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G = Dic5×C23order 460 = 22·5·23

Direct product of C23 and Dic5

direct product, metacyclic, supersoluble, monomial, Z-group, 2-hyperelementary

Aliases: Dic5×C23, C52C92, C1155C4, C10.C46, C46.2D5, C230.3C2, C2.(D5×C23), SmallGroup(460,1)

Series: Derived Chief Lower central Upper central

C1C5 — Dic5×C23
C1C5C10C230 — Dic5×C23
C5 — Dic5×C23
C1C46

Generators and relations for Dic5×C23
 G = < a,b,c | a23=b10=1, c2=b5, ab=ba, ac=ca, cbc-1=b-1 >

5C4
5C92

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

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

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

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

184 conjugacy classes

class 1  2 4A4B5A5B10A10B23A···23V46A···46V92A···92AR115A···115AR230A···230AR
order124455101023···2346···4692···92115···115230···230
size115522221···11···15···52···22···2

184 irreducible representations

dim1111112222
type+++-
imageC1C2C4C23C46C92D5Dic5D5×C23Dic5×C23
kernelDic5×C23C230C115Dic5C10C5C46C23C2C1
# reps112222244224444

Matrix representation of Dic5×C23 in GL3(𝔽461) generated by

100
02620
00262
,
46000
04601
043822
,
4800
020960
0194252
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

Export

Subgroup lattice of Dic5×C23 in TeX

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