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G = C3312Q16order 432 = 24·33

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

metabelian, supersoluble, monomial

Aliases: C3312Q16, C328Dic12, C24.3(C3⋊S3), (C3×C24).13S3, (C3×C6).68D12, C8.(C33⋊C2), (C3×C12).199D6, (C32×C24).1C2, (C32×C6).63D4, C31(C325Q16), C6.9(C12⋊S3), C338Q8.1C2, C2.5(C3312D4), (C32×C12).77C22, C12.66(C2×C3⋊S3), C4.10(C2×C33⋊C2), SmallGroup(432,500)

Series: Derived Chief Lower central Upper central

C1C32×C12 — C3312Q16
C1C3C32C33C32×C6C32×C12C338Q8 — C3312Q16
C33C32×C6C32×C12 — C3312Q16
C1C2C4C8

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 [×13], C4, C4 [×2], C6 [×13], C8, Q8 [×2], C32 [×13], Dic3 [×26], C12 [×13], Q16, C3×C6 [×13], C24 [×13], Dic6 [×26], C33, C3⋊Dic3 [×26], C3×C12 [×13], Dic12 [×13], C32×C6, C3×C24 [×13], C324Q8 [×26], C335C4 [×2], C32×C12, C325Q16 [×13], C32×C24, C338Q8 [×2], C3312Q16
Quotients: C1, C2 [×3], C22, S3 [×13], D4, D6 [×13], Q16, C3⋊S3 [×13], D12 [×13], C2×C3⋊S3 [×13], Dic12 [×13], C33⋊C2, C12⋊S3 [×13], C2×C33⋊C2, C325Q16 [×13], C3312D4, C3312Q16

Smallest permutation representation of C3312Q16
Regular action on 432 points
Generators in S432
(1 284 117)(2 285 118)(3 286 119)(4 287 120)(5 288 113)(6 281 114)(7 282 115)(8 283 116)(9 157 386)(10 158 387)(11 159 388)(12 160 389)(13 153 390)(14 154 391)(15 155 392)(16 156 385)(17 358 66)(18 359 67)(19 360 68)(20 353 69)(21 354 70)(22 355 71)(23 356 72)(24 357 65)(25 418 250)(26 419 251)(27 420 252)(28 421 253)(29 422 254)(30 423 255)(31 424 256)(32 417 249)(33 102 335)(34 103 336)(35 104 329)(36 97 330)(37 98 331)(38 99 332)(39 100 333)(40 101 334)(41 222 148)(42 223 149)(43 224 150)(44 217 151)(45 218 152)(46 219 145)(47 220 146)(48 221 147)(49 347 296)(50 348 289)(51 349 290)(52 350 291)(53 351 292)(54 352 293)(55 345 294)(56 346 295)(57 194 213)(58 195 214)(59 196 215)(60 197 216)(61 198 209)(62 199 210)(63 200 211)(64 193 212)(73 278 175)(74 279 176)(75 280 169)(76 273 170)(77 274 171)(78 275 172)(79 276 173)(80 277 174)(81 298 233)(82 299 234)(83 300 235)(84 301 236)(85 302 237)(86 303 238)(87 304 239)(88 297 240)(89 204 142)(90 205 143)(91 206 144)(92 207 137)(93 208 138)(94 201 139)(95 202 140)(96 203 141)(105 380 344)(106 381 337)(107 382 338)(108 383 339)(109 384 340)(110 377 341)(111 378 342)(112 379 343)(121 231 181)(122 232 182)(123 225 183)(124 226 184)(125 227 177)(126 228 178)(127 229 179)(128 230 180)(129 242 393)(130 243 394)(131 244 395)(132 245 396)(133 246 397)(134 247 398)(135 248 399)(136 241 400)(161 328 373)(162 321 374)(163 322 375)(164 323 376)(165 324 369)(166 325 370)(167 326 371)(168 327 372)(185 405 414)(186 406 415)(187 407 416)(188 408 409)(189 401 410)(190 402 411)(191 403 412)(192 404 413)(257 305 432)(258 306 425)(259 307 426)(260 308 427)(261 309 428)(262 310 429)(263 311 430)(264 312 431)(265 318 362)(266 319 363)(267 320 364)(268 313 365)(269 314 366)(270 315 367)(271 316 368)(272 317 361)
(1 194 20)(2 195 21)(3 196 22)(4 197 23)(5 198 24)(6 199 17)(7 200 18)(8 193 19)(9 332 146)(10 333 147)(11 334 148)(12 335 149)(13 336 150)(14 329 151)(15 330 152)(16 331 145)(25 323 83)(26 324 84)(27 325 85)(28 326 86)(29 327 87)(30 328 88)(31 321 81)(32 322 82)(33 42 160)(34 43 153)(35 44 154)(36 45 155)(37 46 156)(38 47 157)(39 48 158)(40 41 159)(49 188 270)(50 189 271)(51 190 272)(52 191 265)(53 192 266)(54 185 267)(55 186 268)(56 187 269)(57 69 117)(58 70 118)(59 71 119)(60 72 120)(61 65 113)(62 66 114)(63 67 115)(64 68 116)(73 126 96)(74 127 89)(75 128 90)(76 121 91)(77 122 92)(78 123 93)(79 124 94)(80 125 95)(97 218 392)(98 219 385)(99 220 386)(100 221 387)(101 222 388)(102 223 389)(103 224 390)(104 217 391)(105 136 426)(106 129 427)(107 130 428)(108 131 429)(109 132 430)(110 133 431)(111 134 432)(112 135 425)(137 171 182)(138 172 183)(139 173 184)(140 174 177)(141 175 178)(142 176 179)(143 169 180)(144 170 181)(161 240 255)(162 233 256)(163 234 249)(164 235 250)(165 236 251)(166 237 252)(167 238 253)(168 239 254)(201 276 226)(202 277 227)(203 278 228)(204 279 229)(205 280 230)(206 273 231)(207 274 232)(208 275 225)(209 357 288)(210 358 281)(211 359 282)(212 360 283)(213 353 284)(214 354 285)(215 355 286)(216 356 287)(241 259 380)(242 260 381)(243 261 382)(244 262 383)(245 263 384)(246 264 377)(247 257 378)(248 258 379)(289 410 368)(290 411 361)(291 412 362)(292 413 363)(293 414 364)(294 415 365)(295 416 366)(296 409 367)(297 423 373)(298 424 374)(299 417 375)(300 418 376)(301 419 369)(302 420 370)(303 421 371)(304 422 372)(305 342 398)(306 343 399)(307 344 400)(308 337 393)(309 338 394)(310 339 395)(311 340 396)(312 341 397)(313 345 406)(314 346 407)(315 347 408)(316 348 401)(317 349 402)(318 350 403)(319 351 404)(320 352 405)
(1 392 180)(2 385 181)(3 386 182)(4 387 183)(5 388 184)(6 389 177)(7 390 178)(8 391 179)(9 122 286)(10 123 287)(11 124 288)(12 125 281)(13 126 282)(14 127 283)(15 128 284)(16 121 285)(17 223 174)(18 224 175)(19 217 176)(20 218 169)(21 219 170)(22 220 171)(23 221 172)(24 222 173)(25 246 416)(26 247 409)(27 248 410)(28 241 411)(29 242 412)(30 243 413)(31 244 414)(32 245 415)(33 202 62)(34 203 63)(35 204 64)(36 205 57)(37 206 58)(38 207 59)(39 208 60)(40 201 61)(41 276 65)(42 277 66)(43 278 67)(44 279 68)(45 280 69)(46 273 70)(47 274 71)(48 275 72)(49 301 342)(50 302 343)(51 303 344)(52 304 337)(53 297 338)(54 298 339)(55 299 340)(56 300 341)(73 359 150)(74 360 151)(75 353 152)(76 354 145)(77 355 146)(78 356 147)(79 357 148)(80 358 149)(81 383 293)(82 384 294)(83 377 295)(84 378 296)(85 379 289)(86 380 290)(87 381 291)(88 382 292)(89 212 329)(90 213 330)(91 214 331)(92 215 332)(93 216 333)(94 209 334)(95 210 335)(96 211 336)(97 143 194)(98 144 195)(99 137 196)(100 138 197)(101 139 198)(102 140 199)(103 141 200)(104 142 193)(105 349 238)(106 350 239)(107 351 240)(108 352 233)(109 345 234)(110 346 235)(111 347 236)(112 348 237)(113 159 226)(114 160 227)(115 153 228)(116 154 229)(117 155 230)(118 156 231)(119 157 232)(120 158 225)(129 403 254)(130 404 255)(131 405 256)(132 406 249)(133 407 250)(134 408 251)(135 401 252)(136 402 253)(161 428 319)(162 429 320)(163 430 313)(164 431 314)(165 432 315)(166 425 316)(167 426 317)(168 427 318)(185 424 395)(186 417 396)(187 418 397)(188 419 398)(189 420 399)(190 421 400)(191 422 393)(192 423 394)(257 367 324)(258 368 325)(259 361 326)(260 362 327)(261 363 328)(262 364 321)(263 365 322)(264 366 323)(265 372 308)(266 373 309)(267 374 310)(268 375 311)(269 376 312)(270 369 305)(271 370 306)(272 371 307)
(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)(25 222 29 218)(26 221 30 217)(27 220 31 224)(28 219 32 223)(33 371 37 375)(34 370 38 374)(35 369 39 373)(36 376 40 372)(41 422 45 418)(42 421 46 417)(43 420 47 424)(44 419 48 423)(49 225 53 229)(50 232 54 228)(51 231 55 227)(52 230 56 226)(57 312 61 308)(58 311 62 307)(59 310 63 306)(60 309 64 305)(65 393 69 397)(66 400 70 396)(67 399 71 395)(68 398 72 394)(73 401 77 405)(74 408 78 404)(75 407 79 403)(76 406 80 402)(81 390 85 386)(82 389 86 385)(83 388 87 392)(84 387 88 391)(89 315 93 319)(90 314 94 318)(91 313 95 317)(92 320 96 316)(97 323 101 327)(98 322 102 326)(99 321 103 325)(100 328 104 324)(105 285 109 281)(106 284 110 288)(107 283 111 287)(108 282 112 286)(113 337 117 341)(114 344 118 340)(115 343 119 339)(116 342 120 338)(121 345 125 349)(122 352 126 348)(123 351 127 347)(124 350 128 346)(129 353 133 357)(130 360 134 356)(131 359 135 355)(132 358 136 354)(137 364 141 368)(138 363 142 367)(139 362 143 366)(140 361 144 365)(145 249 149 253)(146 256 150 252)(147 255 151 251)(148 254 152 250)(153 302 157 298)(154 301 158 297)(155 300 159 304)(156 299 160 303)(161 329 165 333)(162 336 166 332)(163 335 167 331)(164 334 168 330)(169 416 173 412)(170 415 174 411)(171 414 175 410)(172 413 176 409)(177 290 181 294)(178 289 182 293)(179 296 183 292)(180 295 184 291)(185 278 189 274)(186 277 190 273)(187 276 191 280)(188 275 192 279)(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)| (1,284,117)(2,285,118)(3,286,119)(4,287,120)(5,288,113)(6,281,114)(7,282,115)(8,283,116)(9,157,386)(10,158,387)(11,159,388)(12,160,389)(13,153,390)(14,154,391)(15,155,392)(16,156,385)(17,358,66)(18,359,67)(19,360,68)(20,353,69)(21,354,70)(22,355,71)(23,356,72)(24,357,65)(25,418,250)(26,419,251)(27,420,252)(28,421,253)(29,422,254)(30,423,255)(31,424,256)(32,417,249)(33,102,335)(34,103,336)(35,104,329)(36,97,330)(37,98,331)(38,99,332)(39,100,333)(40,101,334)(41,222,148)(42,223,149)(43,224,150)(44,217,151)(45,218,152)(46,219,145)(47,220,146)(48,221,147)(49,347,296)(50,348,289)(51,349,290)(52,350,291)(53,351,292)(54,352,293)(55,345,294)(56,346,295)(57,194,213)(58,195,214)(59,196,215)(60,197,216)(61,198,209)(62,199,210)(63,200,211)(64,193,212)(73,278,175)(74,279,176)(75,280,169)(76,273,170)(77,274,171)(78,275,172)(79,276,173)(80,277,174)(81,298,233)(82,299,234)(83,300,235)(84,301,236)(85,302,237)(86,303,238)(87,304,239)(88,297,240)(89,204,142)(90,205,143)(91,206,144)(92,207,137)(93,208,138)(94,201,139)(95,202,140)(96,203,141)(105,380,344)(106,381,337)(107,382,338)(108,383,339)(109,384,340)(110,377,341)(111,378,342)(112,379,343)(121,231,181)(122,232,182)(123,225,183)(124,226,184)(125,227,177)(126,228,178)(127,229,179)(128,230,180)(129,242,393)(130,243,394)(131,244,395)(132,245,396)(133,246,397)(134,247,398)(135,248,399)(136,241,400)(161,328,373)(162,321,374)(163,322,375)(164,323,376)(165,324,369)(166,325,370)(167,326,371)(168,327,372)(185,405,414)(186,406,415)(187,407,416)(188,408,409)(189,401,410)(190,402,411)(191,403,412)(192,404,413)(257,305,432)(258,306,425)(259,307,426)(260,308,427)(261,309,428)(262,310,429)(263,311,430)(264,312,431)(265,318,362)(266,319,363)(267,320,364)(268,313,365)(269,314,366)(270,315,367)(271,316,368)(272,317,361), (1,194,20)(2,195,21)(3,196,22)(4,197,23)(5,198,24)(6,199,17)(7,200,18)(8,193,19)(9,332,146)(10,333,147)(11,334,148)(12,335,149)(13,336,150)(14,329,151)(15,330,152)(16,331,145)(25,323,83)(26,324,84)(27,325,85)(28,326,86)(29,327,87)(30,328,88)(31,321,81)(32,322,82)(33,42,160)(34,43,153)(35,44,154)(36,45,155)(37,46,156)(38,47,157)(39,48,158)(40,41,159)(49,188,270)(50,189,271)(51,190,272)(52,191,265)(53,192,266)(54,185,267)(55,186,268)(56,187,269)(57,69,117)(58,70,118)(59,71,119)(60,72,120)(61,65,113)(62,66,114)(63,67,115)(64,68,116)(73,126,96)(74,127,89)(75,128,90)(76,121,91)(77,122,92)(78,123,93)(79,124,94)(80,125,95)(97,218,392)(98,219,385)(99,220,386)(100,221,387)(101,222,388)(102,223,389)(103,224,390)(104,217,391)(105,136,426)(106,129,427)(107,130,428)(108,131,429)(109,132,430)(110,133,431)(111,134,432)(112,135,425)(137,171,182)(138,172,183)(139,173,184)(140,174,177)(141,175,178)(142,176,179)(143,169,180)(144,170,181)(161,240,255)(162,233,256)(163,234,249)(164,235,250)(165,236,251)(166,237,252)(167,238,253)(168,239,254)(201,276,226)(202,277,227)(203,278,228)(204,279,229)(205,280,230)(206,273,231)(207,274,232)(208,275,225)(209,357,288)(210,358,281)(211,359,282)(212,360,283)(213,353,284)(214,354,285)(215,355,286)(216,356,287)(241,259,380)(242,260,381)(243,261,382)(244,262,383)(245,263,384)(246,264,377)(247,257,378)(248,258,379)(289,410,368)(290,411,361)(291,412,362)(292,413,363)(293,414,364)(294,415,365)(295,416,366)(296,409,367)(297,423,373)(298,424,374)(299,417,375)(300,418,376)(301,419,369)(302,420,370)(303,421,371)(304,422,372)(305,342,398)(306,343,399)(307,344,400)(308,337,393)(309,338,394)(310,339,395)(311,340,396)(312,341,397)(313,345,406)(314,346,407)(315,347,408)(316,348,401)(317,349,402)(318,350,403)(319,351,404)(320,352,405), (1,392,180)(2,385,181)(3,386,182)(4,387,183)(5,388,184)(6,389,177)(7,390,178)(8,391,179)(9,122,286)(10,123,287)(11,124,288)(12,125,281)(13,126,282)(14,127,283)(15,128,284)(16,121,285)(17,223,174)(18,224,175)(19,217,176)(20,218,169)(21,219,170)(22,220,171)(23,221,172)(24,222,173)(25,246,416)(26,247,409)(27,248,410)(28,241,411)(29,242,412)(30,243,413)(31,244,414)(32,245,415)(33,202,62)(34,203,63)(35,204,64)(36,205,57)(37,206,58)(38,207,59)(39,208,60)(40,201,61)(41,276,65)(42,277,66)(43,278,67)(44,279,68)(45,280,69)(46,273,70)(47,274,71)(48,275,72)(49,301,342)(50,302,343)(51,303,344)(52,304,337)(53,297,338)(54,298,339)(55,299,340)(56,300,341)(73,359,150)(74,360,151)(75,353,152)(76,354,145)(77,355,146)(78,356,147)(79,357,148)(80,358,149)(81,383,293)(82,384,294)(83,377,295)(84,378,296)(85,379,289)(86,380,290)(87,381,291)(88,382,292)(89,212,329)(90,213,330)(91,214,331)(92,215,332)(93,216,333)(94,209,334)(95,210,335)(96,211,336)(97,143,194)(98,144,195)(99,137,196)(100,138,197)(101,139,198)(102,140,199)(103,141,200)(104,142,193)(105,349,238)(106,350,239)(107,351,240)(108,352,233)(109,345,234)(110,346,235)(111,347,236)(112,348,237)(113,159,226)(114,160,227)(115,153,228)(116,154,229)(117,155,230)(118,156,231)(119,157,232)(120,158,225)(129,403,254)(130,404,255)(131,405,256)(132,406,249)(133,407,250)(134,408,251)(135,401,252)(136,402,253)(161,428,319)(162,429,320)(163,430,313)(164,431,314)(165,432,315)(166,425,316)(167,426,317)(168,427,318)(185,424,395)(186,417,396)(187,418,397)(188,419,398)(189,420,399)(190,421,400)(191,422,393)(192,423,394)(257,367,324)(258,368,325)(259,361,326)(260,362,327)(261,363,328)(262,364,321)(263,365,322)(264,366,323)(265,372,308)(266,373,309)(267,374,310)(268,375,311)(269,376,312)(270,369,305)(271,370,306)(272,371,307), (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)(25,222,29,218)(26,221,30,217)(27,220,31,224)(28,219,32,223)(33,371,37,375)(34,370,38,374)(35,369,39,373)(36,376,40,372)(41,422,45,418)(42,421,46,417)(43,420,47,424)(44,419,48,423)(49,225,53,229)(50,232,54,228)(51,231,55,227)(52,230,56,226)(57,312,61,308)(58,311,62,307)(59,310,63,306)(60,309,64,305)(65,393,69,397)(66,400,70,396)(67,399,71,395)(68,398,72,394)(73,401,77,405)(74,408,78,404)(75,407,79,403)(76,406,80,402)(81,390,85,386)(82,389,86,385)(83,388,87,392)(84,387,88,391)(89,315,93,319)(90,314,94,318)(91,313,95,317)(92,320,96,316)(97,323,101,327)(98,322,102,326)(99,321,103,325)(100,328,104,324)(105,285,109,281)(106,284,110,288)(107,283,111,287)(108,282,112,286)(113,337,117,341)(114,344,118,340)(115,343,119,339)(116,342,120,338)(121,345,125,349)(122,352,126,348)(123,351,127,347)(124,350,128,346)(129,353,133,357)(130,360,134,356)(131,359,135,355)(132,358,136,354)(137,364,141,368)(138,363,142,367)(139,362,143,366)(140,361,144,365)(145,249,149,253)(146,256,150,252)(147,255,151,251)(148,254,152,250)(153,302,157,298)(154,301,158,297)(155,300,159,304)(156,299,160,303)(161,329,165,333)(162,336,166,332)(163,335,167,331)(164,334,168,330)(169,416,173,412)(170,415,174,411)(171,414,175,410)(172,413,176,409)(177,290,181,294)(178,289,182,293)(179,296,183,292)(180,295,184,291)(185,278,189,274)(186,277,190,273)(187,276,191,280)(188,275,192,279)(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( (1,284,117)(2,285,118)(3,286,119)(4,287,120)(5,288,113)(6,281,114)(7,282,115)(8,283,116)(9,157,386)(10,158,387)(11,159,388)(12,160,389)(13,153,390)(14,154,391)(15,155,392)(16,156,385)(17,358,66)(18,359,67)(19,360,68)(20,353,69)(21,354,70)(22,355,71)(23,356,72)(24,357,65)(25,418,250)(26,419,251)(27,420,252)(28,421,253)(29,422,254)(30,423,255)(31,424,256)(32,417,249)(33,102,335)(34,103,336)(35,104,329)(36,97,330)(37,98,331)(38,99,332)(39,100,333)(40,101,334)(41,222,148)(42,223,149)(43,224,150)(44,217,151)(45,218,152)(46,219,145)(47,220,146)(48,221,147)(49,347,296)(50,348,289)(51,349,290)(52,350,291)(53,351,292)(54,352,293)(55,345,294)(56,346,295)(57,194,213)(58,195,214)(59,196,215)(60,197,216)(61,198,209)(62,199,210)(63,200,211)(64,193,212)(73,278,175)(74,279,176)(75,280,169)(76,273,170)(77,274,171)(78,275,172)(79,276,173)(80,277,174)(81,298,233)(82,299,234)(83,300,235)(84,301,236)(85,302,237)(86,303,238)(87,304,239)(88,297,240)(89,204,142)(90,205,143)(91,206,144)(92,207,137)(93,208,138)(94,201,139)(95,202,140)(96,203,141)(105,380,344)(106,381,337)(107,382,338)(108,383,339)(109,384,340)(110,377,341)(111,378,342)(112,379,343)(121,231,181)(122,232,182)(123,225,183)(124,226,184)(125,227,177)(126,228,178)(127,229,179)(128,230,180)(129,242,393)(130,243,394)(131,244,395)(132,245,396)(133,246,397)(134,247,398)(135,248,399)(136,241,400)(161,328,373)(162,321,374)(163,322,375)(164,323,376)(165,324,369)(166,325,370)(167,326,371)(168,327,372)(185,405,414)(186,406,415)(187,407,416)(188,408,409)(189,401,410)(190,402,411)(191,403,412)(192,404,413)(257,305,432)(258,306,425)(259,307,426)(260,308,427)(261,309,428)(262,310,429)(263,311,430)(264,312,431)(265,318,362)(266,319,363)(267,320,364)(268,313,365)(269,314,366)(270,315,367)(271,316,368)(272,317,361), (1,194,20)(2,195,21)(3,196,22)(4,197,23)(5,198,24)(6,199,17)(7,200,18)(8,193,19)(9,332,146)(10,333,147)(11,334,148)(12,335,149)(13,336,150)(14,329,151)(15,330,152)(16,331,145)(25,323,83)(26,324,84)(27,325,85)(28,326,86)(29,327,87)(30,328,88)(31,321,81)(32,322,82)(33,42,160)(34,43,153)(35,44,154)(36,45,155)(37,46,156)(38,47,157)(39,48,158)(40,41,159)(49,188,270)(50,189,271)(51,190,272)(52,191,265)(53,192,266)(54,185,267)(55,186,268)(56,187,269)(57,69,117)(58,70,118)(59,71,119)(60,72,120)(61,65,113)(62,66,114)(63,67,115)(64,68,116)(73,126,96)(74,127,89)(75,128,90)(76,121,91)(77,122,92)(78,123,93)(79,124,94)(80,125,95)(97,218,392)(98,219,385)(99,220,386)(100,221,387)(101,222,388)(102,223,389)(103,224,390)(104,217,391)(105,136,426)(106,129,427)(107,130,428)(108,131,429)(109,132,430)(110,133,431)(111,134,432)(112,135,425)(137,171,182)(138,172,183)(139,173,184)(140,174,177)(141,175,178)(142,176,179)(143,169,180)(144,170,181)(161,240,255)(162,233,256)(163,234,249)(164,235,250)(165,236,251)(166,237,252)(167,238,253)(168,239,254)(201,276,226)(202,277,227)(203,278,228)(204,279,229)(205,280,230)(206,273,231)(207,274,232)(208,275,225)(209,357,288)(210,358,281)(211,359,282)(212,360,283)(213,353,284)(214,354,285)(215,355,286)(216,356,287)(241,259,380)(242,260,381)(243,261,382)(244,262,383)(245,263,384)(246,264,377)(247,257,378)(248,258,379)(289,410,368)(290,411,361)(291,412,362)(292,413,363)(293,414,364)(294,415,365)(295,416,366)(296,409,367)(297,423,373)(298,424,374)(299,417,375)(300,418,376)(301,419,369)(302,420,370)(303,421,371)(304,422,372)(305,342,398)(306,343,399)(307,344,400)(308,337,393)(309,338,394)(310,339,395)(311,340,396)(312,341,397)(313,345,406)(314,346,407)(315,347,408)(316,348,401)(317,349,402)(318,350,403)(319,351,404)(320,352,405), (1,392,180)(2,385,181)(3,386,182)(4,387,183)(5,388,184)(6,389,177)(7,390,178)(8,391,179)(9,122,286)(10,123,287)(11,124,288)(12,125,281)(13,126,282)(14,127,283)(15,128,284)(16,121,285)(17,223,174)(18,224,175)(19,217,176)(20,218,169)(21,219,170)(22,220,171)(23,221,172)(24,222,173)(25,246,416)(26,247,409)(27,248,410)(28,241,411)(29,242,412)(30,243,413)(31,244,414)(32,245,415)(33,202,62)(34,203,63)(35,204,64)(36,205,57)(37,206,58)(38,207,59)(39,208,60)(40,201,61)(41,276,65)(42,277,66)(43,278,67)(44,279,68)(45,280,69)(46,273,70)(47,274,71)(48,275,72)(49,301,342)(50,302,343)(51,303,344)(52,304,337)(53,297,338)(54,298,339)(55,299,340)(56,300,341)(73,359,150)(74,360,151)(75,353,152)(76,354,145)(77,355,146)(78,356,147)(79,357,148)(80,358,149)(81,383,293)(82,384,294)(83,377,295)(84,378,296)(85,379,289)(86,380,290)(87,381,291)(88,382,292)(89,212,329)(90,213,330)(91,214,331)(92,215,332)(93,216,333)(94,209,334)(95,210,335)(96,211,336)(97,143,194)(98,144,195)(99,137,196)(100,138,197)(101,139,198)(102,140,199)(103,141,200)(104,142,193)(105,349,238)(106,350,239)(107,351,240)(108,352,233)(109,345,234)(110,346,235)(111,347,236)(112,348,237)(113,159,226)(114,160,227)(115,153,228)(116,154,229)(117,155,230)(118,156,231)(119,157,232)(120,158,225)(129,403,254)(130,404,255)(131,405,256)(132,406,249)(133,407,250)(134,408,251)(135,401,252)(136,402,253)(161,428,319)(162,429,320)(163,430,313)(164,431,314)(165,432,315)(166,425,316)(167,426,317)(168,427,318)(185,424,395)(186,417,396)(187,418,397)(188,419,398)(189,420,399)(190,421,400)(191,422,393)(192,423,394)(257,367,324)(258,368,325)(259,361,326)(260,362,327)(261,363,328)(262,364,321)(263,365,322)(264,366,323)(265,372,308)(266,373,309)(267,374,310)(268,375,311)(269,376,312)(270,369,305)(271,370,306)(272,371,307), (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)(25,222,29,218)(26,221,30,217)(27,220,31,224)(28,219,32,223)(33,371,37,375)(34,370,38,374)(35,369,39,373)(36,376,40,372)(41,422,45,418)(42,421,46,417)(43,420,47,424)(44,419,48,423)(49,225,53,229)(50,232,54,228)(51,231,55,227)(52,230,56,226)(57,312,61,308)(58,311,62,307)(59,310,63,306)(60,309,64,305)(65,393,69,397)(66,400,70,396)(67,399,71,395)(68,398,72,394)(73,401,77,405)(74,408,78,404)(75,407,79,403)(76,406,80,402)(81,390,85,386)(82,389,86,385)(83,388,87,392)(84,387,88,391)(89,315,93,319)(90,314,94,318)(91,313,95,317)(92,320,96,316)(97,323,101,327)(98,322,102,326)(99,321,103,325)(100,328,104,324)(105,285,109,281)(106,284,110,288)(107,283,111,287)(108,282,112,286)(113,337,117,341)(114,344,118,340)(115,343,119,339)(116,342,120,338)(121,345,125,349)(122,352,126,348)(123,351,127,347)(124,350,128,346)(129,353,133,357)(130,360,134,356)(131,359,135,355)(132,358,136,354)(137,364,141,368)(138,363,142,367)(139,362,143,366)(140,361,144,365)(145,249,149,253)(146,256,150,252)(147,255,151,251)(148,254,152,250)(153,302,157,298)(154,301,158,297)(155,300,159,304)(156,299,160,303)(161,329,165,333)(162,336,166,332)(163,335,167,331)(164,334,168,330)(169,416,173,412)(170,415,174,411)(171,414,175,410)(172,413,176,409)(177,290,181,294)(178,289,182,293)(179,296,183,292)(180,295,184,291)(185,278,189,274)(186,277,190,273)(187,276,191,280)(188,275,192,279)(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([(1,284,117),(2,285,118),(3,286,119),(4,287,120),(5,288,113),(6,281,114),(7,282,115),(8,283,116),(9,157,386),(10,158,387),(11,159,388),(12,160,389),(13,153,390),(14,154,391),(15,155,392),(16,156,385),(17,358,66),(18,359,67),(19,360,68),(20,353,69),(21,354,70),(22,355,71),(23,356,72),(24,357,65),(25,418,250),(26,419,251),(27,420,252),(28,421,253),(29,422,254),(30,423,255),(31,424,256),(32,417,249),(33,102,335),(34,103,336),(35,104,329),(36,97,330),(37,98,331),(38,99,332),(39,100,333),(40,101,334),(41,222,148),(42,223,149),(43,224,150),(44,217,151),(45,218,152),(46,219,145),(47,220,146),(48,221,147),(49,347,296),(50,348,289),(51,349,290),(52,350,291),(53,351,292),(54,352,293),(55,345,294),(56,346,295),(57,194,213),(58,195,214),(59,196,215),(60,197,216),(61,198,209),(62,199,210),(63,200,211),(64,193,212),(73,278,175),(74,279,176),(75,280,169),(76,273,170),(77,274,171),(78,275,172),(79,276,173),(80,277,174),(81,298,233),(82,299,234),(83,300,235),(84,301,236),(85,302,237),(86,303,238),(87,304,239),(88,297,240),(89,204,142),(90,205,143),(91,206,144),(92,207,137),(93,208,138),(94,201,139),(95,202,140),(96,203,141),(105,380,344),(106,381,337),(107,382,338),(108,383,339),(109,384,340),(110,377,341),(111,378,342),(112,379,343),(121,231,181),(122,232,182),(123,225,183),(124,226,184),(125,227,177),(126,228,178),(127,229,179),(128,230,180),(129,242,393),(130,243,394),(131,244,395),(132,245,396),(133,246,397),(134,247,398),(135,248,399),(136,241,400),(161,328,373),(162,321,374),(163,322,375),(164,323,376),(165,324,369),(166,325,370),(167,326,371),(168,327,372),(185,405,414),(186,406,415),(187,407,416),(188,408,409),(189,401,410),(190,402,411),(191,403,412),(192,404,413),(257,305,432),(258,306,425),(259,307,426),(260,308,427),(261,309,428),(262,310,429),(263,311,430),(264,312,431),(265,318,362),(266,319,363),(267,320,364),(268,313,365),(269,314,366),(270,315,367),(271,316,368),(272,317,361)], [(1,194,20),(2,195,21),(3,196,22),(4,197,23),(5,198,24),(6,199,17),(7,200,18),(8,193,19),(9,332,146),(10,333,147),(11,334,148),(12,335,149),(13,336,150),(14,329,151),(15,330,152),(16,331,145),(25,323,83),(26,324,84),(27,325,85),(28,326,86),(29,327,87),(30,328,88),(31,321,81),(32,322,82),(33,42,160),(34,43,153),(35,44,154),(36,45,155),(37,46,156),(38,47,157),(39,48,158),(40,41,159),(49,188,270),(50,189,271),(51,190,272),(52,191,265),(53,192,266),(54,185,267),(55,186,268),(56,187,269),(57,69,117),(58,70,118),(59,71,119),(60,72,120),(61,65,113),(62,66,114),(63,67,115),(64,68,116),(73,126,96),(74,127,89),(75,128,90),(76,121,91),(77,122,92),(78,123,93),(79,124,94),(80,125,95),(97,218,392),(98,219,385),(99,220,386),(100,221,387),(101,222,388),(102,223,389),(103,224,390),(104,217,391),(105,136,426),(106,129,427),(107,130,428),(108,131,429),(109,132,430),(110,133,431),(111,134,432),(112,135,425),(137,171,182),(138,172,183),(139,173,184),(140,174,177),(141,175,178),(142,176,179),(143,169,180),(144,170,181),(161,240,255),(162,233,256),(163,234,249),(164,235,250),(165,236,251),(166,237,252),(167,238,253),(168,239,254),(201,276,226),(202,277,227),(203,278,228),(204,279,229),(205,280,230),(206,273,231),(207,274,232),(208,275,225),(209,357,288),(210,358,281),(211,359,282),(212,360,283),(213,353,284),(214,354,285),(215,355,286),(216,356,287),(241,259,380),(242,260,381),(243,261,382),(244,262,383),(245,263,384),(246,264,377),(247,257,378),(248,258,379),(289,410,368),(290,411,361),(291,412,362),(292,413,363),(293,414,364),(294,415,365),(295,416,366),(296,409,367),(297,423,373),(298,424,374),(299,417,375),(300,418,376),(301,419,369),(302,420,370),(303,421,371),(304,422,372),(305,342,398),(306,343,399),(307,344,400),(308,337,393),(309,338,394),(310,339,395),(311,340,396),(312,341,397),(313,345,406),(314,346,407),(315,347,408),(316,348,401),(317,349,402),(318,350,403),(319,351,404),(320,352,405)], [(1,392,180),(2,385,181),(3,386,182),(4,387,183),(5,388,184),(6,389,177),(7,390,178),(8,391,179),(9,122,286),(10,123,287),(11,124,288),(12,125,281),(13,126,282),(14,127,283),(15,128,284),(16,121,285),(17,223,174),(18,224,175),(19,217,176),(20,218,169),(21,219,170),(22,220,171),(23,221,172),(24,222,173),(25,246,416),(26,247,409),(27,248,410),(28,241,411),(29,242,412),(30,243,413),(31,244,414),(32,245,415),(33,202,62),(34,203,63),(35,204,64),(36,205,57),(37,206,58),(38,207,59),(39,208,60),(40,201,61),(41,276,65),(42,277,66),(43,278,67),(44,279,68),(45,280,69),(46,273,70),(47,274,71),(48,275,72),(49,301,342),(50,302,343),(51,303,344),(52,304,337),(53,297,338),(54,298,339),(55,299,340),(56,300,341),(73,359,150),(74,360,151),(75,353,152),(76,354,145),(77,355,146),(78,356,147),(79,357,148),(80,358,149),(81,383,293),(82,384,294),(83,377,295),(84,378,296),(85,379,289),(86,380,290),(87,381,291),(88,382,292),(89,212,329),(90,213,330),(91,214,331),(92,215,332),(93,216,333),(94,209,334),(95,210,335),(96,211,336),(97,143,194),(98,144,195),(99,137,196),(100,138,197),(101,139,198),(102,140,199),(103,141,200),(104,142,193),(105,349,238),(106,350,239),(107,351,240),(108,352,233),(109,345,234),(110,346,235),(111,347,236),(112,348,237),(113,159,226),(114,160,227),(115,153,228),(116,154,229),(117,155,230),(118,156,231),(119,157,232),(120,158,225),(129,403,254),(130,404,255),(131,405,256),(132,406,249),(133,407,250),(134,408,251),(135,401,252),(136,402,253),(161,428,319),(162,429,320),(163,430,313),(164,431,314),(165,432,315),(166,425,316),(167,426,317),(168,427,318),(185,424,395),(186,417,396),(187,418,397),(188,419,398),(189,420,399),(190,421,400),(191,422,393),(192,423,394),(257,367,324),(258,368,325),(259,361,326),(260,362,327),(261,363,328),(262,364,321),(263,365,322),(264,366,323),(265,372,308),(266,373,309),(267,374,310),(268,375,311),(269,376,312),(270,369,305),(271,370,306),(272,371,307)], [(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),(25,222,29,218),(26,221,30,217),(27,220,31,224),(28,219,32,223),(33,371,37,375),(34,370,38,374),(35,369,39,373),(36,376,40,372),(41,422,45,418),(42,421,46,417),(43,420,47,424),(44,419,48,423),(49,225,53,229),(50,232,54,228),(51,231,55,227),(52,230,56,226),(57,312,61,308),(58,311,62,307),(59,310,63,306),(60,309,64,305),(65,393,69,397),(66,400,70,396),(67,399,71,395),(68,398,72,394),(73,401,77,405),(74,408,78,404),(75,407,79,403),(76,406,80,402),(81,390,85,386),(82,389,86,385),(83,388,87,392),(84,387,88,391),(89,315,93,319),(90,314,94,318),(91,313,95,317),(92,320,96,316),(97,323,101,327),(98,322,102,326),(99,321,103,325),(100,328,104,324),(105,285,109,281),(106,284,110,288),(107,283,111,287),(108,282,112,286),(113,337,117,341),(114,344,118,340),(115,343,119,339),(116,342,120,338),(121,345,125,349),(122,352,126,348),(123,351,127,347),(124,350,128,346),(129,353,133,357),(130,360,134,356),(131,359,135,355),(132,358,136,354),(137,364,141,368),(138,363,142,367),(139,362,143,366),(140,361,144,365),(145,249,149,253),(146,256,150,252),(147,255,151,251),(148,254,152,250),(153,302,157,298),(154,301,158,297),(155,300,159,304),(156,299,160,303),(161,329,165,333),(162,336,166,332),(163,335,167,331),(164,334,168,330),(169,416,173,412),(170,415,174,411),(171,414,175,410),(172,413,176,409),(177,290,181,294),(178,289,182,293),(179,296,183,292),(180,295,184,291),(185,278,189,274),(186,277,190,273),(187,276,191,280),(188,275,192,279),(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···3M4A4B4C6A···6M8A8B12A···12Z24A···24AZ
order123···34446···68812···1224···24
size112···221081082···2222···22···2

111 irreducible representations

dim111222222
type++++++-+-
imageC1C2C2S3D4D6Q16D12Dic12
kernelC3312Q16C32×C24C338Q8C3×C24C32×C6C3×C12C33C3×C6C32
# reps1121311322652

Matrix representation of C3312Q16 in GL6(𝔽73)

72720000
100000
0072100
0072000
00007272
000010
,
010000
72720000
0072100
0072000
000001
00007272
,
010000
72720000
001000
000100
000010
000001
,
100000
010000
0018500
00682300
0000720
0000072
,
66590000
6670000
0054500
00591900
00004163
00002232

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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