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## G = C33⋊12Q16order 432 = 24·33

### 3rd semidirect product of C33 and Q16 acting via Q16/C8=C2

Series: Derived Chief Lower central Upper central

 Derived series C1 — C32×C12 — C33⋊12Q16
 Chief series C1 — C3 — C32 — C33 — C32×C6 — C32×C12 — C33⋊8Q8 — C33⋊12Q16
 Lower central C33 — C32×C6 — C32×C12 — C33⋊12Q16
 Upper central C1 — C2 — C4 — C8

Generators and relations for C3312Q16
G = < a,b,c,d,e | a3=b3=c3=d8=1, e2=d4, ab=ba, ac=ca, ad=da, eae-1=a-1, bc=cb, bd=db, ebe-1=b-1, cd=dc, ece-1=c-1, ede-1=d-1 >

Subgroups: 1400 in 252 conjugacy classes, 115 normal (9 characteristic)
C1, C2, C3, C4, C4, C6, C8, Q8, C32, Dic3, C12, Q16, C3×C6, C24, Dic6, C33, C3⋊Dic3, C3×C12, Dic12, C32×C6, C3×C24, C324Q8, C335C4, C32×C12, C325Q16, C32×C24, C338Q8, C3312Q16
Quotients: C1, C2, C22, S3, D4, D6, Q16, C3⋊S3, D12, C2×C3⋊S3, Dic12, C33⋊C2, C12⋊S3, C2×C33⋊C2, C325Q16, C3312D4, C3312Q16

Smallest permutation representation of C3312Q16
Regular action on 432 points
Generators in S432
```(1 392 117)(2 385 118)(3 386 119)(4 387 120)(5 388 113)(6 389 114)(7 390 115)(8 391 116)(9 184 355)(10 177 356)(11 178 357)(12 179 358)(13 180 359)(14 181 360)(15 182 353)(16 183 354)(17 276 65)(18 277 66)(19 278 67)(20 279 68)(21 280 69)(22 273 70)(23 274 71)(24 275 72)(25 300 235)(26 301 236)(27 302 237)(28 303 238)(29 304 239)(30 297 240)(31 298 233)(32 299 234)(33 125 281)(34 126 282)(35 127 283)(36 128 284)(37 121 285)(38 122 286)(39 123 287)(40 124 288)(41 232 171)(42 225 172)(43 226 173)(44 227 174)(45 228 175)(46 229 176)(47 230 169)(48 231 170)(49 328 396)(50 321 397)(51 322 398)(52 323 399)(53 324 400)(54 325 393)(55 326 394)(56 327 395)(57 194 213)(58 195 214)(59 196 215)(60 197 216)(61 198 209)(62 199 210)(63 200 211)(64 193 212)(73 224 155)(74 217 156)(75 218 157)(76 219 158)(77 220 159)(78 221 160)(79 222 153)(80 223 154)(81 383 320)(82 384 313)(83 377 314)(84 378 315)(85 379 316)(86 380 317)(87 381 318)(88 382 319)(89 204 138)(90 205 139)(91 206 140)(92 207 141)(93 208 142)(94 201 143)(95 202 144)(96 203 137)(97 311 152)(98 312 145)(99 305 146)(100 306 147)(101 307 148)(102 308 149)(103 309 150)(104 310 151)(105 403 292)(106 404 293)(107 405 294)(108 406 295)(109 407 296)(110 408 289)(111 401 290)(112 402 291)(129 241 412)(130 242 413)(131 243 414)(132 244 415)(133 245 416)(134 246 409)(135 247 410)(136 248 411)(161 347 373)(162 348 374)(163 349 375)(164 350 376)(165 351 369)(166 352 370)(167 345 371)(168 346 372)(185 424 256)(186 417 249)(187 418 250)(188 419 251)(189 420 252)(190 421 253)(191 422 254)(192 423 255)(257 332 432)(258 333 425)(259 334 426)(260 335 427)(261 336 428)(262 329 429)(263 330 430)(264 331 431)(265 337 362)(266 338 363)(267 339 364)(268 340 365)(269 341 366)(270 342 367)(271 343 368)(272 344 361)
(1 194 182)(2 195 183)(3 196 184)(4 197 177)(5 198 178)(6 199 179)(7 200 180)(8 193 181)(9 119 59)(10 120 60)(11 113 61)(12 114 62)(13 115 63)(14 116 64)(15 117 57)(16 118 58)(17 124 94)(18 125 95)(19 126 96)(20 127 89)(21 128 90)(22 121 91)(23 122 92)(24 123 93)(25 431 83)(26 432 84)(27 425 85)(28 426 86)(29 427 87)(30 428 88)(31 429 81)(32 430 82)(33 144 66)(34 137 67)(35 138 68)(36 139 69)(37 140 70)(38 141 71)(39 142 72)(40 143 65)(41 146 77)(42 147 78)(43 148 79)(44 149 80)(45 150 73)(46 151 74)(47 152 75)(48 145 76)(49 134 270)(50 135 271)(51 136 272)(52 129 265)(53 130 266)(54 131 267)(55 132 268)(56 133 269)(97 218 230)(98 219 231)(99 220 232)(100 221 225)(101 222 226)(102 223 227)(103 224 228)(104 217 229)(105 190 345)(106 191 346)(107 192 347)(108 185 348)(109 186 349)(110 187 350)(111 188 351)(112 189 352)(153 173 307)(154 174 308)(155 175 309)(156 176 310)(157 169 311)(158 170 312)(159 171 305)(160 172 306)(161 294 255)(162 295 256)(163 296 249)(164 289 250)(165 290 251)(166 291 252)(167 292 253)(168 293 254)(201 276 288)(202 277 281)(203 278 282)(204 279 283)(205 280 284)(206 273 285)(207 274 286)(208 275 287)(209 357 388)(210 358 389)(211 359 390)(212 360 391)(213 353 392)(214 354 385)(215 355 386)(216 356 387)(233 329 320)(234 330 313)(235 331 314)(236 332 315)(237 333 316)(238 334 317)(239 335 318)(240 336 319)(241 337 323)(242 338 324)(243 339 325)(244 340 326)(245 341 327)(246 342 328)(247 343 321)(248 344 322)(257 378 301)(258 379 302)(259 380 303)(260 381 304)(261 382 297)(262 383 298)(263 384 299)(264 377 300)(361 398 411)(362 399 412)(363 400 413)(364 393 414)(365 394 415)(366 395 416)(367 396 409)(368 397 410)(369 401 419)(370 402 420)(371 403 421)(372 404 422)(373 405 423)(374 406 424)(375 407 417)(376 408 418)
(1 230 36)(2 231 37)(3 232 38)(4 225 39)(5 226 40)(6 227 33)(7 228 34)(8 229 35)(9 77 274)(10 78 275)(11 79 276)(12 80 277)(13 73 278)(14 74 279)(15 75 280)(16 76 273)(17 357 153)(18 358 154)(19 359 155)(20 360 156)(21 353 157)(22 354 158)(23 355 159)(24 356 160)(25 245 250)(26 246 251)(27 247 252)(28 248 253)(29 241 254)(30 242 255)(31 243 256)(32 244 249)(41 286 119)(42 287 120)(43 288 113)(44 281 114)(45 282 115)(46 283 116)(47 284 117)(48 285 118)(49 401 315)(50 402 316)(51 403 317)(52 404 318)(53 405 319)(54 406 320)(55 407 313)(56 408 314)(57 152 205)(58 145 206)(59 146 207)(60 147 208)(61 148 201)(62 149 202)(63 150 203)(64 151 204)(65 178 222)(66 179 223)(67 180 224)(68 181 217)(69 182 218)(70 183 219)(71 184 220)(72 177 221)(81 325 295)(82 326 296)(83 327 289)(84 328 290)(85 321 291)(86 322 292)(87 323 293)(88 324 294)(89 212 310)(90 213 311)(91 214 312)(92 215 305)(93 216 306)(94 209 307)(95 210 308)(96 211 309)(97 139 194)(98 140 195)(99 141 196)(100 142 197)(101 143 198)(102 144 199)(103 137 200)(104 138 193)(105 380 398)(106 381 399)(107 382 400)(108 383 393)(109 384 394)(110 377 395)(111 378 396)(112 379 397)(121 385 170)(122 386 171)(123 387 172)(124 388 173)(125 389 174)(126 390 175)(127 391 176)(128 392 169)(129 422 239)(130 423 240)(131 424 233)(132 417 234)(133 418 235)(134 419 236)(135 420 237)(136 421 238)(161 428 338)(162 429 339)(163 430 340)(164 431 341)(165 432 342)(166 425 343)(167 426 344)(168 427 337)(185 298 414)(186 299 415)(187 300 416)(188 301 409)(189 302 410)(190 303 411)(191 304 412)(192 297 413)(257 367 351)(258 368 352)(259 361 345)(260 362 346)(261 363 347)(262 364 348)(263 365 349)(264 366 350)(265 372 335)(266 373 336)(267 374 329)(268 375 330)(269 376 331)(270 369 332)(271 370 333)(272 371 334)
(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)
(1 377 5 381)(2 384 6 380)(3 383 7 379)(4 382 8 378)(9 233 13 237)(10 240 14 236)(11 239 15 235)(12 238 16 234)(17 241 21 245)(18 248 22 244)(19 247 23 243)(20 246 24 242)(25 357 29 353)(26 356 30 360)(27 355 31 359)(28 354 32 358)(33 398 37 394)(34 397 38 393)(35 396 39 400)(36 395 40 399)(41 406 45 402)(42 405 46 401)(43 404 47 408)(44 403 48 407)(49 287 53 283)(50 286 54 282)(51 285 55 281)(52 284 56 288)(57 331 61 335)(58 330 62 334)(59 329 63 333)(60 336 64 332)(65 412 69 416)(66 411 70 415)(67 410 71 414)(68 409 72 413)(73 420 77 424)(74 419 78 423)(75 418 79 422)(76 417 80 421)(81 390 85 386)(82 389 86 385)(83 388 87 392)(84 387 88 391)(89 342 93 338)(90 341 94 337)(91 340 95 344)(92 339 96 343)(97 350 101 346)(98 349 102 345)(99 348 103 352)(100 347 104 351)(105 231 109 227)(106 230 110 226)(107 229 111 225)(108 228 112 232)(113 318 117 314)(114 317 118 313)(115 316 119 320)(116 315 120 319)(121 326 125 322)(122 325 126 321)(123 324 127 328)(124 323 128 327)(129 280 133 276)(130 279 134 275)(131 278 135 274)(132 277 136 273)(137 368 141 364)(138 367 142 363)(139 366 143 362)(140 365 144 361)(145 375 149 371)(146 374 150 370)(147 373 151 369)(148 372 152 376)(153 254 157 250)(154 253 158 249)(155 252 159 256)(156 251 160 255)(161 310 165 306)(162 309 166 305)(163 308 167 312)(164 307 168 311)(169 289 173 293)(170 296 174 292)(171 295 175 291)(172 294 176 290)(177 297 181 301)(178 304 182 300)(179 303 183 299)(180 302 184 298)(185 224 189 220)(186 223 190 219)(187 222 191 218)(188 221 192 217)(193 257 197 261)(194 264 198 260)(195 263 199 259)(196 262 200 258)(201 265 205 269)(202 272 206 268)(203 271 207 267)(204 270 208 266)(209 427 213 431)(210 426 214 430)(211 425 215 429)(212 432 216 428)```

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

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

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

111 conjugacy classes

 class 1 2 3A ··· 3M 4A 4B 4C 6A ··· 6M 8A 8B 12A ··· 12Z 24A ··· 24AZ order 1 2 3 ··· 3 4 4 4 6 ··· 6 8 8 12 ··· 12 24 ··· 24 size 1 1 2 ··· 2 2 108 108 2 ··· 2 2 2 2 ··· 2 2 ··· 2

111 irreducible representations

 dim 1 1 1 2 2 2 2 2 2 type + + + + + + - + - image C1 C2 C2 S3 D4 D6 Q16 D12 Dic12 kernel C33⋊12Q16 C32×C24 C33⋊8Q8 C3×C24 C32×C6 C3×C12 C33 C3×C6 C32 # reps 1 1 2 13 1 13 2 26 52

Matrix representation of C3312Q16 in GL6(𝔽73)

 72 72 0 0 0 0 1 0 0 0 0 0 0 0 72 1 0 0 0 0 72 0 0 0 0 0 0 0 72 72 0 0 0 0 1 0
,
 0 1 0 0 0 0 72 72 0 0 0 0 0 0 72 1 0 0 0 0 72 0 0 0 0 0 0 0 0 1 0 0 0 0 72 72
,
 0 1 0 0 0 0 72 72 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 1
,
 1 0 0 0 0 0 0 1 0 0 0 0 0 0 18 5 0 0 0 0 68 23 0 0 0 0 0 0 72 0 0 0 0 0 0 72
,
 66 59 0 0 0 0 66 7 0 0 0 0 0 0 54 5 0 0 0 0 59 19 0 0 0 0 0 0 41 63 0 0 0 0 22 32

`G:=sub<GL(6,GF(73))| [72,1,0,0,0,0,72,0,0,0,0,0,0,0,72,72,0,0,0,0,1,0,0,0,0,0,0,0,72,1,0,0,0,0,72,0],[0,72,0,0,0,0,1,72,0,0,0,0,0,0,72,72,0,0,0,0,1,0,0,0,0,0,0,0,0,72,0,0,0,0,1,72],[0,72,0,0,0,0,1,72,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,18,68,0,0,0,0,5,23,0,0,0,0,0,0,72,0,0,0,0,0,0,72],[66,66,0,0,0,0,59,7,0,0,0,0,0,0,54,59,0,0,0,0,5,19,0,0,0,0,0,0,41,22,0,0,0,0,63,32] >;`

C3312Q16 in GAP, Magma, Sage, TeX

`C_3^3\rtimes_{12}Q_{16}`
`% in TeX`

`G:=Group("C3^3:12Q16");`
`// GroupNames label`

`G:=SmallGroup(432,500);`
`// by ID`

`G=gap.SmallGroup(432,500);`
`# by ID`

`G:=PCGroup([7,-2,-2,-2,-2,-3,-3,-3,56,85,92,254,58,1124,4037,14118]);`
`// Polycyclic`

`G:=Group<a,b,c,d,e|a^3=b^3=c^3=d^8=1,e^2=d^4,a*b=b*a,a*c=c*a,a*d=d*a,e*a*e^-1=a^-1,b*c=c*b,b*d=d*b,e*b*e^-1=b^-1,c*d=d*c,e*c*e^-1=c^-1,e*d*e^-1=d^-1>;`
`// generators/relations`

׿
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