metabelian, supersoluble, monomial
Aliases: C33⋊15Q16, (C3×C12).134D6, C33⋊7C8.2C2, (C32×C6).83D4, (Q8×C33).3C2, C33⋊8Q8.4C2, C3⋊3(C32⋊7Q16), (Q8×C32).27S3, C32⋊13(C3⋊Q16), C2.7(C33⋊15D4), C6.27(C32⋊7D4), Q8.2(C33⋊C2), (C32×C12).34C22, C12.20(C2×C3⋊S3), C4.4(C2×C33⋊C2), (C3×Q8).13(C3⋊S3), (C3×C6).118(C3⋊D4), SmallGroup(432,510)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C33⋊15Q16
G = < a,b,c,d,e | a3=b3=c3=d8=1, e2=d4, ab=ba, ac=ca, dad-1=a-1, ae=ea, bc=cb, dbd-1=b-1, be=eb, dcd-1=c-1, ce=ec, ede-1=d-1 >
Subgroups: 1088 in 252 conjugacy classes, 115 normal (11 characteristic)
C1, C2, C3, C4, C4, C6, C8, Q8, Q8, C32, Dic3, C12, C12, Q16, C3×C6, C3⋊C8, Dic6, C3×Q8, C33, C3⋊Dic3, C3×C12, C3×C12, C3⋊Q16, C32×C6, C32⋊4C8, C32⋊4Q8, Q8×C32, C33⋊5C4, C32×C12, C32×C12, C32⋊7Q16, C33⋊7C8, C33⋊8Q8, Q8×C33, C33⋊15Q16
Quotients: C1, C2, C22, S3, D4, D6, Q16, C3⋊S3, C3⋊D4, C2×C3⋊S3, C3⋊Q16, C33⋊C2, C32⋊7D4, C2×C33⋊C2, C32⋊7Q16, C33⋊15D4, C33⋊15Q16
►Regular action on 432 points
Generators in S432
(1 401 256)(2 249 402)(3 403 250)(4 251 404)(5 405 252)(6 253 406)(7 407 254)(8 255 408)(9 238 128)(10 121 239)(11 240 122)(12 123 233)(13 234 124)(14 125 235)(15 236 126)(16 127 237)(17 34 136)(18 129 35)(19 36 130)(20 131 37)(21 38 132)(22 133 39)(23 40 134)(24 135 33)(25 248 285)(26 286 241)(27 242 287)(28 288 243)(29 244 281)(30 282 245)(31 246 283)(32 284 247)(41 160 386)(42 387 153)(43 154 388)(44 389 155)(45 156 390)(46 391 157)(47 158 392)(48 385 159)(49 73 220)(50 221 74)(51 75 222)(52 223 76)(53 77 224)(54 217 78)(55 79 218)(56 219 80)(57 292 395)(58 396 293)(59 294 397)(60 398 295)(61 296 399)(62 400 289)(63 290 393)(64 394 291)(65 192 201)(66 202 185)(67 186 203)(68 204 187)(69 188 205)(70 206 189)(71 190 207)(72 208 191)(81 198 340)(82 341 199)(83 200 342)(84 343 193)(85 194 344)(86 337 195)(87 196 338)(88 339 197)(89 179 316)(90 317 180)(91 181 318)(92 319 182)(93 183 320)(94 313 184)(95 177 314)(96 315 178)(97 427 167)(98 168 428)(99 429 161)(100 162 430)(101 431 163)(102 164 432)(103 425 165)(104 166 426)(105 118 175)(106 176 119)(107 120 169)(108 170 113)(109 114 171)(110 172 115)(111 116 173)(112 174 117)(137 350 370)(138 371 351)(139 352 372)(140 373 345)(141 346 374)(142 375 347)(143 348 376)(144 369 349)(145 274 325)(146 326 275)(147 276 327)(148 328 277)(149 278 321)(150 322 279)(151 280 323)(152 324 273)(209 257 333)(210 334 258)(211 259 335)(212 336 260)(213 261 329)(214 330 262)(215 263 331)(216 332 264)(225 266 365)(226 366 267)(227 268 367)(228 368 269)(229 270 361)(230 362 271)(231 272 363)(232 364 265)(297 421 382)(298 383 422)(299 423 384)(300 377 424)(301 417 378)(302 379 418)(303 419 380)(304 381 420)(305 412 356)(306 357 413)(307 414 358)(308 359 415)(309 416 360)(310 353 409)(311 410 354)(312 355 411)
(1 99 371)(2 372 100)(3 101 373)(4 374 102)(5 103 375)(6 376 104)(7 97 369)(8 370 98)(9 59 69)(10 70 60)(11 61 71)(12 72 62)(13 63 65)(14 66 64)(15 57 67)(16 68 58)(17 410 261)(18 262 411)(19 412 263)(20 264 413)(21 414 257)(22 258 415)(23 416 259)(24 260 409)(25 83 419)(26 420 84)(27 85 421)(28 422 86)(29 87 423)(30 424 88)(31 81 417)(32 418 82)(33 336 353)(34 354 329)(35 330 355)(36 356 331)(37 332 357)(38 358 333)(39 334 359)(40 360 335)(41 231 91)(42 92 232)(43 225 93)(44 94 226)(45 227 95)(46 96 228)(47 229 89)(48 90 230)(49 323 112)(50 105 324)(51 325 106)(52 107 326)(53 327 108)(54 109 328)(55 321 110)(56 111 322)(73 151 174)(74 175 152)(75 145 176)(76 169 146)(77 147 170)(78 171 148)(79 149 172)(80 173 150)(113 224 276)(114 277 217)(115 218 278)(116 279 219)(117 220 280)(118 273 221)(119 222 274)(120 275 223)(121 206 398)(122 399 207)(123 208 400)(124 393 201)(125 202 394)(126 395 203)(127 204 396)(128 397 205)(129 214 312)(130 305 215)(131 216 306)(132 307 209)(133 210 308)(134 309 211)(135 212 310)(136 311 213)(137 168 255)(138 256 161)(139 162 249)(140 250 163)(141 164 251)(142 252 165)(143 166 253)(144 254 167)(153 182 265)(154 266 183)(155 184 267)(156 268 177)(157 178 269)(158 270 179)(159 180 271)(160 272 181)(185 291 235)(186 236 292)(187 293 237)(188 238 294)(189 295 239)(190 240 296)(191 289 233)(192 234 290)(193 241 381)(194 382 242)(195 243 383)(196 384 244)(197 245 377)(198 378 246)(199 247 379)(200 380 248)(281 338 299)(282 300 339)(283 340 301)(284 302 341)(285 342 303)(286 304 343)(287 344 297)(288 298 337)(313 366 389)(314 390 367)(315 368 391)(316 392 361)(317 362 385)(318 386 363)(319 364 387)(320 388 365)(345 403 431)(346 432 404)(347 405 425)(348 426 406)(349 407 427)(350 428 408)(351 401 429)(352 430 402)
(1 85 221)(2 222 86)(3 87 223)(4 224 88)(5 81 217)(6 218 82)(7 83 219)(8 220 84)(9 130 46)(10 47 131)(11 132 48)(12 41 133)(13 134 42)(14 43 135)(15 136 44)(16 45 129)(17 389 236)(18 237 390)(19 391 238)(20 239 392)(21 385 240)(22 233 386)(23 387 234)(24 235 388)(25 279 369)(26 370 280)(27 273 371)(28 372 274)(29 275 373)(30 374 276)(31 277 375)(32 376 278)(33 125 154)(34 155 126)(35 127 156)(36 157 128)(37 121 158)(38 159 122)(39 123 160)(40 153 124)(49 343 255)(50 256 344)(51 337 249)(52 250 338)(53 339 251)(54 252 340)(55 341 253)(56 254 342)(57 311 94)(58 95 312)(59 305 96)(60 89 306)(61 307 90)(62 91 308)(63 309 92)(64 93 310)(65 211 232)(66 225 212)(67 213 226)(68 227 214)(69 215 228)(70 229 216)(71 209 230)(72 231 210)(73 193 408)(74 401 194)(75 195 402)(76 403 196)(77 197 404)(78 405 198)(79 199 406)(80 407 200)(97 419 116)(98 117 420)(99 421 118)(100 119 422)(101 423 120)(102 113 424)(103 417 114)(104 115 418)(105 161 297)(106 298 162)(107 163 299)(108 300 164)(109 165 301)(110 302 166)(111 167 303)(112 304 168)(137 323 286)(138 287 324)(139 325 288)(140 281 326)(141 327 282)(142 283 328)(143 321 284)(144 285 322)(145 243 352)(146 345 244)(147 245 346)(148 347 246)(149 247 348)(150 349 248)(151 241 350)(152 351 242)(169 431 384)(170 377 432)(171 425 378)(172 379 426)(173 427 380)(174 381 428)(175 429 382)(176 383 430)(177 355 396)(178 397 356)(179 357 398)(180 399 358)(181 359 400)(182 393 360)(183 353 394)(184 395 354)(185 365 260)(186 261 366)(187 367 262)(188 263 368)(189 361 264)(190 257 362)(191 363 258)(192 259 364)(201 335 265)(202 266 336)(203 329 267)(204 268 330)(205 331 269)(206 270 332)(207 333 271)(208 272 334)(289 318 415)(290 416 319)(291 320 409)(292 410 313)(293 314 411)(294 412 315)(295 316 413)(296 414 317)
(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)
(1 204 5 208)(2 203 6 207)(3 202 7 206)(4 201 8 205)(9 141 13 137)(10 140 14 144)(11 139 15 143)(12 138 16 142)(17 149 21 145)(18 148 22 152)(19 147 23 151)(20 146 24 150)(25 158 29 154)(26 157 30 153)(27 156 31 160)(28 155 32 159)(33 279 37 275)(34 278 38 274)(35 277 39 273)(36 276 40 280)(41 287 45 283)(42 286 46 282)(43 285 47 281)(44 284 48 288)(49 215 53 211)(50 214 54 210)(51 213 55 209)(52 212 56 216)(57 166 61 162)(58 165 62 161)(59 164 63 168)(60 163 64 167)(65 255 69 251)(66 254 70 250)(67 253 71 249)(68 252 72 256)(73 263 77 259)(74 262 78 258)(75 261 79 257)(76 260 80 264)(81 272 85 268)(82 271 86 267)(83 270 87 266)(84 269 88 265)(89 299 93 303)(90 298 94 302)(91 297 95 301)(92 304 96 300)(97 398 101 394)(98 397 102 393)(99 396 103 400)(100 395 104 399)(105 312 109 308)(106 311 110 307)(107 310 111 306)(108 309 112 305)(113 360 117 356)(114 359 118 355)(115 358 119 354)(116 357 120 353)(121 373 125 369)(122 372 126 376)(123 371 127 375)(124 370 128 374)(129 328 133 324)(130 327 134 323)(131 326 135 322)(132 325 136 321)(169 409 173 413)(170 416 174 412)(171 415 175 411)(172 414 176 410)(177 417 181 421)(178 424 182 420)(179 423 183 419)(180 422 184 418)(185 407 189 403)(186 406 190 402)(187 405 191 401)(188 404 192 408)(193 368 197 364)(194 367 198 363)(195 366 199 362)(196 365 200 361)(217 334 221 330)(218 333 222 329)(219 332 223 336)(220 331 224 335)(225 342 229 338)(226 341 230 337)(227 340 231 344)(228 339 232 343)(233 351 237 347)(234 350 238 346)(235 349 239 345)(236 348 240 352)(241 391 245 387)(242 390 246 386)(243 389 247 385)(244 388 248 392)(289 429 293 425)(290 428 294 432)(291 427 295 431)(292 426 296 430)(313 379 317 383)(314 378 318 382)(315 377 319 381)(316 384 320 380)
G:=sub<Sym(432)| (1,401,256)(2,249,402)(3,403,250)(4,251,404)(5,405,252)(6,253,406)(7,407,254)(8,255,408)(9,238,128)(10,121,239)(11,240,122)(12,123,233)(13,234,124)(14,125,235)(15,236,126)(16,127,237)(17,34,136)(18,129,35)(19,36,130)(20,131,37)(21,38,132)(22,133,39)(23,40,134)(24,135,33)(25,248,285)(26,286,241)(27,242,287)(28,288,243)(29,244,281)(30,282,245)(31,246,283)(32,284,247)(41,160,386)(42,387,153)(43,154,388)(44,389,155)(45,156,390)(46,391,157)(47,158,392)(48,385,159)(49,73,220)(50,221,74)(51,75,222)(52,223,76)(53,77,224)(54,217,78)(55,79,218)(56,219,80)(57,292,395)(58,396,293)(59,294,397)(60,398,295)(61,296,399)(62,400,289)(63,290,393)(64,394,291)(65,192,201)(66,202,185)(67,186,203)(68,204,187)(69,188,205)(70,206,189)(71,190,207)(72,208,191)(81,198,340)(82,341,199)(83,200,342)(84,343,193)(85,194,344)(86,337,195)(87,196,338)(88,339,197)(89,179,316)(90,317,180)(91,181,318)(92,319,182)(93,183,320)(94,313,184)(95,177,314)(96,315,178)(97,427,167)(98,168,428)(99,429,161)(100,162,430)(101,431,163)(102,164,432)(103,425,165)(104,166,426)(105,118,175)(106,176,119)(107,120,169)(108,170,113)(109,114,171)(110,172,115)(111,116,173)(112,174,117)(137,350,370)(138,371,351)(139,352,372)(140,373,345)(141,346,374)(142,375,347)(143,348,376)(144,369,349)(145,274,325)(146,326,275)(147,276,327)(148,328,277)(149,278,321)(150,322,279)(151,280,323)(152,324,273)(209,257,333)(210,334,258)(211,259,335)(212,336,260)(213,261,329)(214,330,262)(215,263,331)(216,332,264)(225,266,365)(226,366,267)(227,268,367)(228,368,269)(229,270,361)(230,362,271)(231,272,363)(232,364,265)(297,421,382)(298,383,422)(299,423,384)(300,377,424)(301,417,378)(302,379,418)(303,419,380)(304,381,420)(305,412,356)(306,357,413)(307,414,358)(308,359,415)(309,416,360)(310,353,409)(311,410,354)(312,355,411), (1,99,371)(2,372,100)(3,101,373)(4,374,102)(5,103,375)(6,376,104)(7,97,369)(8,370,98)(9,59,69)(10,70,60)(11,61,71)(12,72,62)(13,63,65)(14,66,64)(15,57,67)(16,68,58)(17,410,261)(18,262,411)(19,412,263)(20,264,413)(21,414,257)(22,258,415)(23,416,259)(24,260,409)(25,83,419)(26,420,84)(27,85,421)(28,422,86)(29,87,423)(30,424,88)(31,81,417)(32,418,82)(33,336,353)(34,354,329)(35,330,355)(36,356,331)(37,332,357)(38,358,333)(39,334,359)(40,360,335)(41,231,91)(42,92,232)(43,225,93)(44,94,226)(45,227,95)(46,96,228)(47,229,89)(48,90,230)(49,323,112)(50,105,324)(51,325,106)(52,107,326)(53,327,108)(54,109,328)(55,321,110)(56,111,322)(73,151,174)(74,175,152)(75,145,176)(76,169,146)(77,147,170)(78,171,148)(79,149,172)(80,173,150)(113,224,276)(114,277,217)(115,218,278)(116,279,219)(117,220,280)(118,273,221)(119,222,274)(120,275,223)(121,206,398)(122,399,207)(123,208,400)(124,393,201)(125,202,394)(126,395,203)(127,204,396)(128,397,205)(129,214,312)(130,305,215)(131,216,306)(132,307,209)(133,210,308)(134,309,211)(135,212,310)(136,311,213)(137,168,255)(138,256,161)(139,162,249)(140,250,163)(141,164,251)(142,252,165)(143,166,253)(144,254,167)(153,182,265)(154,266,183)(155,184,267)(156,268,177)(157,178,269)(158,270,179)(159,180,271)(160,272,181)(185,291,235)(186,236,292)(187,293,237)(188,238,294)(189,295,239)(190,240,296)(191,289,233)(192,234,290)(193,241,381)(194,382,242)(195,243,383)(196,384,244)(197,245,377)(198,378,246)(199,247,379)(200,380,248)(281,338,299)(282,300,339)(283,340,301)(284,302,341)(285,342,303)(286,304,343)(287,344,297)(288,298,337)(313,366,389)(314,390,367)(315,368,391)(316,392,361)(317,362,385)(318,386,363)(319,364,387)(320,388,365)(345,403,431)(346,432,404)(347,405,425)(348,426,406)(349,407,427)(350,428,408)(351,401,429)(352,430,402), (1,85,221)(2,222,86)(3,87,223)(4,224,88)(5,81,217)(6,218,82)(7,83,219)(8,220,84)(9,130,46)(10,47,131)(11,132,48)(12,41,133)(13,134,42)(14,43,135)(15,136,44)(16,45,129)(17,389,236)(18,237,390)(19,391,238)(20,239,392)(21,385,240)(22,233,386)(23,387,234)(24,235,388)(25,279,369)(26,370,280)(27,273,371)(28,372,274)(29,275,373)(30,374,276)(31,277,375)(32,376,278)(33,125,154)(34,155,126)(35,127,156)(36,157,128)(37,121,158)(38,159,122)(39,123,160)(40,153,124)(49,343,255)(50,256,344)(51,337,249)(52,250,338)(53,339,251)(54,252,340)(55,341,253)(56,254,342)(57,311,94)(58,95,312)(59,305,96)(60,89,306)(61,307,90)(62,91,308)(63,309,92)(64,93,310)(65,211,232)(66,225,212)(67,213,226)(68,227,214)(69,215,228)(70,229,216)(71,209,230)(72,231,210)(73,193,408)(74,401,194)(75,195,402)(76,403,196)(77,197,404)(78,405,198)(79,199,406)(80,407,200)(97,419,116)(98,117,420)(99,421,118)(100,119,422)(101,423,120)(102,113,424)(103,417,114)(104,115,418)(105,161,297)(106,298,162)(107,163,299)(108,300,164)(109,165,301)(110,302,166)(111,167,303)(112,304,168)(137,323,286)(138,287,324)(139,325,288)(140,281,326)(141,327,282)(142,283,328)(143,321,284)(144,285,322)(145,243,352)(146,345,244)(147,245,346)(148,347,246)(149,247,348)(150,349,248)(151,241,350)(152,351,242)(169,431,384)(170,377,432)(171,425,378)(172,379,426)(173,427,380)(174,381,428)(175,429,382)(176,383,430)(177,355,396)(178,397,356)(179,357,398)(180,399,358)(181,359,400)(182,393,360)(183,353,394)(184,395,354)(185,365,260)(186,261,366)(187,367,262)(188,263,368)(189,361,264)(190,257,362)(191,363,258)(192,259,364)(201,335,265)(202,266,336)(203,329,267)(204,268,330)(205,331,269)(206,270,332)(207,333,271)(208,272,334)(289,318,415)(290,416,319)(291,320,409)(292,410,313)(293,314,411)(294,412,315)(295,316,413)(296,414,317), (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), (1,204,5,208)(2,203,6,207)(3,202,7,206)(4,201,8,205)(9,141,13,137)(10,140,14,144)(11,139,15,143)(12,138,16,142)(17,149,21,145)(18,148,22,152)(19,147,23,151)(20,146,24,150)(25,158,29,154)(26,157,30,153)(27,156,31,160)(28,155,32,159)(33,279,37,275)(34,278,38,274)(35,277,39,273)(36,276,40,280)(41,287,45,283)(42,286,46,282)(43,285,47,281)(44,284,48,288)(49,215,53,211)(50,214,54,210)(51,213,55,209)(52,212,56,216)(57,166,61,162)(58,165,62,161)(59,164,63,168)(60,163,64,167)(65,255,69,251)(66,254,70,250)(67,253,71,249)(68,252,72,256)(73,263,77,259)(74,262,78,258)(75,261,79,257)(76,260,80,264)(81,272,85,268)(82,271,86,267)(83,270,87,266)(84,269,88,265)(89,299,93,303)(90,298,94,302)(91,297,95,301)(92,304,96,300)(97,398,101,394)(98,397,102,393)(99,396,103,400)(100,395,104,399)(105,312,109,308)(106,311,110,307)(107,310,111,306)(108,309,112,305)(113,360,117,356)(114,359,118,355)(115,358,119,354)(116,357,120,353)(121,373,125,369)(122,372,126,376)(123,371,127,375)(124,370,128,374)(129,328,133,324)(130,327,134,323)(131,326,135,322)(132,325,136,321)(169,409,173,413)(170,416,174,412)(171,415,175,411)(172,414,176,410)(177,417,181,421)(178,424,182,420)(179,423,183,419)(180,422,184,418)(185,407,189,403)(186,406,190,402)(187,405,191,401)(188,404,192,408)(193,368,197,364)(194,367,198,363)(195,366,199,362)(196,365,200,361)(217,334,221,330)(218,333,222,329)(219,332,223,336)(220,331,224,335)(225,342,229,338)(226,341,230,337)(227,340,231,344)(228,339,232,343)(233,351,237,347)(234,350,238,346)(235,349,239,345)(236,348,240,352)(241,391,245,387)(242,390,246,386)(243,389,247,385)(244,388,248,392)(289,429,293,425)(290,428,294,432)(291,427,295,431)(292,426,296,430)(313,379,317,383)(314,378,318,382)(315,377,319,381)(316,384,320,380)>;
G:=Group( (1,401,256)(2,249,402)(3,403,250)(4,251,404)(5,405,252)(6,253,406)(7,407,254)(8,255,408)(9,238,128)(10,121,239)(11,240,122)(12,123,233)(13,234,124)(14,125,235)(15,236,126)(16,127,237)(17,34,136)(18,129,35)(19,36,130)(20,131,37)(21,38,132)(22,133,39)(23,40,134)(24,135,33)(25,248,285)(26,286,241)(27,242,287)(28,288,243)(29,244,281)(30,282,245)(31,246,283)(32,284,247)(41,160,386)(42,387,153)(43,154,388)(44,389,155)(45,156,390)(46,391,157)(47,158,392)(48,385,159)(49,73,220)(50,221,74)(51,75,222)(52,223,76)(53,77,224)(54,217,78)(55,79,218)(56,219,80)(57,292,395)(58,396,293)(59,294,397)(60,398,295)(61,296,399)(62,400,289)(63,290,393)(64,394,291)(65,192,201)(66,202,185)(67,186,203)(68,204,187)(69,188,205)(70,206,189)(71,190,207)(72,208,191)(81,198,340)(82,341,199)(83,200,342)(84,343,193)(85,194,344)(86,337,195)(87,196,338)(88,339,197)(89,179,316)(90,317,180)(91,181,318)(92,319,182)(93,183,320)(94,313,184)(95,177,314)(96,315,178)(97,427,167)(98,168,428)(99,429,161)(100,162,430)(101,431,163)(102,164,432)(103,425,165)(104,166,426)(105,118,175)(106,176,119)(107,120,169)(108,170,113)(109,114,171)(110,172,115)(111,116,173)(112,174,117)(137,350,370)(138,371,351)(139,352,372)(140,373,345)(141,346,374)(142,375,347)(143,348,376)(144,369,349)(145,274,325)(146,326,275)(147,276,327)(148,328,277)(149,278,321)(150,322,279)(151,280,323)(152,324,273)(209,257,333)(210,334,258)(211,259,335)(212,336,260)(213,261,329)(214,330,262)(215,263,331)(216,332,264)(225,266,365)(226,366,267)(227,268,367)(228,368,269)(229,270,361)(230,362,271)(231,272,363)(232,364,265)(297,421,382)(298,383,422)(299,423,384)(300,377,424)(301,417,378)(302,379,418)(303,419,380)(304,381,420)(305,412,356)(306,357,413)(307,414,358)(308,359,415)(309,416,360)(310,353,409)(311,410,354)(312,355,411), (1,99,371)(2,372,100)(3,101,373)(4,374,102)(5,103,375)(6,376,104)(7,97,369)(8,370,98)(9,59,69)(10,70,60)(11,61,71)(12,72,62)(13,63,65)(14,66,64)(15,57,67)(16,68,58)(17,410,261)(18,262,411)(19,412,263)(20,264,413)(21,414,257)(22,258,415)(23,416,259)(24,260,409)(25,83,419)(26,420,84)(27,85,421)(28,422,86)(29,87,423)(30,424,88)(31,81,417)(32,418,82)(33,336,353)(34,354,329)(35,330,355)(36,356,331)(37,332,357)(38,358,333)(39,334,359)(40,360,335)(41,231,91)(42,92,232)(43,225,93)(44,94,226)(45,227,95)(46,96,228)(47,229,89)(48,90,230)(49,323,112)(50,105,324)(51,325,106)(52,107,326)(53,327,108)(54,109,328)(55,321,110)(56,111,322)(73,151,174)(74,175,152)(75,145,176)(76,169,146)(77,147,170)(78,171,148)(79,149,172)(80,173,150)(113,224,276)(114,277,217)(115,218,278)(116,279,219)(117,220,280)(118,273,221)(119,222,274)(120,275,223)(121,206,398)(122,399,207)(123,208,400)(124,393,201)(125,202,394)(126,395,203)(127,204,396)(128,397,205)(129,214,312)(130,305,215)(131,216,306)(132,307,209)(133,210,308)(134,309,211)(135,212,310)(136,311,213)(137,168,255)(138,256,161)(139,162,249)(140,250,163)(141,164,251)(142,252,165)(143,166,253)(144,254,167)(153,182,265)(154,266,183)(155,184,267)(156,268,177)(157,178,269)(158,270,179)(159,180,271)(160,272,181)(185,291,235)(186,236,292)(187,293,237)(188,238,294)(189,295,239)(190,240,296)(191,289,233)(192,234,290)(193,241,381)(194,382,242)(195,243,383)(196,384,244)(197,245,377)(198,378,246)(199,247,379)(200,380,248)(281,338,299)(282,300,339)(283,340,301)(284,302,341)(285,342,303)(286,304,343)(287,344,297)(288,298,337)(313,366,389)(314,390,367)(315,368,391)(316,392,361)(317,362,385)(318,386,363)(319,364,387)(320,388,365)(345,403,431)(346,432,404)(347,405,425)(348,426,406)(349,407,427)(350,428,408)(351,401,429)(352,430,402), (1,85,221)(2,222,86)(3,87,223)(4,224,88)(5,81,217)(6,218,82)(7,83,219)(8,220,84)(9,130,46)(10,47,131)(11,132,48)(12,41,133)(13,134,42)(14,43,135)(15,136,44)(16,45,129)(17,389,236)(18,237,390)(19,391,238)(20,239,392)(21,385,240)(22,233,386)(23,387,234)(24,235,388)(25,279,369)(26,370,280)(27,273,371)(28,372,274)(29,275,373)(30,374,276)(31,277,375)(32,376,278)(33,125,154)(34,155,126)(35,127,156)(36,157,128)(37,121,158)(38,159,122)(39,123,160)(40,153,124)(49,343,255)(50,256,344)(51,337,249)(52,250,338)(53,339,251)(54,252,340)(55,341,253)(56,254,342)(57,311,94)(58,95,312)(59,305,96)(60,89,306)(61,307,90)(62,91,308)(63,309,92)(64,93,310)(65,211,232)(66,225,212)(67,213,226)(68,227,214)(69,215,228)(70,229,216)(71,209,230)(72,231,210)(73,193,408)(74,401,194)(75,195,402)(76,403,196)(77,197,404)(78,405,198)(79,199,406)(80,407,200)(97,419,116)(98,117,420)(99,421,118)(100,119,422)(101,423,120)(102,113,424)(103,417,114)(104,115,418)(105,161,297)(106,298,162)(107,163,299)(108,300,164)(109,165,301)(110,302,166)(111,167,303)(112,304,168)(137,323,286)(138,287,324)(139,325,288)(140,281,326)(141,327,282)(142,283,328)(143,321,284)(144,285,322)(145,243,352)(146,345,244)(147,245,346)(148,347,246)(149,247,348)(150,349,248)(151,241,350)(152,351,242)(169,431,384)(170,377,432)(171,425,378)(172,379,426)(173,427,380)(174,381,428)(175,429,382)(176,383,430)(177,355,396)(178,397,356)(179,357,398)(180,399,358)(181,359,400)(182,393,360)(183,353,394)(184,395,354)(185,365,260)(186,261,366)(187,367,262)(188,263,368)(189,361,264)(190,257,362)(191,363,258)(192,259,364)(201,335,265)(202,266,336)(203,329,267)(204,268,330)(205,331,269)(206,270,332)(207,333,271)(208,272,334)(289,318,415)(290,416,319)(291,320,409)(292,410,313)(293,314,411)(294,412,315)(295,316,413)(296,414,317), (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), (1,204,5,208)(2,203,6,207)(3,202,7,206)(4,201,8,205)(9,141,13,137)(10,140,14,144)(11,139,15,143)(12,138,16,142)(17,149,21,145)(18,148,22,152)(19,147,23,151)(20,146,24,150)(25,158,29,154)(26,157,30,153)(27,156,31,160)(28,155,32,159)(33,279,37,275)(34,278,38,274)(35,277,39,273)(36,276,40,280)(41,287,45,283)(42,286,46,282)(43,285,47,281)(44,284,48,288)(49,215,53,211)(50,214,54,210)(51,213,55,209)(52,212,56,216)(57,166,61,162)(58,165,62,161)(59,164,63,168)(60,163,64,167)(65,255,69,251)(66,254,70,250)(67,253,71,249)(68,252,72,256)(73,263,77,259)(74,262,78,258)(75,261,79,257)(76,260,80,264)(81,272,85,268)(82,271,86,267)(83,270,87,266)(84,269,88,265)(89,299,93,303)(90,298,94,302)(91,297,95,301)(92,304,96,300)(97,398,101,394)(98,397,102,393)(99,396,103,400)(100,395,104,399)(105,312,109,308)(106,311,110,307)(107,310,111,306)(108,309,112,305)(113,360,117,356)(114,359,118,355)(115,358,119,354)(116,357,120,353)(121,373,125,369)(122,372,126,376)(123,371,127,375)(124,370,128,374)(129,328,133,324)(130,327,134,323)(131,326,135,322)(132,325,136,321)(169,409,173,413)(170,416,174,412)(171,415,175,411)(172,414,176,410)(177,417,181,421)(178,424,182,420)(179,423,183,419)(180,422,184,418)(185,407,189,403)(186,406,190,402)(187,405,191,401)(188,404,192,408)(193,368,197,364)(194,367,198,363)(195,366,199,362)(196,365,200,361)(217,334,221,330)(218,333,222,329)(219,332,223,336)(220,331,224,335)(225,342,229,338)(226,341,230,337)(227,340,231,344)(228,339,232,343)(233,351,237,347)(234,350,238,346)(235,349,239,345)(236,348,240,352)(241,391,245,387)(242,390,246,386)(243,389,247,385)(244,388,248,392)(289,429,293,425)(290,428,294,432)(291,427,295,431)(292,426,296,430)(313,379,317,383)(314,378,318,382)(315,377,319,381)(316,384,320,380) );
G=PermutationGroup([[(1,401,256),(2,249,402),(3,403,250),(4,251,404),(5,405,252),(6,253,406),(7,407,254),(8,255,408),(9,238,128),(10,121,239),(11,240,122),(12,123,233),(13,234,124),(14,125,235),(15,236,126),(16,127,237),(17,34,136),(18,129,35),(19,36,130),(20,131,37),(21,38,132),(22,133,39),(23,40,134),(24,135,33),(25,248,285),(26,286,241),(27,242,287),(28,288,243),(29,244,281),(30,282,245),(31,246,283),(32,284,247),(41,160,386),(42,387,153),(43,154,388),(44,389,155),(45,156,390),(46,391,157),(47,158,392),(48,385,159),(49,73,220),(50,221,74),(51,75,222),(52,223,76),(53,77,224),(54,217,78),(55,79,218),(56,219,80),(57,292,395),(58,396,293),(59,294,397),(60,398,295),(61,296,399),(62,400,289),(63,290,393),(64,394,291),(65,192,201),(66,202,185),(67,186,203),(68,204,187),(69,188,205),(70,206,189),(71,190,207),(72,208,191),(81,198,340),(82,341,199),(83,200,342),(84,343,193),(85,194,344),(86,337,195),(87,196,338),(88,339,197),(89,179,316),(90,317,180),(91,181,318),(92,319,182),(93,183,320),(94,313,184),(95,177,314),(96,315,178),(97,427,167),(98,168,428),(99,429,161),(100,162,430),(101,431,163),(102,164,432),(103,425,165),(104,166,426),(105,118,175),(106,176,119),(107,120,169),(108,170,113),(109,114,171),(110,172,115),(111,116,173),(112,174,117),(137,350,370),(138,371,351),(139,352,372),(140,373,345),(141,346,374),(142,375,347),(143,348,376),(144,369,349),(145,274,325),(146,326,275),(147,276,327),(148,328,277),(149,278,321),(150,322,279),(151,280,323),(152,324,273),(209,257,333),(210,334,258),(211,259,335),(212,336,260),(213,261,329),(214,330,262),(215,263,331),(216,332,264),(225,266,365),(226,366,267),(227,268,367),(228,368,269),(229,270,361),(230,362,271),(231,272,363),(232,364,265),(297,421,382),(298,383,422),(299,423,384),(300,377,424),(301,417,378),(302,379,418),(303,419,380),(304,381,420),(305,412,356),(306,357,413),(307,414,358),(308,359,415),(309,416,360),(310,353,409),(311,410,354),(312,355,411)], [(1,99,371),(2,372,100),(3,101,373),(4,374,102),(5,103,375),(6,376,104),(7,97,369),(8,370,98),(9,59,69),(10,70,60),(11,61,71),(12,72,62),(13,63,65),(14,66,64),(15,57,67),(16,68,58),(17,410,261),(18,262,411),(19,412,263),(20,264,413),(21,414,257),(22,258,415),(23,416,259),(24,260,409),(25,83,419),(26,420,84),(27,85,421),(28,422,86),(29,87,423),(30,424,88),(31,81,417),(32,418,82),(33,336,353),(34,354,329),(35,330,355),(36,356,331),(37,332,357),(38,358,333),(39,334,359),(40,360,335),(41,231,91),(42,92,232),(43,225,93),(44,94,226),(45,227,95),(46,96,228),(47,229,89),(48,90,230),(49,323,112),(50,105,324),(51,325,106),(52,107,326),(53,327,108),(54,109,328),(55,321,110),(56,111,322),(73,151,174),(74,175,152),(75,145,176),(76,169,146),(77,147,170),(78,171,148),(79,149,172),(80,173,150),(113,224,276),(114,277,217),(115,218,278),(116,279,219),(117,220,280),(118,273,221),(119,222,274),(120,275,223),(121,206,398),(122,399,207),(123,208,400),(124,393,201),(125,202,394),(126,395,203),(127,204,396),(128,397,205),(129,214,312),(130,305,215),(131,216,306),(132,307,209),(133,210,308),(134,309,211),(135,212,310),(136,311,213),(137,168,255),(138,256,161),(139,162,249),(140,250,163),(141,164,251),(142,252,165),(143,166,253),(144,254,167),(153,182,265),(154,266,183),(155,184,267),(156,268,177),(157,178,269),(158,270,179),(159,180,271),(160,272,181),(185,291,235),(186,236,292),(187,293,237),(188,238,294),(189,295,239),(190,240,296),(191,289,233),(192,234,290),(193,241,381),(194,382,242),(195,243,383),(196,384,244),(197,245,377),(198,378,246),(199,247,379),(200,380,248),(281,338,299),(282,300,339),(283,340,301),(284,302,341),(285,342,303),(286,304,343),(287,344,297),(288,298,337),(313,366,389),(314,390,367),(315,368,391),(316,392,361),(317,362,385),(318,386,363),(319,364,387),(320,388,365),(345,403,431),(346,432,404),(347,405,425),(348,426,406),(349,407,427),(350,428,408),(351,401,429),(352,430,402)], [(1,85,221),(2,222,86),(3,87,223),(4,224,88),(5,81,217),(6,218,82),(7,83,219),(8,220,84),(9,130,46),(10,47,131),(11,132,48),(12,41,133),(13,134,42),(14,43,135),(15,136,44),(16,45,129),(17,389,236),(18,237,390),(19,391,238),(20,239,392),(21,385,240),(22,233,386),(23,387,234),(24,235,388),(25,279,369),(26,370,280),(27,273,371),(28,372,274),(29,275,373),(30,374,276),(31,277,375),(32,376,278),(33,125,154),(34,155,126),(35,127,156),(36,157,128),(37,121,158),(38,159,122),(39,123,160),(40,153,124),(49,343,255),(50,256,344),(51,337,249),(52,250,338),(53,339,251),(54,252,340),(55,341,253),(56,254,342),(57,311,94),(58,95,312),(59,305,96),(60,89,306),(61,307,90),(62,91,308),(63,309,92),(64,93,310),(65,211,232),(66,225,212),(67,213,226),(68,227,214),(69,215,228),(70,229,216),(71,209,230),(72,231,210),(73,193,408),(74,401,194),(75,195,402),(76,403,196),(77,197,404),(78,405,198),(79,199,406),(80,407,200),(97,419,116),(98,117,420),(99,421,118),(100,119,422),(101,423,120),(102,113,424),(103,417,114),(104,115,418),(105,161,297),(106,298,162),(107,163,299),(108,300,164),(109,165,301),(110,302,166),(111,167,303),(112,304,168),(137,323,286),(138,287,324),(139,325,288),(140,281,326),(141,327,282),(142,283,328),(143,321,284),(144,285,322),(145,243,352),(146,345,244),(147,245,346),(148,347,246),(149,247,348),(150,349,248),(151,241,350),(152,351,242),(169,431,384),(170,377,432),(171,425,378),(172,379,426),(173,427,380),(174,381,428),(175,429,382),(176,383,430),(177,355,396),(178,397,356),(179,357,398),(180,399,358),(181,359,400),(182,393,360),(183,353,394),(184,395,354),(185,365,260),(186,261,366),(187,367,262),(188,263,368),(189,361,264),(190,257,362),(191,363,258),(192,259,364),(201,335,265),(202,266,336),(203,329,267),(204,268,330),(205,331,269),(206,270,332),(207,333,271),(208,272,334),(289,318,415),(290,416,319),(291,320,409),(292,410,313),(293,314,411),(294,412,315),(295,316,413),(296,414,317)], [(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)], [(1,204,5,208),(2,203,6,207),(3,202,7,206),(4,201,8,205),(9,141,13,137),(10,140,14,144),(11,139,15,143),(12,138,16,142),(17,149,21,145),(18,148,22,152),(19,147,23,151),(20,146,24,150),(25,158,29,154),(26,157,30,153),(27,156,31,160),(28,155,32,159),(33,279,37,275),(34,278,38,274),(35,277,39,273),(36,276,40,280),(41,287,45,283),(42,286,46,282),(43,285,47,281),(44,284,48,288),(49,215,53,211),(50,214,54,210),(51,213,55,209),(52,212,56,216),(57,166,61,162),(58,165,62,161),(59,164,63,168),(60,163,64,167),(65,255,69,251),(66,254,70,250),(67,253,71,249),(68,252,72,256),(73,263,77,259),(74,262,78,258),(75,261,79,257),(76,260,80,264),(81,272,85,268),(82,271,86,267),(83,270,87,266),(84,269,88,265),(89,299,93,303),(90,298,94,302),(91,297,95,301),(92,304,96,300),(97,398,101,394),(98,397,102,393),(99,396,103,400),(100,395,104,399),(105,312,109,308),(106,311,110,307),(107,310,111,306),(108,309,112,305),(113,360,117,356),(114,359,118,355),(115,358,119,354),(116,357,120,353),(121,373,125,369),(122,372,126,376),(123,371,127,375),(124,370,128,374),(129,328,133,324),(130,327,134,323),(131,326,135,322),(132,325,136,321),(169,409,173,413),(170,416,174,412),(171,415,175,411),(172,414,176,410),(177,417,181,421),(178,424,182,420),(179,423,183,419),(180,422,184,418),(185,407,189,403),(186,406,190,402),(187,405,191,401),(188,404,192,408),(193,368,197,364),(194,367,198,363),(195,366,199,362),(196,365,200,361),(217,334,221,330),(218,333,222,329),(219,332,223,336),(220,331,224,335),(225,342,229,338),(226,341,230,337),(227,340,231,344),(228,339,232,343),(233,351,237,347),(234,350,238,346),(235,349,239,345),(236,348,240,352),(241,391,245,387),(242,390,246,386),(243,389,247,385),(244,388,248,392),(289,429,293,425),(290,428,294,432),(291,427,295,431),(292,426,296,430),(313,379,317,383),(314,378,318,382),(315,377,319,381),(316,384,320,380)]])
72 conjugacy classes
| class | 1 | 2 | 3A | ··· | 3M | 4A | 4B | 4C | 6A | ··· | 6M | 8A | 8B | 12A | ··· | 12AM |
| order | 1 | 2 | 3 | ··· | 3 | 4 | 4 | 4 | 6 | ··· | 6 | 8 | 8 | 12 | ··· | 12 |
| size | 1 | 1 | 2 | ··· | 2 | 2 | 4 | 108 | 2 | ··· | 2 | 54 | 54 | 4 | ··· | 4 |
72 irreducible representations
| dim | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 4 |
| type | + | + | + | + | + | + | + | - | - | |
| image | C1 | C2 | C2 | C2 | S3 | D4 | D6 | Q16 | C3⋊D4 | C3⋊Q16 |
| kernel | C33⋊15Q16 | C33⋊7C8 | C33⋊8Q8 | Q8×C33 | Q8×C32 | C32×C6 | C3×C12 | C33 | C3×C6 | C32 |
| # reps | 1 | 1 | 1 | 1 | 13 | 1 | 13 | 2 | 26 | 13 |
Matrix representation of C33⋊15Q16 ►in GL8(𝔽73)
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 71 | 70 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
| 64 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 52 | 8 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 3 | 0 | 0 | 0 | 0 |
| 0 | 0 | 72 | 71 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 72 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 72 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
| 8 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 21 | 64 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 72 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 72 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
| 72 | 46 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 10 | 14 | 0 | 0 | 0 | 0 |
| 0 | 0 | 19 | 63 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 11 | 2 | 0 | 0 |
| 0 | 0 | 0 | 0 | 13 | 62 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 16 | 57 |
| 0 | 0 | 0 | 0 | 0 | 0 | 16 | 16 |
| 72 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 72 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 23 | 28 |
| 0 | 0 | 0 | 0 | 0 | 0 | 28 | 50 |
G:=sub<GL(8,GF(73))| [1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,71,1,0,0,0,0,0,0,70,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1],[64,52,0,0,0,0,0,0,0,8,0,0,0,0,0,0,0,0,1,72,0,0,0,0,0,0,3,71,0,0,0,0,0,0,0,0,72,72,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1],[8,21,0,0,0,0,0,0,0,64,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,72,72,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1],[72,0,0,0,0,0,0,0,46,1,0,0,0,0,0,0,0,0,10,19,0,0,0,0,0,0,14,63,0,0,0,0,0,0,0,0,11,13,0,0,0,0,0,0,2,62,0,0,0,0,0,0,0,0,16,16,0,0,0,0,0,0,57,16],[72,0,0,0,0,0,0,0,0,72,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,23,28,0,0,0,0,0,0,28,50] >;
C33⋊15Q16 in GAP, Magma, Sage, TeX
C_3^3\rtimes_{15}Q_{16} % in TeX
G:=Group("C3^3:15Q16"); // GroupNames label
G:=SmallGroup(432,510);
// by ID
G=gap.SmallGroup(432,510);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-3,-3,-3,56,85,64,254,135,58,1124,4037,14118]);
// 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,d*a*d^-1=a^-1,a*e=e*a,b*c=c*b,d*b*d^-1=b^-1,b*e=e*b,d*c*d^-1=c^-1,c*e=e*c,e*d*e^-1=d^-1>;
// generators/relations