direct product, metacyclic, supersoluble, monomial, Z-group, 2-hyperelementary
Aliases: Dic5×C23, C5⋊2C92, C115⋊5C4, C10.C46, C46.2D5, C230.3C2, C2.(D5×C23), SmallGroup(460,1)
Series: Derived ►Chief ►Lower central ►Upper central
| C5 — Dic5×C23 |
Generators and relations for Dic5×C23
G = < a,b,c | a23=b10=1, c2=b5, ab=ba, ac=ca, cbc-1=b-1 >
Smallest permutation representation of Dic5×C23
►Regular action on 460 points
Generators in S460
(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)
(1 373 179 56 255 300 142 398 420 252)(2 374 180 57 256 301 143 399 421 253)(3 375 181 58 257 302 144 400 422 231)(4 376 182 59 258 303 145 401 423 232)(5 377 183 60 259 304 146 402 424 233)(6 378 184 61 260 305 147 403 425 234)(7 379 162 62 261 306 148 404 426 235)(8 380 163 63 262 307 149 405 427 236)(9 381 164 64 263 308 150 406 428 237)(10 382 165 65 264 309 151 407 429 238)(11 383 166 66 265 310 152 408 430 239)(12 384 167 67 266 311 153 409 431 240)(13 385 168 68 267 312 154 410 432 241)(14 386 169 69 268 313 155 411 433 242)(15 387 170 47 269 314 156 412 434 243)(16 388 171 48 270 315 157 413 435 244)(17 389 172 49 271 316 158 414 436 245)(18 390 173 50 272 317 159 392 437 246)(19 391 174 51 273 318 160 393 415 247)(20 369 175 52 274 319 161 394 416 248)(21 370 176 53 275 320 139 395 417 249)(22 371 177 54 276 321 140 396 418 250)(23 372 178 55 254 322 141 397 419 251)(24 191 129 107 439 288 355 74 214 331)(25 192 130 108 440 289 356 75 215 332)(26 193 131 109 441 290 357 76 216 333)(27 194 132 110 442 291 358 77 217 334)(28 195 133 111 443 292 359 78 218 335)(29 196 134 112 444 293 360 79 219 336)(30 197 135 113 445 294 361 80 220 337)(31 198 136 114 446 295 362 81 221 338)(32 199 137 115 447 296 363 82 222 339)(33 200 138 93 448 297 364 83 223 340)(34 201 116 94 449 298 365 84 224 341)(35 202 117 95 450 299 366 85 225 342)(36 203 118 96 451 277 367 86 226 343)(37 204 119 97 452 278 368 87 227 344)(38 205 120 98 453 279 346 88 228 345)(39 206 121 99 454 280 347 89 229 323)(40 207 122 100 455 281 348 90 230 324)(41 185 123 101 456 282 349 91 208 325)(42 186 124 102 457 283 350 92 209 326)(43 187 125 103 458 284 351 70 210 327)(44 188 126 104 459 285 352 71 211 328)(45 189 127 105 460 286 353 72 212 329)(46 190 128 106 438 287 354 73 213 330)
(1 442 300 334)(2 443 301 335)(3 444 302 336)(4 445 303 337)(5 446 304 338)(6 447 305 339)(7 448 306 340)(8 449 307 341)(9 450 308 342)(10 451 309 343)(11 452 310 344)(12 453 311 345)(13 454 312 323)(14 455 313 324)(15 456 314 325)(16 457 315 326)(17 458 316 327)(18 459 317 328)(19 460 318 329)(20 438 319 330)(21 439 320 331)(22 440 321 332)(23 441 322 333)(24 249 288 275)(25 250 289 276)(26 251 290 254)(27 252 291 255)(28 253 292 256)(29 231 293 257)(30 232 294 258)(31 233 295 259)(32 234 296 260)(33 235 297 261)(34 236 298 262)(35 237 299 263)(36 238 277 264)(37 239 278 265)(38 240 279 266)(39 241 280 267)(40 242 281 268)(41 243 282 269)(42 244 283 270)(43 245 284 271)(44 246 285 272)(45 247 286 273)(46 248 287 274)(47 185 434 349)(48 186 435 350)(49 187 436 351)(50 188 437 352)(51 189 415 353)(52 190 416 354)(53 191 417 355)(54 192 418 356)(55 193 419 357)(56 194 420 358)(57 195 421 359)(58 196 422 360)(59 197 423 361)(60 198 424 362)(61 199 425 363)(62 200 426 364)(63 201 427 365)(64 202 428 366)(65 203 429 367)(66 204 430 368)(67 205 431 346)(68 206 432 347)(69 207 433 348)(70 172 125 414)(71 173 126 392)(72 174 127 393)(73 175 128 394)(74 176 129 395)(75 177 130 396)(76 178 131 397)(77 179 132 398)(78 180 133 399)(79 181 134 400)(80 182 135 401)(81 183 136 402)(82 184 137 403)(83 162 138 404)(84 163 116 405)(85 164 117 406)(86 165 118 407)(87 166 119 408)(88 167 120 409)(89 168 121 410)(90 169 122 411)(91 170 123 412)(92 171 124 413)(93 148 223 379)(94 149 224 380)(95 150 225 381)(96 151 226 382)(97 152 227 383)(98 153 228 384)(99 154 229 385)(100 155 230 386)(101 156 208 387)(102 157 209 388)(103 158 210 389)(104 159 211 390)(105 160 212 391)(106 161 213 369)(107 139 214 370)(108 140 215 371)(109 141 216 372)(110 142 217 373)(111 143 218 374)(112 144 219 375)(113 145 220 376)(114 146 221 377)(115 147 222 378)
G:=sub<Sym(460)| (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), (1,373,179,56,255,300,142,398,420,252)(2,374,180,57,256,301,143,399,421,253)(3,375,181,58,257,302,144,400,422,231)(4,376,182,59,258,303,145,401,423,232)(5,377,183,60,259,304,146,402,424,233)(6,378,184,61,260,305,147,403,425,234)(7,379,162,62,261,306,148,404,426,235)(8,380,163,63,262,307,149,405,427,236)(9,381,164,64,263,308,150,406,428,237)(10,382,165,65,264,309,151,407,429,238)(11,383,166,66,265,310,152,408,430,239)(12,384,167,67,266,311,153,409,431,240)(13,385,168,68,267,312,154,410,432,241)(14,386,169,69,268,313,155,411,433,242)(15,387,170,47,269,314,156,412,434,243)(16,388,171,48,270,315,157,413,435,244)(17,389,172,49,271,316,158,414,436,245)(18,390,173,50,272,317,159,392,437,246)(19,391,174,51,273,318,160,393,415,247)(20,369,175,52,274,319,161,394,416,248)(21,370,176,53,275,320,139,395,417,249)(22,371,177,54,276,321,140,396,418,250)(23,372,178,55,254,322,141,397,419,251)(24,191,129,107,439,288,355,74,214,331)(25,192,130,108,440,289,356,75,215,332)(26,193,131,109,441,290,357,76,216,333)(27,194,132,110,442,291,358,77,217,334)(28,195,133,111,443,292,359,78,218,335)(29,196,134,112,444,293,360,79,219,336)(30,197,135,113,445,294,361,80,220,337)(31,198,136,114,446,295,362,81,221,338)(32,199,137,115,447,296,363,82,222,339)(33,200,138,93,448,297,364,83,223,340)(34,201,116,94,449,298,365,84,224,341)(35,202,117,95,450,299,366,85,225,342)(36,203,118,96,451,277,367,86,226,343)(37,204,119,97,452,278,368,87,227,344)(38,205,120,98,453,279,346,88,228,345)(39,206,121,99,454,280,347,89,229,323)(40,207,122,100,455,281,348,90,230,324)(41,185,123,101,456,282,349,91,208,325)(42,186,124,102,457,283,350,92,209,326)(43,187,125,103,458,284,351,70,210,327)(44,188,126,104,459,285,352,71,211,328)(45,189,127,105,460,286,353,72,212,329)(46,190,128,106,438,287,354,73,213,330), (1,442,300,334)(2,443,301,335)(3,444,302,336)(4,445,303,337)(5,446,304,338)(6,447,305,339)(7,448,306,340)(8,449,307,341)(9,450,308,342)(10,451,309,343)(11,452,310,344)(12,453,311,345)(13,454,312,323)(14,455,313,324)(15,456,314,325)(16,457,315,326)(17,458,316,327)(18,459,317,328)(19,460,318,329)(20,438,319,330)(21,439,320,331)(22,440,321,332)(23,441,322,333)(24,249,288,275)(25,250,289,276)(26,251,290,254)(27,252,291,255)(28,253,292,256)(29,231,293,257)(30,232,294,258)(31,233,295,259)(32,234,296,260)(33,235,297,261)(34,236,298,262)(35,237,299,263)(36,238,277,264)(37,239,278,265)(38,240,279,266)(39,241,280,267)(40,242,281,268)(41,243,282,269)(42,244,283,270)(43,245,284,271)(44,246,285,272)(45,247,286,273)(46,248,287,274)(47,185,434,349)(48,186,435,350)(49,187,436,351)(50,188,437,352)(51,189,415,353)(52,190,416,354)(53,191,417,355)(54,192,418,356)(55,193,419,357)(56,194,420,358)(57,195,421,359)(58,196,422,360)(59,197,423,361)(60,198,424,362)(61,199,425,363)(62,200,426,364)(63,201,427,365)(64,202,428,366)(65,203,429,367)(66,204,430,368)(67,205,431,346)(68,206,432,347)(69,207,433,348)(70,172,125,414)(71,173,126,392)(72,174,127,393)(73,175,128,394)(74,176,129,395)(75,177,130,396)(76,178,131,397)(77,179,132,398)(78,180,133,399)(79,181,134,400)(80,182,135,401)(81,183,136,402)(82,184,137,403)(83,162,138,404)(84,163,116,405)(85,164,117,406)(86,165,118,407)(87,166,119,408)(88,167,120,409)(89,168,121,410)(90,169,122,411)(91,170,123,412)(92,171,124,413)(93,148,223,379)(94,149,224,380)(95,150,225,381)(96,151,226,382)(97,152,227,383)(98,153,228,384)(99,154,229,385)(100,155,230,386)(101,156,208,387)(102,157,209,388)(103,158,210,389)(104,159,211,390)(105,160,212,391)(106,161,213,369)(107,139,214,370)(108,140,215,371)(109,141,216,372)(110,142,217,373)(111,143,218,374)(112,144,219,375)(113,145,220,376)(114,146,221,377)(115,147,222,378)>;
G:=Group( (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), (1,373,179,56,255,300,142,398,420,252)(2,374,180,57,256,301,143,399,421,253)(3,375,181,58,257,302,144,400,422,231)(4,376,182,59,258,303,145,401,423,232)(5,377,183,60,259,304,146,402,424,233)(6,378,184,61,260,305,147,403,425,234)(7,379,162,62,261,306,148,404,426,235)(8,380,163,63,262,307,149,405,427,236)(9,381,164,64,263,308,150,406,428,237)(10,382,165,65,264,309,151,407,429,238)(11,383,166,66,265,310,152,408,430,239)(12,384,167,67,266,311,153,409,431,240)(13,385,168,68,267,312,154,410,432,241)(14,386,169,69,268,313,155,411,433,242)(15,387,170,47,269,314,156,412,434,243)(16,388,171,48,270,315,157,413,435,244)(17,389,172,49,271,316,158,414,436,245)(18,390,173,50,272,317,159,392,437,246)(19,391,174,51,273,318,160,393,415,247)(20,369,175,52,274,319,161,394,416,248)(21,370,176,53,275,320,139,395,417,249)(22,371,177,54,276,321,140,396,418,250)(23,372,178,55,254,322,141,397,419,251)(24,191,129,107,439,288,355,74,214,331)(25,192,130,108,440,289,356,75,215,332)(26,193,131,109,441,290,357,76,216,333)(27,194,132,110,442,291,358,77,217,334)(28,195,133,111,443,292,359,78,218,335)(29,196,134,112,444,293,360,79,219,336)(30,197,135,113,445,294,361,80,220,337)(31,198,136,114,446,295,362,81,221,338)(32,199,137,115,447,296,363,82,222,339)(33,200,138,93,448,297,364,83,223,340)(34,201,116,94,449,298,365,84,224,341)(35,202,117,95,450,299,366,85,225,342)(36,203,118,96,451,277,367,86,226,343)(37,204,119,97,452,278,368,87,227,344)(38,205,120,98,453,279,346,88,228,345)(39,206,121,99,454,280,347,89,229,323)(40,207,122,100,455,281,348,90,230,324)(41,185,123,101,456,282,349,91,208,325)(42,186,124,102,457,283,350,92,209,326)(43,187,125,103,458,284,351,70,210,327)(44,188,126,104,459,285,352,71,211,328)(45,189,127,105,460,286,353,72,212,329)(46,190,128,106,438,287,354,73,213,330), (1,442,300,334)(2,443,301,335)(3,444,302,336)(4,445,303,337)(5,446,304,338)(6,447,305,339)(7,448,306,340)(8,449,307,341)(9,450,308,342)(10,451,309,343)(11,452,310,344)(12,453,311,345)(13,454,312,323)(14,455,313,324)(15,456,314,325)(16,457,315,326)(17,458,316,327)(18,459,317,328)(19,460,318,329)(20,438,319,330)(21,439,320,331)(22,440,321,332)(23,441,322,333)(24,249,288,275)(25,250,289,276)(26,251,290,254)(27,252,291,255)(28,253,292,256)(29,231,293,257)(30,232,294,258)(31,233,295,259)(32,234,296,260)(33,235,297,261)(34,236,298,262)(35,237,299,263)(36,238,277,264)(37,239,278,265)(38,240,279,266)(39,241,280,267)(40,242,281,268)(41,243,282,269)(42,244,283,270)(43,245,284,271)(44,246,285,272)(45,247,286,273)(46,248,287,274)(47,185,434,349)(48,186,435,350)(49,187,436,351)(50,188,437,352)(51,189,415,353)(52,190,416,354)(53,191,417,355)(54,192,418,356)(55,193,419,357)(56,194,420,358)(57,195,421,359)(58,196,422,360)(59,197,423,361)(60,198,424,362)(61,199,425,363)(62,200,426,364)(63,201,427,365)(64,202,428,366)(65,203,429,367)(66,204,430,368)(67,205,431,346)(68,206,432,347)(69,207,433,348)(70,172,125,414)(71,173,126,392)(72,174,127,393)(73,175,128,394)(74,176,129,395)(75,177,130,396)(76,178,131,397)(77,179,132,398)(78,180,133,399)(79,181,134,400)(80,182,135,401)(81,183,136,402)(82,184,137,403)(83,162,138,404)(84,163,116,405)(85,164,117,406)(86,165,118,407)(87,166,119,408)(88,167,120,409)(89,168,121,410)(90,169,122,411)(91,170,123,412)(92,171,124,413)(93,148,223,379)(94,149,224,380)(95,150,225,381)(96,151,226,382)(97,152,227,383)(98,153,228,384)(99,154,229,385)(100,155,230,386)(101,156,208,387)(102,157,209,388)(103,158,210,389)(104,159,211,390)(105,160,212,391)(106,161,213,369)(107,139,214,370)(108,140,215,371)(109,141,216,372)(110,142,217,373)(111,143,218,374)(112,144,219,375)(113,145,220,376)(114,146,221,377)(115,147,222,378) );
G=PermutationGroup([[(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)], [(1,373,179,56,255,300,142,398,420,252),(2,374,180,57,256,301,143,399,421,253),(3,375,181,58,257,302,144,400,422,231),(4,376,182,59,258,303,145,401,423,232),(5,377,183,60,259,304,146,402,424,233),(6,378,184,61,260,305,147,403,425,234),(7,379,162,62,261,306,148,404,426,235),(8,380,163,63,262,307,149,405,427,236),(9,381,164,64,263,308,150,406,428,237),(10,382,165,65,264,309,151,407,429,238),(11,383,166,66,265,310,152,408,430,239),(12,384,167,67,266,311,153,409,431,240),(13,385,168,68,267,312,154,410,432,241),(14,386,169,69,268,313,155,411,433,242),(15,387,170,47,269,314,156,412,434,243),(16,388,171,48,270,315,157,413,435,244),(17,389,172,49,271,316,158,414,436,245),(18,390,173,50,272,317,159,392,437,246),(19,391,174,51,273,318,160,393,415,247),(20,369,175,52,274,319,161,394,416,248),(21,370,176,53,275,320,139,395,417,249),(22,371,177,54,276,321,140,396,418,250),(23,372,178,55,254,322,141,397,419,251),(24,191,129,107,439,288,355,74,214,331),(25,192,130,108,440,289,356,75,215,332),(26,193,131,109,441,290,357,76,216,333),(27,194,132,110,442,291,358,77,217,334),(28,195,133,111,443,292,359,78,218,335),(29,196,134,112,444,293,360,79,219,336),(30,197,135,113,445,294,361,80,220,337),(31,198,136,114,446,295,362,81,221,338),(32,199,137,115,447,296,363,82,222,339),(33,200,138,93,448,297,364,83,223,340),(34,201,116,94,449,298,365,84,224,341),(35,202,117,95,450,299,366,85,225,342),(36,203,118,96,451,277,367,86,226,343),(37,204,119,97,452,278,368,87,227,344),(38,205,120,98,453,279,346,88,228,345),(39,206,121,99,454,280,347,89,229,323),(40,207,122,100,455,281,348,90,230,324),(41,185,123,101,456,282,349,91,208,325),(42,186,124,102,457,283,350,92,209,326),(43,187,125,103,458,284,351,70,210,327),(44,188,126,104,459,285,352,71,211,328),(45,189,127,105,460,286,353,72,212,329),(46,190,128,106,438,287,354,73,213,330)], [(1,442,300,334),(2,443,301,335),(3,444,302,336),(4,445,303,337),(5,446,304,338),(6,447,305,339),(7,448,306,340),(8,449,307,341),(9,450,308,342),(10,451,309,343),(11,452,310,344),(12,453,311,345),(13,454,312,323),(14,455,313,324),(15,456,314,325),(16,457,315,326),(17,458,316,327),(18,459,317,328),(19,460,318,329),(20,438,319,330),(21,439,320,331),(22,440,321,332),(23,441,322,333),(24,249,288,275),(25,250,289,276),(26,251,290,254),(27,252,291,255),(28,253,292,256),(29,231,293,257),(30,232,294,258),(31,233,295,259),(32,234,296,260),(33,235,297,261),(34,236,298,262),(35,237,299,263),(36,238,277,264),(37,239,278,265),(38,240,279,266),(39,241,280,267),(40,242,281,268),(41,243,282,269),(42,244,283,270),(43,245,284,271),(44,246,285,272),(45,247,286,273),(46,248,287,274),(47,185,434,349),(48,186,435,350),(49,187,436,351),(50,188,437,352),(51,189,415,353),(52,190,416,354),(53,191,417,355),(54,192,418,356),(55,193,419,357),(56,194,420,358),(57,195,421,359),(58,196,422,360),(59,197,423,361),(60,198,424,362),(61,199,425,363),(62,200,426,364),(63,201,427,365),(64,202,428,366),(65,203,429,367),(66,204,430,368),(67,205,431,346),(68,206,432,347),(69,207,433,348),(70,172,125,414),(71,173,126,392),(72,174,127,393),(73,175,128,394),(74,176,129,395),(75,177,130,396),(76,178,131,397),(77,179,132,398),(78,180,133,399),(79,181,134,400),(80,182,135,401),(81,183,136,402),(82,184,137,403),(83,162,138,404),(84,163,116,405),(85,164,117,406),(86,165,118,407),(87,166,119,408),(88,167,120,409),(89,168,121,410),(90,169,122,411),(91,170,123,412),(92,171,124,413),(93,148,223,379),(94,149,224,380),(95,150,225,381),(96,151,226,382),(97,152,227,383),(98,153,228,384),(99,154,229,385),(100,155,230,386),(101,156,208,387),(102,157,209,388),(103,158,210,389),(104,159,211,390),(105,160,212,391),(106,161,213,369),(107,139,214,370),(108,140,215,371),(109,141,216,372),(110,142,217,373),(111,143,218,374),(112,144,219,375),(113,145,220,376),(114,146,221,377),(115,147,222,378)]])
184 conjugacy classes
| class | 1 | 2 | 4A | 4B | 5A | 5B | 10A | 10B | 23A | ··· | 23V | 46A | ··· | 46V | 92A | ··· | 92AR | 115A | ··· | 115AR | 230A | ··· | 230AR |
| order | 1 | 2 | 4 | 4 | 5 | 5 | 10 | 10 | 23 | ··· | 23 | 46 | ··· | 46 | 92 | ··· | 92 | 115 | ··· | 115 | 230 | ··· | 230 |
| size | 1 | 1 | 5 | 5 | 2 | 2 | 2 | 2 | 1 | ··· | 1 | 1 | ··· | 1 | 5 | ··· | 5 | 2 | ··· | 2 | 2 | ··· | 2 |
184 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 |
| type | + | + | + | - | ||||||
| image | C1 | C2 | C4 | C23 | C46 | C92 | D5 | Dic5 | D5×C23 | Dic5×C23 |
| kernel | Dic5×C23 | C230 | C115 | Dic5 | C10 | C5 | C46 | C23 | C2 | C1 |
| # reps | 1 | 1 | 2 | 22 | 22 | 44 | 2 | 2 | 44 | 44 |
Matrix representation of Dic5×C23 ►in GL3(𝔽461) generated by
| 1 | 0 | 0 |
| 0 | 262 | 0 |
| 0 | 0 | 262 |
| 460 | 0 | 0 |
| 0 | 460 | 1 |
| 0 | 438 | 22 |
| 48 | 0 | 0 |
| 0 | 209 | 60 |
| 0 | 194 | 252 |
G:=sub<GL(3,GF(461))| [1,0,0,0,262,0,0,0,262],[460,0,0,0,460,438,0,1,22],[48,0,0,0,209,194,0,60,252] >;
Dic5×C23 in GAP, Magma, Sage, TeX
{\rm Dic}_5\times C_{23} % in TeX
G:=Group("Dic5xC23"); // GroupNames label
G:=SmallGroup(460,1);
// by ID
G=gap.SmallGroup(460,1);
# by ID
G:=PCGroup([4,-2,-23,-2,-5,184,5891]);
// Polycyclic
G:=Group<a,b,c|a^23=b^10=1,c^2=b^5,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations
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