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G = C32×Dic13order 468 = 22·32·13

Direct product of C32 and Dic13

direct product, metacyclic, supersoluble, monomial, A-group

Aliases: C32×Dic13, C3910C12, C78.12C6, (C3×C39)⋊9C4, C135(C3×C12), (C3×C78).3C2, C26.3(C3×C6), C6.4(C3×D13), (C3×C6).3D13, C2.(C32×D13), SmallGroup(468,23)

Series: Derived Chief Lower central Upper central

C1C13 — C32×Dic13
C1C13C26C78C3×C78 — C32×Dic13
C13 — C32×Dic13
C1C3×C6

Generators and relations for C32×Dic13
 G = < a,b,c,d | a3=b3=c26=1, d2=c13, ab=ba, ac=ca, ad=da, bc=cb, bd=db, dcd-1=c-1 >

13C4
13C12
13C12
13C12
13C12
13C3×C12

Smallest permutation representation of C32×Dic13
Regular action on 468 points
Generators in S468
(1 210 114)(2 211 115)(3 212 116)(4 213 117)(5 214 118)(6 215 119)(7 216 120)(8 217 121)(9 218 122)(10 219 123)(11 220 124)(12 221 125)(13 222 126)(14 223 127)(15 224 128)(16 225 129)(17 226 130)(18 227 105)(19 228 106)(20 229 107)(21 230 108)(22 231 109)(23 232 110)(24 233 111)(25 234 112)(26 209 113)(27 164 153)(28 165 154)(29 166 155)(30 167 156)(31 168 131)(32 169 132)(33 170 133)(34 171 134)(35 172 135)(36 173 136)(37 174 137)(38 175 138)(39 176 139)(40 177 140)(41 178 141)(42 179 142)(43 180 143)(44 181 144)(45 182 145)(46 157 146)(47 158 147)(48 159 148)(49 160 149)(50 161 150)(51 162 151)(52 163 152)(53 184 95)(54 185 96)(55 186 97)(56 187 98)(57 188 99)(58 189 100)(59 190 101)(60 191 102)(61 192 103)(62 193 104)(63 194 79)(64 195 80)(65 196 81)(66 197 82)(67 198 83)(68 199 84)(69 200 85)(70 201 86)(71 202 87)(72 203 88)(73 204 89)(74 205 90)(75 206 91)(76 207 92)(77 208 93)(78 183 94)(235 456 352)(236 457 353)(237 458 354)(238 459 355)(239 460 356)(240 461 357)(241 462 358)(242 463 359)(243 464 360)(244 465 361)(245 466 362)(246 467 363)(247 468 364)(248 443 339)(249 444 340)(250 445 341)(251 446 342)(252 447 343)(253 448 344)(254 449 345)(255 450 346)(256 451 347)(257 452 348)(258 453 349)(259 454 350)(260 455 351)(261 391 378)(262 392 379)(263 393 380)(264 394 381)(265 395 382)(266 396 383)(267 397 384)(268 398 385)(269 399 386)(270 400 387)(271 401 388)(272 402 389)(273 403 390)(274 404 365)(275 405 366)(276 406 367)(277 407 368)(278 408 369)(279 409 370)(280 410 371)(281 411 372)(282 412 373)(283 413 374)(284 414 375)(285 415 376)(286 416 377)(287 430 326)(288 431 327)(289 432 328)(290 433 329)(291 434 330)(292 435 331)(293 436 332)(294 437 333)(295 438 334)(296 439 335)(297 440 336)(298 441 337)(299 442 338)(300 417 313)(301 418 314)(302 419 315)(303 420 316)(304 421 317)(305 422 318)(306 423 319)(307 424 320)(308 425 321)(309 426 322)(310 427 323)(311 428 324)(312 429 325)
(1 53 32)(2 54 33)(3 55 34)(4 56 35)(5 57 36)(6 58 37)(7 59 38)(8 60 39)(9 61 40)(10 62 41)(11 63 42)(12 64 43)(13 65 44)(14 66 45)(15 67 46)(16 68 47)(17 69 48)(18 70 49)(19 71 50)(20 72 51)(21 73 52)(22 74 27)(23 75 28)(24 76 29)(25 77 30)(26 78 31)(79 142 124)(80 143 125)(81 144 126)(82 145 127)(83 146 128)(84 147 129)(85 148 130)(86 149 105)(87 150 106)(88 151 107)(89 152 108)(90 153 109)(91 154 110)(92 155 111)(93 156 112)(94 131 113)(95 132 114)(96 133 115)(97 134 116)(98 135 117)(99 136 118)(100 137 119)(101 138 120)(102 139 121)(103 140 122)(104 141 123)(157 224 198)(158 225 199)(159 226 200)(160 227 201)(161 228 202)(162 229 203)(163 230 204)(164 231 205)(165 232 206)(166 233 207)(167 234 208)(168 209 183)(169 210 184)(170 211 185)(171 212 186)(172 213 187)(173 214 188)(174 215 189)(175 216 190)(176 217 191)(177 218 192)(178 219 193)(179 220 194)(180 221 195)(181 222 196)(182 223 197)(235 287 274)(236 288 275)(237 289 276)(238 290 277)(239 291 278)(240 292 279)(241 293 280)(242 294 281)(243 295 282)(244 296 283)(245 297 284)(246 298 285)(247 299 286)(248 300 261)(249 301 262)(250 302 263)(251 303 264)(252 304 265)(253 305 266)(254 306 267)(255 307 268)(256 308 269)(257 309 270)(258 310 271)(259 311 272)(260 312 273)(313 378 339)(314 379 340)(315 380 341)(316 381 342)(317 382 343)(318 383 344)(319 384 345)(320 385 346)(321 386 347)(322 387 348)(323 388 349)(324 389 350)(325 390 351)(326 365 352)(327 366 353)(328 367 354)(329 368 355)(330 369 356)(331 370 357)(332 371 358)(333 372 359)(334 373 360)(335 374 361)(336 375 362)(337 376 363)(338 377 364)(391 443 417)(392 444 418)(393 445 419)(394 446 420)(395 447 421)(396 448 422)(397 449 423)(398 450 424)(399 451 425)(400 452 426)(401 453 427)(402 454 428)(403 455 429)(404 456 430)(405 457 431)(406 458 432)(407 459 433)(408 460 434)(409 461 435)(410 462 436)(411 463 437)(412 464 438)(413 465 439)(414 466 440)(415 467 441)(416 468 442)
(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26)(27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52)(53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78)(79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104)(105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130)(131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156)(157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182)(183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208)(209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234)(235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260)(261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286)(287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312)(313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338)(339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364)(365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390)(391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416)(417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442)(443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468)
(1 235 14 248)(2 260 15 247)(3 259 16 246)(4 258 17 245)(5 257 18 244)(6 256 19 243)(7 255 20 242)(8 254 21 241)(9 253 22 240)(10 252 23 239)(11 251 24 238)(12 250 25 237)(13 249 26 236)(27 279 40 266)(28 278 41 265)(29 277 42 264)(30 276 43 263)(31 275 44 262)(32 274 45 261)(33 273 46 286)(34 272 47 285)(35 271 48 284)(36 270 49 283)(37 269 50 282)(38 268 51 281)(39 267 52 280)(53 287 66 300)(54 312 67 299)(55 311 68 298)(56 310 69 297)(57 309 70 296)(58 308 71 295)(59 307 72 294)(60 306 73 293)(61 305 74 292)(62 304 75 291)(63 303 76 290)(64 302 77 289)(65 301 78 288)(79 316 92 329)(80 315 93 328)(81 314 94 327)(82 313 95 326)(83 338 96 325)(84 337 97 324)(85 336 98 323)(86 335 99 322)(87 334 100 321)(88 333 101 320)(89 332 102 319)(90 331 103 318)(91 330 104 317)(105 361 118 348)(106 360 119 347)(107 359 120 346)(108 358 121 345)(109 357 122 344)(110 356 123 343)(111 355 124 342)(112 354 125 341)(113 353 126 340)(114 352 127 339)(115 351 128 364)(116 350 129 363)(117 349 130 362)(131 366 144 379)(132 365 145 378)(133 390 146 377)(134 389 147 376)(135 388 148 375)(136 387 149 374)(137 386 150 373)(138 385 151 372)(139 384 152 371)(140 383 153 370)(141 382 154 369)(142 381 155 368)(143 380 156 367)(157 416 170 403)(158 415 171 402)(159 414 172 401)(160 413 173 400)(161 412 174 399)(162 411 175 398)(163 410 176 397)(164 409 177 396)(165 408 178 395)(166 407 179 394)(167 406 180 393)(168 405 181 392)(169 404 182 391)(183 431 196 418)(184 430 197 417)(185 429 198 442)(186 428 199 441)(187 427 200 440)(188 426 201 439)(189 425 202 438)(190 424 203 437)(191 423 204 436)(192 422 205 435)(193 421 206 434)(194 420 207 433)(195 419 208 432)(209 457 222 444)(210 456 223 443)(211 455 224 468)(212 454 225 467)(213 453 226 466)(214 452 227 465)(215 451 228 464)(216 450 229 463)(217 449 230 462)(218 448 231 461)(219 447 232 460)(220 446 233 459)(221 445 234 458)

G:=sub<Sym(468)| (1,210,114)(2,211,115)(3,212,116)(4,213,117)(5,214,118)(6,215,119)(7,216,120)(8,217,121)(9,218,122)(10,219,123)(11,220,124)(12,221,125)(13,222,126)(14,223,127)(15,224,128)(16,225,129)(17,226,130)(18,227,105)(19,228,106)(20,229,107)(21,230,108)(22,231,109)(23,232,110)(24,233,111)(25,234,112)(26,209,113)(27,164,153)(28,165,154)(29,166,155)(30,167,156)(31,168,131)(32,169,132)(33,170,133)(34,171,134)(35,172,135)(36,173,136)(37,174,137)(38,175,138)(39,176,139)(40,177,140)(41,178,141)(42,179,142)(43,180,143)(44,181,144)(45,182,145)(46,157,146)(47,158,147)(48,159,148)(49,160,149)(50,161,150)(51,162,151)(52,163,152)(53,184,95)(54,185,96)(55,186,97)(56,187,98)(57,188,99)(58,189,100)(59,190,101)(60,191,102)(61,192,103)(62,193,104)(63,194,79)(64,195,80)(65,196,81)(66,197,82)(67,198,83)(68,199,84)(69,200,85)(70,201,86)(71,202,87)(72,203,88)(73,204,89)(74,205,90)(75,206,91)(76,207,92)(77,208,93)(78,183,94)(235,456,352)(236,457,353)(237,458,354)(238,459,355)(239,460,356)(240,461,357)(241,462,358)(242,463,359)(243,464,360)(244,465,361)(245,466,362)(246,467,363)(247,468,364)(248,443,339)(249,444,340)(250,445,341)(251,446,342)(252,447,343)(253,448,344)(254,449,345)(255,450,346)(256,451,347)(257,452,348)(258,453,349)(259,454,350)(260,455,351)(261,391,378)(262,392,379)(263,393,380)(264,394,381)(265,395,382)(266,396,383)(267,397,384)(268,398,385)(269,399,386)(270,400,387)(271,401,388)(272,402,389)(273,403,390)(274,404,365)(275,405,366)(276,406,367)(277,407,368)(278,408,369)(279,409,370)(280,410,371)(281,411,372)(282,412,373)(283,413,374)(284,414,375)(285,415,376)(286,416,377)(287,430,326)(288,431,327)(289,432,328)(290,433,329)(291,434,330)(292,435,331)(293,436,332)(294,437,333)(295,438,334)(296,439,335)(297,440,336)(298,441,337)(299,442,338)(300,417,313)(301,418,314)(302,419,315)(303,420,316)(304,421,317)(305,422,318)(306,423,319)(307,424,320)(308,425,321)(309,426,322)(310,427,323)(311,428,324)(312,429,325), (1,53,32)(2,54,33)(3,55,34)(4,56,35)(5,57,36)(6,58,37)(7,59,38)(8,60,39)(9,61,40)(10,62,41)(11,63,42)(12,64,43)(13,65,44)(14,66,45)(15,67,46)(16,68,47)(17,69,48)(18,70,49)(19,71,50)(20,72,51)(21,73,52)(22,74,27)(23,75,28)(24,76,29)(25,77,30)(26,78,31)(79,142,124)(80,143,125)(81,144,126)(82,145,127)(83,146,128)(84,147,129)(85,148,130)(86,149,105)(87,150,106)(88,151,107)(89,152,108)(90,153,109)(91,154,110)(92,155,111)(93,156,112)(94,131,113)(95,132,114)(96,133,115)(97,134,116)(98,135,117)(99,136,118)(100,137,119)(101,138,120)(102,139,121)(103,140,122)(104,141,123)(157,224,198)(158,225,199)(159,226,200)(160,227,201)(161,228,202)(162,229,203)(163,230,204)(164,231,205)(165,232,206)(166,233,207)(167,234,208)(168,209,183)(169,210,184)(170,211,185)(171,212,186)(172,213,187)(173,214,188)(174,215,189)(175,216,190)(176,217,191)(177,218,192)(178,219,193)(179,220,194)(180,221,195)(181,222,196)(182,223,197)(235,287,274)(236,288,275)(237,289,276)(238,290,277)(239,291,278)(240,292,279)(241,293,280)(242,294,281)(243,295,282)(244,296,283)(245,297,284)(246,298,285)(247,299,286)(248,300,261)(249,301,262)(250,302,263)(251,303,264)(252,304,265)(253,305,266)(254,306,267)(255,307,268)(256,308,269)(257,309,270)(258,310,271)(259,311,272)(260,312,273)(313,378,339)(314,379,340)(315,380,341)(316,381,342)(317,382,343)(318,383,344)(319,384,345)(320,385,346)(321,386,347)(322,387,348)(323,388,349)(324,389,350)(325,390,351)(326,365,352)(327,366,353)(328,367,354)(329,368,355)(330,369,356)(331,370,357)(332,371,358)(333,372,359)(334,373,360)(335,374,361)(336,375,362)(337,376,363)(338,377,364)(391,443,417)(392,444,418)(393,445,419)(394,446,420)(395,447,421)(396,448,422)(397,449,423)(398,450,424)(399,451,425)(400,452,426)(401,453,427)(402,454,428)(403,455,429)(404,456,430)(405,457,431)(406,458,432)(407,459,433)(408,460,434)(409,461,435)(410,462,436)(411,463,437)(412,464,438)(413,465,439)(414,466,440)(415,467,441)(416,468,442), (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26)(27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52)(53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78)(79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104)(105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130)(131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156)(157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182)(183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208)(209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234)(235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260)(261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286)(287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312)(313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338)(339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364)(365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390)(391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416)(417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442)(443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468), (1,235,14,248)(2,260,15,247)(3,259,16,246)(4,258,17,245)(5,257,18,244)(6,256,19,243)(7,255,20,242)(8,254,21,241)(9,253,22,240)(10,252,23,239)(11,251,24,238)(12,250,25,237)(13,249,26,236)(27,279,40,266)(28,278,41,265)(29,277,42,264)(30,276,43,263)(31,275,44,262)(32,274,45,261)(33,273,46,286)(34,272,47,285)(35,271,48,284)(36,270,49,283)(37,269,50,282)(38,268,51,281)(39,267,52,280)(53,287,66,300)(54,312,67,299)(55,311,68,298)(56,310,69,297)(57,309,70,296)(58,308,71,295)(59,307,72,294)(60,306,73,293)(61,305,74,292)(62,304,75,291)(63,303,76,290)(64,302,77,289)(65,301,78,288)(79,316,92,329)(80,315,93,328)(81,314,94,327)(82,313,95,326)(83,338,96,325)(84,337,97,324)(85,336,98,323)(86,335,99,322)(87,334,100,321)(88,333,101,320)(89,332,102,319)(90,331,103,318)(91,330,104,317)(105,361,118,348)(106,360,119,347)(107,359,120,346)(108,358,121,345)(109,357,122,344)(110,356,123,343)(111,355,124,342)(112,354,125,341)(113,353,126,340)(114,352,127,339)(115,351,128,364)(116,350,129,363)(117,349,130,362)(131,366,144,379)(132,365,145,378)(133,390,146,377)(134,389,147,376)(135,388,148,375)(136,387,149,374)(137,386,150,373)(138,385,151,372)(139,384,152,371)(140,383,153,370)(141,382,154,369)(142,381,155,368)(143,380,156,367)(157,416,170,403)(158,415,171,402)(159,414,172,401)(160,413,173,400)(161,412,174,399)(162,411,175,398)(163,410,176,397)(164,409,177,396)(165,408,178,395)(166,407,179,394)(167,406,180,393)(168,405,181,392)(169,404,182,391)(183,431,196,418)(184,430,197,417)(185,429,198,442)(186,428,199,441)(187,427,200,440)(188,426,201,439)(189,425,202,438)(190,424,203,437)(191,423,204,436)(192,422,205,435)(193,421,206,434)(194,420,207,433)(195,419,208,432)(209,457,222,444)(210,456,223,443)(211,455,224,468)(212,454,225,467)(213,453,226,466)(214,452,227,465)(215,451,228,464)(216,450,229,463)(217,449,230,462)(218,448,231,461)(219,447,232,460)(220,446,233,459)(221,445,234,458)>;

G:=Group( (1,210,114)(2,211,115)(3,212,116)(4,213,117)(5,214,118)(6,215,119)(7,216,120)(8,217,121)(9,218,122)(10,219,123)(11,220,124)(12,221,125)(13,222,126)(14,223,127)(15,224,128)(16,225,129)(17,226,130)(18,227,105)(19,228,106)(20,229,107)(21,230,108)(22,231,109)(23,232,110)(24,233,111)(25,234,112)(26,209,113)(27,164,153)(28,165,154)(29,166,155)(30,167,156)(31,168,131)(32,169,132)(33,170,133)(34,171,134)(35,172,135)(36,173,136)(37,174,137)(38,175,138)(39,176,139)(40,177,140)(41,178,141)(42,179,142)(43,180,143)(44,181,144)(45,182,145)(46,157,146)(47,158,147)(48,159,148)(49,160,149)(50,161,150)(51,162,151)(52,163,152)(53,184,95)(54,185,96)(55,186,97)(56,187,98)(57,188,99)(58,189,100)(59,190,101)(60,191,102)(61,192,103)(62,193,104)(63,194,79)(64,195,80)(65,196,81)(66,197,82)(67,198,83)(68,199,84)(69,200,85)(70,201,86)(71,202,87)(72,203,88)(73,204,89)(74,205,90)(75,206,91)(76,207,92)(77,208,93)(78,183,94)(235,456,352)(236,457,353)(237,458,354)(238,459,355)(239,460,356)(240,461,357)(241,462,358)(242,463,359)(243,464,360)(244,465,361)(245,466,362)(246,467,363)(247,468,364)(248,443,339)(249,444,340)(250,445,341)(251,446,342)(252,447,343)(253,448,344)(254,449,345)(255,450,346)(256,451,347)(257,452,348)(258,453,349)(259,454,350)(260,455,351)(261,391,378)(262,392,379)(263,393,380)(264,394,381)(265,395,382)(266,396,383)(267,397,384)(268,398,385)(269,399,386)(270,400,387)(271,401,388)(272,402,389)(273,403,390)(274,404,365)(275,405,366)(276,406,367)(277,407,368)(278,408,369)(279,409,370)(280,410,371)(281,411,372)(282,412,373)(283,413,374)(284,414,375)(285,415,376)(286,416,377)(287,430,326)(288,431,327)(289,432,328)(290,433,329)(291,434,330)(292,435,331)(293,436,332)(294,437,333)(295,438,334)(296,439,335)(297,440,336)(298,441,337)(299,442,338)(300,417,313)(301,418,314)(302,419,315)(303,420,316)(304,421,317)(305,422,318)(306,423,319)(307,424,320)(308,425,321)(309,426,322)(310,427,323)(311,428,324)(312,429,325), (1,53,32)(2,54,33)(3,55,34)(4,56,35)(5,57,36)(6,58,37)(7,59,38)(8,60,39)(9,61,40)(10,62,41)(11,63,42)(12,64,43)(13,65,44)(14,66,45)(15,67,46)(16,68,47)(17,69,48)(18,70,49)(19,71,50)(20,72,51)(21,73,52)(22,74,27)(23,75,28)(24,76,29)(25,77,30)(26,78,31)(79,142,124)(80,143,125)(81,144,126)(82,145,127)(83,146,128)(84,147,129)(85,148,130)(86,149,105)(87,150,106)(88,151,107)(89,152,108)(90,153,109)(91,154,110)(92,155,111)(93,156,112)(94,131,113)(95,132,114)(96,133,115)(97,134,116)(98,135,117)(99,136,118)(100,137,119)(101,138,120)(102,139,121)(103,140,122)(104,141,123)(157,224,198)(158,225,199)(159,226,200)(160,227,201)(161,228,202)(162,229,203)(163,230,204)(164,231,205)(165,232,206)(166,233,207)(167,234,208)(168,209,183)(169,210,184)(170,211,185)(171,212,186)(172,213,187)(173,214,188)(174,215,189)(175,216,190)(176,217,191)(177,218,192)(178,219,193)(179,220,194)(180,221,195)(181,222,196)(182,223,197)(235,287,274)(236,288,275)(237,289,276)(238,290,277)(239,291,278)(240,292,279)(241,293,280)(242,294,281)(243,295,282)(244,296,283)(245,297,284)(246,298,285)(247,299,286)(248,300,261)(249,301,262)(250,302,263)(251,303,264)(252,304,265)(253,305,266)(254,306,267)(255,307,268)(256,308,269)(257,309,270)(258,310,271)(259,311,272)(260,312,273)(313,378,339)(314,379,340)(315,380,341)(316,381,342)(317,382,343)(318,383,344)(319,384,345)(320,385,346)(321,386,347)(322,387,348)(323,388,349)(324,389,350)(325,390,351)(326,365,352)(327,366,353)(328,367,354)(329,368,355)(330,369,356)(331,370,357)(332,371,358)(333,372,359)(334,373,360)(335,374,361)(336,375,362)(337,376,363)(338,377,364)(391,443,417)(392,444,418)(393,445,419)(394,446,420)(395,447,421)(396,448,422)(397,449,423)(398,450,424)(399,451,425)(400,452,426)(401,453,427)(402,454,428)(403,455,429)(404,456,430)(405,457,431)(406,458,432)(407,459,433)(408,460,434)(409,461,435)(410,462,436)(411,463,437)(412,464,438)(413,465,439)(414,466,440)(415,467,441)(416,468,442), (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26)(27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52)(53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78)(79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104)(105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130)(131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156)(157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182)(183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208)(209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234)(235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260)(261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286)(287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312)(313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338)(339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364)(365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390)(391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416)(417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442)(443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468), (1,235,14,248)(2,260,15,247)(3,259,16,246)(4,258,17,245)(5,257,18,244)(6,256,19,243)(7,255,20,242)(8,254,21,241)(9,253,22,240)(10,252,23,239)(11,251,24,238)(12,250,25,237)(13,249,26,236)(27,279,40,266)(28,278,41,265)(29,277,42,264)(30,276,43,263)(31,275,44,262)(32,274,45,261)(33,273,46,286)(34,272,47,285)(35,271,48,284)(36,270,49,283)(37,269,50,282)(38,268,51,281)(39,267,52,280)(53,287,66,300)(54,312,67,299)(55,311,68,298)(56,310,69,297)(57,309,70,296)(58,308,71,295)(59,307,72,294)(60,306,73,293)(61,305,74,292)(62,304,75,291)(63,303,76,290)(64,302,77,289)(65,301,78,288)(79,316,92,329)(80,315,93,328)(81,314,94,327)(82,313,95,326)(83,338,96,325)(84,337,97,324)(85,336,98,323)(86,335,99,322)(87,334,100,321)(88,333,101,320)(89,332,102,319)(90,331,103,318)(91,330,104,317)(105,361,118,348)(106,360,119,347)(107,359,120,346)(108,358,121,345)(109,357,122,344)(110,356,123,343)(111,355,124,342)(112,354,125,341)(113,353,126,340)(114,352,127,339)(115,351,128,364)(116,350,129,363)(117,349,130,362)(131,366,144,379)(132,365,145,378)(133,390,146,377)(134,389,147,376)(135,388,148,375)(136,387,149,374)(137,386,150,373)(138,385,151,372)(139,384,152,371)(140,383,153,370)(141,382,154,369)(142,381,155,368)(143,380,156,367)(157,416,170,403)(158,415,171,402)(159,414,172,401)(160,413,173,400)(161,412,174,399)(162,411,175,398)(163,410,176,397)(164,409,177,396)(165,408,178,395)(166,407,179,394)(167,406,180,393)(168,405,181,392)(169,404,182,391)(183,431,196,418)(184,430,197,417)(185,429,198,442)(186,428,199,441)(187,427,200,440)(188,426,201,439)(189,425,202,438)(190,424,203,437)(191,423,204,436)(192,422,205,435)(193,421,206,434)(194,420,207,433)(195,419,208,432)(209,457,222,444)(210,456,223,443)(211,455,224,468)(212,454,225,467)(213,453,226,466)(214,452,227,465)(215,451,228,464)(216,450,229,463)(217,449,230,462)(218,448,231,461)(219,447,232,460)(220,446,233,459)(221,445,234,458) );

G=PermutationGroup([(1,210,114),(2,211,115),(3,212,116),(4,213,117),(5,214,118),(6,215,119),(7,216,120),(8,217,121),(9,218,122),(10,219,123),(11,220,124),(12,221,125),(13,222,126),(14,223,127),(15,224,128),(16,225,129),(17,226,130),(18,227,105),(19,228,106),(20,229,107),(21,230,108),(22,231,109),(23,232,110),(24,233,111),(25,234,112),(26,209,113),(27,164,153),(28,165,154),(29,166,155),(30,167,156),(31,168,131),(32,169,132),(33,170,133),(34,171,134),(35,172,135),(36,173,136),(37,174,137),(38,175,138),(39,176,139),(40,177,140),(41,178,141),(42,179,142),(43,180,143),(44,181,144),(45,182,145),(46,157,146),(47,158,147),(48,159,148),(49,160,149),(50,161,150),(51,162,151),(52,163,152),(53,184,95),(54,185,96),(55,186,97),(56,187,98),(57,188,99),(58,189,100),(59,190,101),(60,191,102),(61,192,103),(62,193,104),(63,194,79),(64,195,80),(65,196,81),(66,197,82),(67,198,83),(68,199,84),(69,200,85),(70,201,86),(71,202,87),(72,203,88),(73,204,89),(74,205,90),(75,206,91),(76,207,92),(77,208,93),(78,183,94),(235,456,352),(236,457,353),(237,458,354),(238,459,355),(239,460,356),(240,461,357),(241,462,358),(242,463,359),(243,464,360),(244,465,361),(245,466,362),(246,467,363),(247,468,364),(248,443,339),(249,444,340),(250,445,341),(251,446,342),(252,447,343),(253,448,344),(254,449,345),(255,450,346),(256,451,347),(257,452,348),(258,453,349),(259,454,350),(260,455,351),(261,391,378),(262,392,379),(263,393,380),(264,394,381),(265,395,382),(266,396,383),(267,397,384),(268,398,385),(269,399,386),(270,400,387),(271,401,388),(272,402,389),(273,403,390),(274,404,365),(275,405,366),(276,406,367),(277,407,368),(278,408,369),(279,409,370),(280,410,371),(281,411,372),(282,412,373),(283,413,374),(284,414,375),(285,415,376),(286,416,377),(287,430,326),(288,431,327),(289,432,328),(290,433,329),(291,434,330),(292,435,331),(293,436,332),(294,437,333),(295,438,334),(296,439,335),(297,440,336),(298,441,337),(299,442,338),(300,417,313),(301,418,314),(302,419,315),(303,420,316),(304,421,317),(305,422,318),(306,423,319),(307,424,320),(308,425,321),(309,426,322),(310,427,323),(311,428,324),(312,429,325)], [(1,53,32),(2,54,33),(3,55,34),(4,56,35),(5,57,36),(6,58,37),(7,59,38),(8,60,39),(9,61,40),(10,62,41),(11,63,42),(12,64,43),(13,65,44),(14,66,45),(15,67,46),(16,68,47),(17,69,48),(18,70,49),(19,71,50),(20,72,51),(21,73,52),(22,74,27),(23,75,28),(24,76,29),(25,77,30),(26,78,31),(79,142,124),(80,143,125),(81,144,126),(82,145,127),(83,146,128),(84,147,129),(85,148,130),(86,149,105),(87,150,106),(88,151,107),(89,152,108),(90,153,109),(91,154,110),(92,155,111),(93,156,112),(94,131,113),(95,132,114),(96,133,115),(97,134,116),(98,135,117),(99,136,118),(100,137,119),(101,138,120),(102,139,121),(103,140,122),(104,141,123),(157,224,198),(158,225,199),(159,226,200),(160,227,201),(161,228,202),(162,229,203),(163,230,204),(164,231,205),(165,232,206),(166,233,207),(167,234,208),(168,209,183),(169,210,184),(170,211,185),(171,212,186),(172,213,187),(173,214,188),(174,215,189),(175,216,190),(176,217,191),(177,218,192),(178,219,193),(179,220,194),(180,221,195),(181,222,196),(182,223,197),(235,287,274),(236,288,275),(237,289,276),(238,290,277),(239,291,278),(240,292,279),(241,293,280),(242,294,281),(243,295,282),(244,296,283),(245,297,284),(246,298,285),(247,299,286),(248,300,261),(249,301,262),(250,302,263),(251,303,264),(252,304,265),(253,305,266),(254,306,267),(255,307,268),(256,308,269),(257,309,270),(258,310,271),(259,311,272),(260,312,273),(313,378,339),(314,379,340),(315,380,341),(316,381,342),(317,382,343),(318,383,344),(319,384,345),(320,385,346),(321,386,347),(322,387,348),(323,388,349),(324,389,350),(325,390,351),(326,365,352),(327,366,353),(328,367,354),(329,368,355),(330,369,356),(331,370,357),(332,371,358),(333,372,359),(334,373,360),(335,374,361),(336,375,362),(337,376,363),(338,377,364),(391,443,417),(392,444,418),(393,445,419),(394,446,420),(395,447,421),(396,448,422),(397,449,423),(398,450,424),(399,451,425),(400,452,426),(401,453,427),(402,454,428),(403,455,429),(404,456,430),(405,457,431),(406,458,432),(407,459,433),(408,460,434),(409,461,435),(410,462,436),(411,463,437),(412,464,438),(413,465,439),(414,466,440),(415,467,441),(416,468,442)], [(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26),(27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52),(53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78),(79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104),(105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130),(131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156),(157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182),(183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208),(209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234),(235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260),(261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286),(287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312),(313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338),(339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364),(365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390),(391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416),(417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442),(443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468)], [(1,235,14,248),(2,260,15,247),(3,259,16,246),(4,258,17,245),(5,257,18,244),(6,256,19,243),(7,255,20,242),(8,254,21,241),(9,253,22,240),(10,252,23,239),(11,251,24,238),(12,250,25,237),(13,249,26,236),(27,279,40,266),(28,278,41,265),(29,277,42,264),(30,276,43,263),(31,275,44,262),(32,274,45,261),(33,273,46,286),(34,272,47,285),(35,271,48,284),(36,270,49,283),(37,269,50,282),(38,268,51,281),(39,267,52,280),(53,287,66,300),(54,312,67,299),(55,311,68,298),(56,310,69,297),(57,309,70,296),(58,308,71,295),(59,307,72,294),(60,306,73,293),(61,305,74,292),(62,304,75,291),(63,303,76,290),(64,302,77,289),(65,301,78,288),(79,316,92,329),(80,315,93,328),(81,314,94,327),(82,313,95,326),(83,338,96,325),(84,337,97,324),(85,336,98,323),(86,335,99,322),(87,334,100,321),(88,333,101,320),(89,332,102,319),(90,331,103,318),(91,330,104,317),(105,361,118,348),(106,360,119,347),(107,359,120,346),(108,358,121,345),(109,357,122,344),(110,356,123,343),(111,355,124,342),(112,354,125,341),(113,353,126,340),(114,352,127,339),(115,351,128,364),(116,350,129,363),(117,349,130,362),(131,366,144,379),(132,365,145,378),(133,390,146,377),(134,389,147,376),(135,388,148,375),(136,387,149,374),(137,386,150,373),(138,385,151,372),(139,384,152,371),(140,383,153,370),(141,382,154,369),(142,381,155,368),(143,380,156,367),(157,416,170,403),(158,415,171,402),(159,414,172,401),(160,413,173,400),(161,412,174,399),(162,411,175,398),(163,410,176,397),(164,409,177,396),(165,408,178,395),(166,407,179,394),(167,406,180,393),(168,405,181,392),(169,404,182,391),(183,431,196,418),(184,430,197,417),(185,429,198,442),(186,428,199,441),(187,427,200,440),(188,426,201,439),(189,425,202,438),(190,424,203,437),(191,423,204,436),(192,422,205,435),(193,421,206,434),(194,420,207,433),(195,419,208,432),(209,457,222,444),(210,456,223,443),(211,455,224,468),(212,454,225,467),(213,453,226,466),(214,452,227,465),(215,451,228,464),(216,450,229,463),(217,449,230,462),(218,448,231,461),(219,447,232,460),(220,446,233,459),(221,445,234,458)])

144 conjugacy classes

class 1  2 3A···3H4A4B6A···6H12A···12P13A···13F26A···26F39A···39AV78A···78AV
order123···3446···612···1213···1326···2639···3978···78
size111···113131···113···132···22···22···22···2

144 irreducible representations

dim1111112222
type+++-
imageC1C2C3C4C6C12D13Dic13C3×D13C3×Dic13
kernelC32×Dic13C3×C78C3×Dic13C3×C39C78C39C3×C6C32C6C3
# reps1182816664848

Matrix representation of C32×Dic13 in GL3(𝔽157) generated by

1200
01440
00144
,
100
01440
00144
,
15600
001
0156124
,
2800
094136
01763
G:=sub<GL(3,GF(157))| [12,0,0,0,144,0,0,0,144],[1,0,0,0,144,0,0,0,144],[156,0,0,0,0,156,0,1,124],[28,0,0,0,94,17,0,136,63] >;

C32×Dic13 in GAP, Magma, Sage, TeX

C_3^2\times {\rm Dic}_{13}
% in TeX

G:=Group("C3^2xDic13");
// GroupNames label

G:=SmallGroup(468,23);
// by ID

G=gap.SmallGroup(468,23);
# by ID

G:=PCGroup([5,-2,-3,-3,-2,-13,90,10804]);
// Polycyclic

G:=Group<a,b,c,d|a^3=b^3=c^26=1,d^2=c^13,a*b=b*a,a*c=c*a,a*d=d*a,b*c=c*b,b*d=d*b,d*c*d^-1=c^-1>;
// generators/relations

Export

Subgroup lattice of C32×Dic13 in TeX

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×
𝔽