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## G = C2×C33⋊8Q8order 432 = 24·33

### Direct product of C2 and C33⋊8Q8

Series: Derived Chief Lower central Upper central

 Derived series C1 — C32×C6 — C2×C33⋊8Q8
 Chief series C1 — C3 — C32 — C33 — C32×C6 — C33⋊5C4 — C2×C33⋊5C4 — C2×C33⋊8Q8
 Lower central C33 — C32×C6 — C2×C33⋊8Q8
 Upper central C1 — C22 — C2×C4

Generators and relations for C2×C338Q8
G = < a,b,c,d,e,f | a2=b3=c3=d3=e4=1, f2=e2, ab=ba, ac=ca, ad=da, ae=ea, af=fa, bc=cb, bd=db, be=eb, fbf-1=b-1, cd=dc, ce=ec, fcf-1=c-1, de=ed, fdf-1=d-1, fef-1=e-1 >

Subgroups: 2248 in 532 conjugacy classes, 235 normal (9 characteristic)
C1, C2, C2, C3, C4, C4, C22, C6, C2×C4, C2×C4, Q8, C32, Dic3, C12, C2×C6, C2×Q8, C3×C6, Dic6, C2×Dic3, C2×C12, C33, C3⋊Dic3, C3×C12, C62, C2×Dic6, C32×C6, C32×C6, C324Q8, C2×C3⋊Dic3, C6×C12, C335C4, C32×C12, C3×C62, C2×C324Q8, C338Q8, C2×C335C4, C3×C6×C12, C2×C338Q8
Quotients: C1, C2, C22, S3, Q8, C23, D6, C2×Q8, C3⋊S3, Dic6, C22×S3, C2×C3⋊S3, C2×Dic6, C33⋊C2, C324Q8, C22×C3⋊S3, C2×C33⋊C2, C2×C324Q8, C338Q8, C22×C33⋊C2, C2×C338Q8

Smallest permutation representation of C2×C338Q8
Regular action on 432 points
Generators in S432
(1 148)(2 145)(3 146)(4 147)(5 143)(6 144)(7 141)(8 142)(9 198)(10 199)(11 200)(12 197)(13 202)(14 203)(15 204)(16 201)(17 206)(18 207)(19 208)(20 205)(21 210)(22 211)(23 212)(24 209)(25 382)(26 383)(27 384)(28 381)(29 115)(30 116)(31 113)(32 114)(33 176)(34 173)(35 174)(36 175)(37 180)(38 177)(39 178)(40 179)(41 184)(42 181)(43 182)(44 183)(45 188)(46 185)(47 186)(48 187)(49 192)(50 189)(51 190)(52 191)(53 356)(54 353)(55 354)(56 355)(57 169)(58 170)(59 171)(60 172)(61 193)(62 194)(63 195)(64 196)(65 123)(66 124)(67 121)(68 122)(69 127)(70 128)(71 125)(72 126)(73 131)(74 132)(75 129)(76 130)(77 135)(78 136)(79 133)(80 134)(81 326)(82 327)(83 328)(84 325)(85 119)(86 120)(87 117)(88 118)(89 151)(90 152)(91 149)(92 150)(93 155)(94 156)(95 153)(96 154)(97 159)(98 160)(99 157)(100 158)(101 163)(102 164)(103 161)(104 162)(105 213)(106 214)(107 215)(108 216)(109 248)(110 245)(111 246)(112 247)(137 218)(138 219)(139 220)(140 217)(165 273)(166 274)(167 275)(168 276)(221 329)(222 330)(223 331)(224 332)(225 333)(226 334)(227 335)(228 336)(229 337)(230 338)(231 339)(232 340)(233 341)(234 342)(235 343)(236 344)(237 345)(238 346)(239 347)(240 348)(241 349)(242 350)(243 351)(244 352)(249 357)(250 358)(251 359)(252 360)(253 361)(254 362)(255 363)(256 364)(257 365)(258 366)(259 367)(260 368)(261 369)(262 370)(263 371)(264 372)(265 373)(266 374)(267 375)(268 376)(269 377)(270 378)(271 379)(272 380)(277 385)(278 386)(279 387)(280 388)(281 389)(282 390)(283 391)(284 392)(285 393)(286 394)(287 395)(288 396)(289 397)(290 398)(291 399)(292 400)(293 401)(294 402)(295 403)(296 404)(297 405)(298 406)(299 407)(300 408)(301 409)(302 410)(303 411)(304 412)(305 413)(306 414)(307 415)(308 416)(309 417)(310 418)(311 419)(312 420)(313 421)(314 422)(315 423)(316 424)(317 425)(318 426)(319 427)(320 428)(321 429)(322 430)(323 431)(324 432)
(1 110 20)(2 111 17)(3 112 18)(4 109 19)(5 77 14)(6 78 15)(7 79 16)(8 80 13)(9 168 74)(10 165 75)(11 166 76)(12 167 73)(21 91 58)(22 92 59)(23 89 60)(24 90 57)(25 414 373)(26 415 374)(27 416 375)(28 413 376)(29 97 40)(30 98 37)(31 99 38)(32 100 39)(33 106 96)(34 107 93)(35 108 94)(36 105 95)(41 87 101)(42 88 102)(43 85 103)(44 86 104)(45 65 139)(46 66 140)(47 67 137)(48 68 138)(49 71 64)(50 72 61)(51 69 62)(52 70 63)(53 334 424)(54 335 421)(55 336 422)(56 333 423)(81 366 402)(82 367 403)(83 368 404)(84 365 401)(113 157 177)(114 158 178)(115 159 179)(116 160 180)(117 163 184)(118 164 181)(119 161 182)(120 162 183)(121 218 186)(122 219 187)(123 220 188)(124 217 185)(125 196 192)(126 193 189)(127 194 190)(128 195 191)(129 199 273)(130 200 274)(131 197 275)(132 198 276)(133 201 141)(134 202 142)(135 203 143)(136 204 144)(145 246 206)(146 247 207)(147 248 208)(148 245 205)(149 170 210)(150 171 211)(151 172 212)(152 169 209)(153 175 213)(154 176 214)(155 173 215)(156 174 216)(221 312 269)(222 309 270)(223 310 271)(224 311 272)(225 315 355)(226 316 356)(227 313 353)(228 314 354)(229 319 277)(230 320 278)(231 317 279)(232 318 280)(233 324 284)(234 321 281)(235 322 282)(236 323 283)(237 249 286)(238 250 287)(239 251 288)(240 252 285)(241 255 289)(242 256 290)(243 253 291)(244 254 292)(257 293 325)(258 294 326)(259 295 327)(260 296 328)(261 299 301)(262 300 302)(263 297 303)(264 298 304)(265 382 306)(266 383 307)(267 384 308)(268 381 305)(329 420 377)(330 417 378)(331 418 379)(332 419 380)(337 427 385)(338 428 386)(339 425 387)(340 426 388)(341 432 392)(342 429 389)(343 430 390)(344 431 391)(345 357 394)(346 358 395)(347 359 396)(348 360 393)(349 363 397)(350 364 398)(351 361 399)(352 362 400)(369 407 409)(370 408 410)(371 405 411)(372 406 412)
(1 49 29)(2 50 30)(3 51 31)(4 52 32)(5 48 108)(6 45 105)(7 46 106)(8 47 107)(9 43 57)(10 44 58)(11 41 59)(12 42 60)(13 137 34)(14 138 35)(15 139 36)(16 140 33)(17 61 37)(18 62 38)(19 63 39)(20 64 40)(21 165 86)(22 166 87)(23 167 88)(24 168 85)(25 427 362)(26 428 363)(27 425 364)(28 426 361)(53 347 369)(54 348 370)(55 345 371)(56 346 372)(65 95 78)(66 96 79)(67 93 80)(68 94 77)(69 99 112)(70 100 109)(71 97 110)(72 98 111)(73 102 89)(74 103 90)(75 104 91)(76 101 92)(81 420 391)(82 417 392)(83 418 389)(84 419 390)(113 146 190)(114 147 191)(115 148 192)(116 145 189)(117 211 274)(118 212 275)(119 209 276)(120 210 273)(121 155 134)(122 156 135)(123 153 136)(124 154 133)(125 159 245)(126 160 246)(127 157 247)(128 158 248)(129 162 149)(130 163 150)(131 164 151)(132 161 152)(141 185 214)(142 186 215)(143 187 216)(144 188 213)(169 198 182)(170 199 183)(171 200 184)(172 197 181)(173 202 218)(174 203 219)(175 204 220)(176 201 217)(177 207 194)(178 208 195)(179 205 196)(180 206 193)(221 323 294)(222 324 295)(223 321 296)(224 322 293)(225 250 298)(226 251 299)(227 252 300)(228 249 297)(229 244 265)(230 241 266)(231 242 267)(232 243 268)(233 259 270)(234 260 271)(235 257 272)(236 258 269)(237 263 354)(238 264 355)(239 261 356)(240 262 353)(253 381 318)(254 382 319)(255 383 320)(256 384 317)(277 292 306)(278 289 307)(279 290 308)(280 291 305)(281 328 310)(282 325 311)(283 326 312)(284 327 309)(285 302 313)(286 303 314)(287 304 315)(288 301 316)(329 431 402)(330 432 403)(331 429 404)(332 430 401)(333 358 406)(334 359 407)(335 360 408)(336 357 405)(337 352 373)(338 349 374)(339 350 375)(340 351 376)(341 367 378)(342 368 379)(343 365 380)(344 366 377)(385 400 414)(386 397 415)(387 398 416)(388 399 413)(393 410 421)(394 411 422)(395 412 423)(396 409 424)
(1 80 43)(2 77 44)(3 78 41)(4 79 42)(5 104 17)(6 101 18)(7 102 19)(8 103 20)(9 29 93)(10 30 94)(11 31 95)(12 32 96)(13 85 110)(14 86 111)(15 87 112)(16 88 109)(21 72 138)(22 69 139)(23 70 140)(24 71 137)(25 389 346)(26 390 347)(27 391 348)(28 392 345)(33 167 100)(34 168 97)(35 165 98)(36 166 99)(37 108 75)(38 105 76)(39 106 73)(40 107 74)(45 92 62)(46 89 63)(47 90 64)(48 91 61)(49 67 57)(50 68 58)(51 65 59)(52 66 60)(53 363 419)(54 364 420)(55 361 417)(56 362 418)(81 370 425)(82 371 426)(83 372 427)(84 369 428)(113 153 200)(114 154 197)(115 155 198)(116 156 199)(117 247 204)(118 248 201)(119 245 202)(120 246 203)(121 169 192)(122 170 189)(123 171 190)(124 172 191)(125 218 209)(126 219 210)(127 220 211)(128 217 212)(129 180 216)(130 177 213)(131 178 214)(132 179 215)(133 181 147)(134 182 148)(135 183 145)(136 184 146)(141 164 208)(142 161 205)(143 162 206)(144 163 207)(149 193 187)(150 194 188)(151 195 185)(152 196 186)(157 175 274)(158 176 275)(159 173 276)(160 174 273)(221 313 242)(222 314 243)(223 315 244)(224 316 241)(225 292 271)(226 289 272)(227 290 269)(228 291 270)(229 296 304)(230 293 301)(231 294 302)(232 295 303)(233 249 305)(234 250 306)(235 251 307)(236 252 308)(237 381 284)(238 382 281)(239 383 282)(240 384 283)(253 309 354)(254 310 355)(255 311 356)(256 312 353)(257 299 278)(258 300 279)(259 297 280)(260 298 277)(261 320 325)(262 317 326)(263 318 327)(264 319 328)(265 321 287)(266 322 288)(267 323 285)(268 324 286)(329 421 350)(330 422 351)(331 423 352)(332 424 349)(333 400 379)(334 397 380)(335 398 377)(336 399 378)(337 404 412)(338 401 409)(339 402 410)(340 403 411)(341 357 413)(342 358 414)(343 359 415)(344 360 416)(365 407 386)(366 408 387)(367 405 388)(368 406 385)(373 429 395)(374 430 396)(375 431 393)(376 432 394)
(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)
(1 227 3 225)(2 226 4 228)(5 224 7 222)(6 223 8 221)(9 308 11 306)(10 307 12 305)(13 312 15 310)(14 311 16 309)(17 316 19 314)(18 315 20 313)(21 320 23 318)(22 319 24 317)(25 276 27 274)(26 275 28 273)(29 252 31 250)(30 251 32 249)(33 284 35 282)(34 283 36 281)(37 288 39 286)(38 287 40 285)(41 292 43 290)(42 291 44 289)(45 296 47 294)(46 295 48 293)(49 300 51 298)(50 299 52 297)(53 248 55 246)(54 247 56 245)(57 279 59 277)(58 278 60 280)(61 301 63 303)(62 304 64 302)(65 260 67 258)(66 259 68 257)(69 264 71 262)(70 263 72 261)(73 268 75 266)(74 267 76 265)(77 272 79 270)(78 271 80 269)(81 220 83 218)(82 219 84 217)(85 256 87 254)(86 255 88 253)(89 232 91 230)(90 231 92 229)(93 236 95 234)(94 235 96 233)(97 240 99 238)(98 239 100 237)(101 244 103 242)(102 243 104 241)(105 321 107 323)(106 324 108 322)(109 354 111 356)(110 353 112 355)(113 358 115 360)(114 357 116 359)(117 362 119 364)(118 361 120 363)(121 366 123 368)(122 365 124 367)(125 370 127 372)(126 369 128 371)(129 374 131 376)(130 373 132 375)(133 378 135 380)(134 377 136 379)(137 326 139 328)(138 325 140 327)(141 330 143 332)(142 329 144 331)(145 334 147 336)(146 333 148 335)(149 338 151 340)(150 337 152 339)(153 342 155 344)(154 341 156 343)(157 346 159 348)(158 345 160 347)(161 350 163 352)(162 349 164 351)(165 383 167 381)(166 382 168 384)(169 387 171 385)(170 386 172 388)(173 391 175 389)(174 390 176 392)(177 395 179 393)(178 394 180 396)(181 399 183 397)(182 398 184 400)(185 403 187 401)(186 402 188 404)(189 407 191 405)(190 406 192 408)(193 409 195 411)(194 412 196 410)(197 413 199 415)(198 416 200 414)(201 417 203 419)(202 420 204 418)(205 421 207 423)(206 424 208 422)(209 425 211 427)(210 428 212 426)(213 429 215 431)(214 432 216 430)

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

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

114 conjugacy classes

 class 1 2A 2B 2C 3A ··· 3M 4A 4B 4C 4D 4E 4F 6A ··· 6AM 12A ··· 12AZ order 1 2 2 2 3 ··· 3 4 4 4 4 4 4 6 ··· 6 12 ··· 12 size 1 1 1 1 2 ··· 2 2 2 54 54 54 54 2 ··· 2 2 ··· 2

114 irreducible representations

 dim 1 1 1 1 2 2 2 2 2 type + + + + + - + + - image C1 C2 C2 C2 S3 Q8 D6 D6 Dic6 kernel C2×C33⋊8Q8 C33⋊8Q8 C2×C33⋊5C4 C3×C6×C12 C6×C12 C32×C6 C3×C12 C62 C3×C6 # reps 1 4 2 1 13 2 26 13 52

Matrix representation of C2×C338Q8 in GL6(𝔽13)

 12 0 0 0 0 0 0 12 0 0 0 0 0 0 12 0 0 0 0 0 0 12 0 0 0 0 0 0 12 0 0 0 0 0 0 12
,
 9 0 0 0 0 0 0 3 0 0 0 0 0 0 9 0 0 0 0 0 0 3 0 0 0 0 0 0 3 0 0 0 0 0 9 9
,
 3 0 0 0 0 0 0 9 0 0 0 0 0 0 3 0 0 0 0 0 0 9 0 0 0 0 0 0 1 0 0 0 0 0 0 1
,
 3 0 0 0 0 0 0 9 0 0 0 0 0 0 9 0 0 0 0 0 0 3 0 0 0 0 0 0 1 0 0 0 0 0 0 1
,
 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 8 0 0 0 0 0 2 5
,
 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 5 0 0 0 0 10 12

G:=sub<GL(6,GF(13))| [12,0,0,0,0,0,0,12,0,0,0,0,0,0,12,0,0,0,0,0,0,12,0,0,0,0,0,0,12,0,0,0,0,0,0,12],[9,0,0,0,0,0,0,3,0,0,0,0,0,0,9,0,0,0,0,0,0,3,0,0,0,0,0,0,3,9,0,0,0,0,0,9],[3,0,0,0,0,0,0,9,0,0,0,0,0,0,3,0,0,0,0,0,0,9,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[3,0,0,0,0,0,0,9,0,0,0,0,0,0,9,0,0,0,0,0,0,3,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,8,2,0,0,0,0,0,5],[0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,1,10,0,0,0,0,5,12] >;

C2×C338Q8 in GAP, Magma, Sage, TeX

C_2\times C_3^3\rtimes_8Q_8
% in TeX

G:=Group("C2xC3^3:8Q8");
// GroupNames label

G:=SmallGroup(432,720);
// by ID

G=gap.SmallGroup(432,720);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-3,-3,-3,56,254,58,1124,4037,14118]);
// Polycyclic

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

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