Copied to
clipboard

## G = Q8×C32×C6order 432 = 24·33

### Direct product of C32×C6 and Q8

direct product, metabelian, nilpotent (class 2), monomial

Series: Derived Chief Lower central Upper central

 Derived series C1 — C2 — Q8×C32×C6
 Chief series C1 — C2 — C6 — C3×C6 — C32×C6 — C32×C12 — Q8×C33 — Q8×C32×C6
 Lower central C1 — C2 — Q8×C32×C6
 Upper central C1 — C3×C62 — Q8×C32×C6

Generators and relations for Q8×C32×C6
G = < a,b,c,d,e | a3=b3=c6=d4=1, e2=d2, ab=ba, ac=ca, ad=da, ae=ea, bc=cb, bd=db, be=eb, cd=dc, ce=ec, ede-1=d-1 >

Subgroups: 532, all normal (8 characteristic)
C1, C2, C2, C3, C4, C22, C6, C2×C4, Q8, C32, C12, C2×C6, C2×Q8, C3×C6, C2×C12, C3×Q8, C33, C3×C12, C62, C6×Q8, C32×C6, C32×C6, C6×C12, Q8×C32, C32×C12, C3×C62, Q8×C3×C6, C3×C6×C12, Q8×C33, Q8×C32×C6
Quotients: C1, C2, C3, C22, C6, Q8, C23, C32, C2×C6, C2×Q8, C3×C6, C3×Q8, C22×C6, C33, C62, C6×Q8, C32×C6, Q8×C32, C2×C62, C3×C62, Q8×C3×C6, Q8×C33, C63, Q8×C32×C6

Smallest permutation representation of Q8×C32×C6
Regular action on 432 points
Generators in S432
(1 112 48)(2 113 43)(3 114 44)(4 109 45)(5 110 46)(6 111 47)(7 33 23)(8 34 24)(9 35 19)(10 36 20)(11 31 21)(12 32 22)(13 84 68)(14 79 69)(15 80 70)(16 81 71)(17 82 72)(18 83 67)(25 78 62)(26 73 63)(27 74 64)(28 75 65)(29 76 66)(30 77 61)(37 104 94)(38 105 95)(39 106 96)(40 107 91)(41 108 92)(42 103 93)(49 98 88)(50 99 89)(51 100 90)(52 101 85)(53 102 86)(54 97 87)(55 372 356)(56 367 357)(57 368 358)(58 369 359)(59 370 360)(60 371 355)(115 182 131)(116 183 132)(117 184 127)(118 185 128)(119 186 129)(120 181 130)(121 170 137)(122 171 138)(123 172 133)(124 173 134)(125 174 135)(126 169 136)(139 219 155)(140 220 156)(141 221 151)(142 222 152)(143 217 153)(144 218 154)(145 212 202)(146 213 203)(147 214 204)(148 215 199)(149 216 200)(150 211 201)(157 206 196)(158 207 197)(159 208 198)(160 209 193)(161 210 194)(162 205 195)(163 189 179)(164 190 180)(165 191 175)(166 192 176)(167 187 177)(168 188 178)(223 290 239)(224 291 240)(225 292 235)(226 293 236)(227 294 237)(228 289 238)(229 278 245)(230 279 246)(231 280 241)(232 281 242)(233 282 243)(234 277 244)(247 327 263)(248 328 264)(249 329 259)(250 330 260)(251 325 261)(252 326 262)(253 320 310)(254 321 311)(255 322 312)(256 323 307)(257 324 308)(258 319 309)(265 314 304)(266 315 305)(267 316 306)(268 317 301)(269 318 302)(270 313 303)(271 297 287)(272 298 288)(273 299 283)(274 300 284)(275 295 285)(276 296 286)(331 398 347)(332 399 348)(333 400 343)(334 401 344)(335 402 345)(336 397 346)(337 386 353)(338 387 354)(339 388 349)(340 389 350)(341 390 351)(342 385 352)(361 428 418)(362 429 419)(363 430 420)(364 431 415)(365 432 416)(366 427 417)(373 422 412)(374 423 413)(375 424 414)(376 425 409)(377 426 410)(378 421 411)(379 405 395)(380 406 396)(381 407 391)(382 408 392)(383 403 393)(384 404 394)
(1 38 85)(2 39 86)(3 40 87)(4 41 88)(5 42 89)(6 37 90)(7 13 64)(8 14 65)(9 15 66)(10 16 61)(11 17 62)(12 18 63)(19 70 76)(20 71 77)(21 72 78)(22 67 73)(23 68 74)(24 69 75)(25 31 82)(26 32 83)(27 33 84)(28 34 79)(29 35 80)(30 36 81)(43 96 102)(44 91 97)(45 92 98)(46 93 99)(47 94 100)(48 95 101)(49 109 108)(50 110 103)(51 111 104)(52 112 105)(53 113 106)(54 114 107)(55 429 376)(56 430 377)(57 431 378)(58 432 373)(59 427 374)(60 428 375)(115 168 174)(116 163 169)(117 164 170)(118 165 171)(119 166 172)(120 167 173)(121 127 180)(122 128 175)(123 129 176)(124 130 177)(125 131 178)(126 132 179)(133 186 192)(134 181 187)(135 182 188)(136 183 189)(137 184 190)(138 185 191)(139 145 198)(140 146 193)(141 147 194)(142 148 195)(143 149 196)(144 150 197)(151 204 210)(152 199 205)(153 200 206)(154 201 207)(155 202 208)(156 203 209)(157 217 216)(158 218 211)(159 219 212)(160 220 213)(161 221 214)(162 222 215)(223 276 282)(224 271 277)(225 272 278)(226 273 279)(227 274 280)(228 275 281)(229 235 288)(230 236 283)(231 237 284)(232 238 285)(233 239 286)(234 240 287)(241 294 300)(242 289 295)(243 290 296)(244 291 297)(245 292 298)(246 293 299)(247 253 306)(248 254 301)(249 255 302)(250 256 303)(251 257 304)(252 258 305)(259 312 318)(260 307 313)(261 308 314)(262 309 315)(263 310 316)(264 311 317)(265 325 324)(266 326 319)(267 327 320)(268 328 321)(269 329 322)(270 330 323)(331 384 390)(332 379 385)(333 380 386)(334 381 387)(335 382 388)(336 383 389)(337 343 396)(338 344 391)(339 345 392)(340 346 393)(341 347 394)(342 348 395)(349 402 408)(350 397 403)(351 398 404)(352 399 405)(353 400 406)(354 401 407)(355 361 414)(356 362 409)(357 363 410)(358 364 411)(359 365 412)(360 366 413)(367 420 426)(368 415 421)(369 416 422)(370 417 423)(371 418 424)(372 419 425)
(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)
(1 143 10 163)(2 144 11 164)(3 139 12 165)(4 140 7 166)(5 141 8 167)(6 142 9 168)(13 172 41 146)(14 173 42 147)(15 174 37 148)(16 169 38 149)(17 170 39 150)(18 171 40 145)(19 178 47 152)(20 179 48 153)(21 180 43 154)(22 175 44 155)(23 176 45 156)(24 177 46 151)(25 184 53 158)(26 185 54 159)(27 186 49 160)(28 181 50 161)(29 182 51 162)(30 183 52 157)(31 190 113 218)(32 191 114 219)(33 192 109 220)(34 187 110 221)(35 188 111 222)(36 189 112 217)(55 325 408 297)(56 326 403 298)(57 327 404 299)(58 328 405 300)(59 329 406 295)(60 330 407 296)(61 116 85 196)(62 117 86 197)(63 118 87 198)(64 119 88 193)(65 120 89 194)(66 115 90 195)(67 122 91 202)(68 123 92 203)(69 124 93 204)(70 125 94 199)(71 126 95 200)(72 121 96 201)(73 128 97 208)(74 129 98 209)(75 130 99 210)(76 131 100 205)(77 132 101 206)(78 127 102 207)(79 134 103 214)(80 135 104 215)(81 136 105 216)(82 137 106 211)(83 138 107 212)(84 133 108 213)(223 414 303 334)(224 409 304 335)(225 410 305 336)(226 411 306 331)(227 412 301 332)(228 413 302 333)(229 420 309 340)(230 415 310 341)(231 416 311 342)(232 417 312 337)(233 418 307 338)(234 419 308 339)(235 426 315 346)(236 421 316 347)(237 422 317 348)(238 423 318 343)(239 424 313 344)(240 425 314 345)(241 432 321 352)(242 427 322 353)(243 428 323 354)(244 429 324 349)(245 430 319 350)(246 431 320 351)(247 384 273 358)(248 379 274 359)(249 380 275 360)(250 381 276 355)(251 382 271 356)(252 383 272 357)(253 390 279 364)(254 385 280 365)(255 386 281 366)(256 387 282 361)(257 388 277 362)(258 389 278 363)(259 396 285 370)(260 391 286 371)(261 392 287 372)(262 393 288 367)(263 394 283 368)(264 395 284 369)(265 402 291 376)(266 397 292 377)(267 398 293 378)(268 399 294 373)(269 400 289 374)(270 401 290 375)
(1 251 10 271)(2 252 11 272)(3 247 12 273)(4 248 7 274)(5 249 8 275)(6 250 9 276)(13 280 41 254)(14 281 42 255)(15 282 37 256)(16 277 38 257)(17 278 39 258)(18 279 40 253)(19 286 47 260)(20 287 48 261)(21 288 43 262)(22 283 44 263)(23 284 45 264)(24 285 46 259)(25 292 53 266)(26 293 54 267)(27 294 49 268)(28 289 50 269)(29 290 51 270)(30 291 52 265)(31 298 113 326)(32 299 114 327)(33 300 109 328)(34 295 110 329)(35 296 111 330)(36 297 112 325)(55 189 408 217)(56 190 403 218)(57 191 404 219)(58 192 405 220)(59 187 406 221)(60 188 407 222)(61 224 85 304)(62 225 86 305)(63 226 87 306)(64 227 88 301)(65 228 89 302)(66 223 90 303)(67 230 91 310)(68 231 92 311)(69 232 93 312)(70 233 94 307)(71 234 95 308)(72 229 96 309)(73 236 97 316)(74 237 98 317)(75 238 99 318)(76 239 100 313)(77 240 101 314)(78 235 102 315)(79 242 103 322)(80 243 104 323)(81 244 105 324)(82 245 106 319)(83 246 107 320)(84 241 108 321)(115 334 195 414)(116 335 196 409)(117 336 197 410)(118 331 198 411)(119 332 193 412)(120 333 194 413)(121 340 201 420)(122 341 202 415)(123 342 203 416)(124 337 204 417)(125 338 199 418)(126 339 200 419)(127 346 207 426)(128 347 208 421)(129 348 209 422)(130 343 210 423)(131 344 205 424)(132 345 206 425)(133 352 213 432)(134 353 214 427)(135 354 215 428)(136 349 216 429)(137 350 211 430)(138 351 212 431)(139 358 165 384)(140 359 166 379)(141 360 167 380)(142 355 168 381)(143 356 163 382)(144 357 164 383)(145 364 171 390)(146 365 172 385)(147 366 173 386)(148 361 174 387)(149 362 169 388)(150 363 170 389)(151 370 177 396)(152 371 178 391)(153 372 179 392)(154 367 180 393)(155 368 175 394)(156 369 176 395)(157 376 183 402)(158 377 184 397)(159 378 185 398)(160 373 186 399)(161 374 181 400)(162 375 182 401)

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

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

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

270 conjugacy classes

 class 1 2A 2B 2C 3A ··· 3Z 4A ··· 4F 6A ··· 6BZ 12A ··· 12EZ order 1 2 2 2 3 ··· 3 4 ··· 4 6 ··· 6 12 ··· 12 size 1 1 1 1 1 ··· 1 2 ··· 2 1 ··· 1 2 ··· 2

270 irreducible representations

 dim 1 1 1 1 1 1 2 2 type + + + - image C1 C2 C2 C3 C6 C6 Q8 C3×Q8 kernel Q8×C32×C6 C3×C6×C12 Q8×C33 Q8×C3×C6 C6×C12 Q8×C32 C32×C6 C3×C6 # reps 1 3 4 26 78 104 2 52

Matrix representation of Q8×C32×C6 in GL4(𝔽13) generated by

 1 0 0 0 0 1 0 0 0 0 9 0 0 0 0 9
,
 3 0 0 0 0 9 0 0 0 0 3 0 0 0 0 3
,
 10 0 0 0 0 3 0 0 0 0 9 0 0 0 0 9
,
 1 0 0 0 0 12 0 0 0 0 8 0 0 0 0 5
,
 1 0 0 0 0 1 0 0 0 0 0 12 0 0 1 0
G:=sub<GL(4,GF(13))| [1,0,0,0,0,1,0,0,0,0,9,0,0,0,0,9],[3,0,0,0,0,9,0,0,0,0,3,0,0,0,0,3],[10,0,0,0,0,3,0,0,0,0,9,0,0,0,0,9],[1,0,0,0,0,12,0,0,0,0,8,0,0,0,0,5],[1,0,0,0,0,1,0,0,0,0,0,1,0,0,12,0] >;

Q8×C32×C6 in GAP, Magma, Sage, TeX

Q_8\times C_3^2\times C_6
% in TeX

G:=Group("Q8xC3^2xC6");
// GroupNames label

G:=SmallGroup(432,732);
// by ID

G=gap.SmallGroup(432,732);
# by ID

G:=PCGroup([7,-2,-2,-2,-3,-3,-3,-2,1512,3053,1520]);
// Polycyclic

G:=Group<a,b,c,d,e|a^3=b^3=c^6=d^4=1,e^2=d^2,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,b*c=c*b,b*d=d*b,b*e=e*b,c*d=d*c,c*e=e*c,e*d*e^-1=d^-1>;
// generators/relations

׿
×
𝔽