129,353)(107,329,130,352)(108,328,131,351)(109,327,132,350)(110,326,133,349)(111,325,134,348)(112,324,135,347)(113,323,136,346)(114,368,137,345)(115,367,138,344)(139,393,162,370)(140,392,163,369)(141,391,164,414)(142,390,165,413)(143,389,166,412)(144,388,167,411)(145,387,168,410)(146,386,169,409)(147,385,170,408)(148,384,171,407)(149,383,172,406)(150,382,173,405)(151,381,174,404)(152,380,175,403)(153,379,176,402)(154,378,177,401)(155,377,178,400)(156,376,179,399)(157,375,180,398)(158,374,181,397)(159,373,182,396)(160,372,183,395)(161,371,184,394)(185,446,208,423)(186,445,209,422)(187,444,210,421)(188,443,211,420)(189,442,212,419)(190,441,213,418)(191,440,214,417)(192,439,215,416)(193,438,216,415)(194,437,217,460)(195,436,218,459)(196,435,219,458)(197,434,220,457)(198,433,221,456)(199,432,222,455)(200,431,223,454)(201,430,224,453)(202,429,225,452)(203,428,226,451)(204,427,227,450)(205,426,228,449)(206,425,229,448)(207,424,230,447) );
G=PermutationGroup([[(1,193,163,113,72),(2,194,164,114,73),(3,195,165,115,74),(4,196,166,116,75),(5,197,167,117,76),(6,198,168,118,77),(7,199,169,119,78),(8,200,170,120,79),(9,201,171,121,80),(10,202,172,122,81),(11,203,173,123,82),(12,204,174,124,83),(13,205,175,125,84),(14,206,176,126,85),(15,207,177,127,86),(16,208,178,128,87),(17,209,179,129,88),(18,210,180,130,89),(19,211,181,131,90),(20,212,182,132,91),(21,213,183,133,92),(22,214,184,134,47),(23,215,139,135,48),(24,216,140,136,49),(25,217,141,137,50),(26,218,142,138,51),(27,219,143,93,52),(28,220,144,94,53),(29,221,145,95,54),(30,222,146,96,55),(31,223,147,97,56),(32,224,148,98,57),(33,225,149,99,58),(34,226,150,100,59),(35,227,151,101,60),(36,228,152,102,61),(37,229,153,103,62),(38,230,154,104,63),(39,185,155,105,64),(40,186,156,106,65),(41,187,157,107,66),(42,188,158,108,67),(43,189,159,109,68),(44,190,160,110,69),(45,191,161,111,70),(46,192,162,112,71),(231,438,369,323,300),(232,439,370,324,301),(233,440,371,325,302),(234,441,372,326,303),(235,442,373,327,304),(236,443,374,328,305),(237,444,375,329,306),(238,445,376,330,307),(239,446,377,331,308),(240,447,378,332,309),(241,448,379,333,310),(242,449,380,334,311),(243,450,381,335,312),(244,451,382,336,313),(245,452,383,337,314),(246,453,384,338,315),(247,454,385,339,316),(248,455,386,340,317),(249,456,387,341,318),(250,457,388,342,319),(251,458,389,343,320),(252,459,390,344,321),(253,460,391,345,322),(254,415,392,346,277),(255,416,393,347,278),(256,417,394,348,279),(257,418,395,349,280),(258,419,396,350,281),(259,420,397,351,282),(260,421,398,352,283),(261,422,399,353,284),(262,423,400,354,285),(263,424,401,355,286),(264,425,402,356,287),(265,426,403,357,288),(266,427,404,358,289),(267,428,405,359,290),(268,429,406,360,291),(269,430,407,361,292),(270,431,408,362,293),(271,432,409,363,294),(272,433,410,364,295),(273,434,411,365,296),(274,435,412,366,297),(275,436,413,367,298),(276,437,414,368,299)], [(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)], [(1,231,24,254),(2,276,25,253),(3,275,26,252),(4,274,27,251),(5,273,28,250),(6,272,29,249),(7,271,30,248),(8,270,31,247),(9,269,32,246),(10,268,33,245),(11,267,34,244),(12,266,35,243),(13,265,36,242),(14,264,37,241),(15,263,38,240),(16,262,39,239),(17,261,40,238),(18,260,41,237),(19,259,42,236),(20,258,43,235),(21,257,44,234),(22,256,45,233),(23,255,46,232),(47,279,70,302),(48,278,71,301),(49,277,72,300),(50,322,73,299),(51,321,74,298),(52,320,75,297),(53,319,76,296),(54,318,77,295),(55,317,78,294),(56,316,79,293),(57,315,80,292),(58,314,81,291),(59,313,82,290),(60,312,83,289),(61,311,84,288),(62,310,85,287),(63,309,86,286),(64,308,87,285),(65,307,88,284),(66,306,89,283),(67,305,90,282),(68,304,91,281),(69,303,92,280),(93,343,116,366),(94,342,117,365),(95,341,118,364),(96,340,119,363),(97,339,120,362),(98,338,121,361),(99,337,122,360),(100,336,123,359),(101,335,124,358),(102,334,125,357),(103,333,126,356),(104,332,127,355),(105,331,128,354),(106,330,129,353),(107,329,130,352),(108,328,131,351),(109,327,132,350),(110,326,133,349),(111,325,134,348),(112,324,135,347),(113,323,136,346),(114,368,137,345),(115,367,138,344),(139,393,162,370),(140,392,163,369),(141,391,164,414),(142,390,165,413),(143,389,166,412),(144,388,167,411),(145,387,168,410),(146,386,169,409),(147,385,170,408),(148,384,171,407),(149,383,172,406),(150,382,173,405),(151,381,174,404),(152,380,175,403),(153,379,176,402),(154,378,177,401),(155,377,178,400),(156,376,179,399),(157,375,180,398),(158,374,181,397),(159,373,182,396),(160,372,183,395),(161,371,184,394),(185,446,208,423),(186,445,209,422),(187,444,210,421),(188,443,211,420),(189,442,212,419),(190,441,213,418),(191,440,214,417),(192,439,215,416),(193,438,216,415),(194,437,217,460),(195,436,218,459),(196,435,219,458),(197,434,220,457),(198,433,221,456),(199,432,222,455),(200,431,223,454),(201,430,224,453),(202,429,225,452),(203,428,226,451),(204,427,227,450),(205,426,228,449),(206,425,229,448),(207,424,230,447)]])
130 conjugacy classes
| class | 1 | 2 | 4A | 4B | 5A | 5B | 5C | 5D | 10A | 10B | 10C | 10D | 20A | ··· | 20H | 23A | ··· | 23K | 46A | ··· | 46K | 115A | ··· | 115AR | 230A | ··· | 230AR |
| order | 1 | 2 | 4 | 4 | 5 | 5 | 5 | 5 | 10 | 10 | 10 | 10 | 20 | ··· | 20 | 23 | ··· | 23 | 46 | ··· | 46 | 115 | ··· | 115 | 230 | ··· | 230 |
| size | 1 | 1 | 23 | 23 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 23 | ··· | 23 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
130 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 |
| type | + | + | + | - | ||||||
| image | C1 | C2 | C4 | C5 | C10 | C20 | D23 | Dic23 | C5×D23 | C5×Dic23 |
| kernel | C5×Dic23 | C230 | C115 | Dic23 | C46 | C23 | C10 | C5 | C2 | C1 |
| # reps | 1 | 1 | 2 | 4 | 4 | 8 | 11 | 11 | 44 | 44 |
Matrix representation of C5×Dic23 ►in GL3(𝔽461) generated by
| 114 | 0 | 0 |
| 0 | 351 | 0 |
| 0 | 0 | 351 |
| 460 | 0 | 0 |
| 0 | 0 | 1 |
| 0 | 460 | 3 |
| 413 | 0 | 0 |
| 0 | 274 | 140 |
| 0 | 40 | 187 |
G:=sub<GL(3,GF(461))| [114,0,0,0,351,0,0,0,351],[460,0,0,0,0,460,0,1,3],[413,0,0,0,274,40,0,140,187] >;
C5×Dic23 in GAP, Magma, Sage, TeX
C_5\times {\rm Dic}_{23} % in TeX
G:=Group("C5xDic23"); // GroupNames label
G:=SmallGroup(460,2);
// by ID
G=gap.SmallGroup(460,2);
# by ID
G:=PCGroup([4,-2,-5,-2,-23,40,7043]);
// Polycyclic
G:=Group<a,b,c|a^5=b^46=1,c^2=b^23,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations
Export