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G = C5×Dic23order 460 = 22·5·23

Direct product of C5 and Dic23

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

Aliases: C5×Dic23, C23⋊C20, C1154C4, C46.C10, C230.2C2, C10.2D23, C2.(C5×D23), SmallGroup(460,2)

Series: Derived Chief Lower central Upper central

C1C23 — C5×Dic23
C1C23C46C230 — C5×Dic23
C23 — C5×Dic23
C1C10

Generators and relations for C5×Dic23
 G = < a,b,c | a5=b46=1, c2=b23, ab=ba, ac=ca, cbc-1=b-1 >

23C4
23C20

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

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

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

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

130 conjugacy classes

class 1  2 4A4B5A5B5C5D10A10B10C10D20A···20H23A···23K46A···46K115A···115AR230A···230AR
order124455551010101020···2023···2346···46115···115230···230
size1123231111111123···232···22···22···22···2

130 irreducible representations

dim1111112222
type+++-
imageC1C2C4C5C10C20D23Dic23C5×D23C5×Dic23
kernelC5×Dic23C230C115Dic23C46C23C10C5C2C1
# reps11244811114444

Matrix representation of C5×Dic23 in GL3(𝔽461) generated by

11400
03510
00351
,
46000
001
04603
,
41300
0274140
040187
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

Subgroup lattice of C5×Dic23 in TeX

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