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G = Q16×C33  order 432 = 24·33

Direct product of C33 and Q16

direct product, metabelian, nilpotent (class 3), monomial

Aliases: Q16×C33, C12.35C62, C8.(C32×C6), C24.8(C3×C6), (C3×C24).18C6, C4.3(C3×C62), C2.5(D4×C33), (C32×C24).4C2, C6.28(D4×C32), (C32×C6).89D4, Q8.2(C32×C6), (Q8×C33).4C2, (Q8×C32).26C6, (C32×C12).104C22, (C3×C6).84(C3×D4), (C3×Q8).20(C3×C6), (C3×C12).109(C2×C6), SmallGroup(432,519)

Series: Derived ►Chief ►Lower central ►Upper central

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

Generators and relations for Q16×C33
 G = < a,b,c,d,e | a3=b3=c3=d8=1, e2=d4, ab=ba, ac=ca, ad=da, ae=ea, bc=cb, bd=db, be=eb, cd=dc, ce=ec, ede-1=d-1 >

Subgroups: 308 in 252 conjugacy classes, 196 normal (10 characteristic)
C1, C2, C3, C4, C4, C6, C8, Q8, C32, C12, C12, Q16, C3×C6, C24, C3×Q8, C33, C3×C12, C3×C12, C3×Q16, C32×C6, C3×C24, Q8×C32, C32×C12, C32×C12, C32×Q16, C32×C24, Q8×C33, Q16×C33
Quotients: C1, C2, C3, C22, C6, D4, C32, C2×C6, Q16, C3×C6, C3×D4, C33, C62, C3×Q16, C32×C6, D4×C32, C3×C62, C32×Q16, D4×C33, Q16×C33

Smallest permutation representation of Q16×C33
►Regular action on 432 points
Generators in S432
(1 322 247)(2 323 248)(3 324 241)(4 325 242)(5 326 243)(6 327 244)(7 328 245)(8 321 246)(9 211 296)(10 212 289)(11 213 290)(12 214 291)(13 215 292)(14 216 293)(15 209 294)(16 210 295)(17 365 357)(18 366 358)(19 367 359)(20 368 360)(21 361 353)(22 362 354)(23 363 355)(24 364 356)(25 179 312)(26 180 305)(27 181 306)(28 182 307)(29 183 308)(30 184 309)(31 177 310)(32 178 311)(33 163 320)(34 164 313)(35 165 314)(36 166 315)(37 167 316)(38 168 317)(39 161 318)(40 162 319)(41 171 304)(42 172 297)(43 173 298)(44 174 299)(45 175 300)(46 176 301)(47 169 302)(48 170 303)(49 349 341)(50 350 342)(51 351 343)(52 352 344)(53 345 337)(54 346 338)(55 347 339)(56 348 340)(57 187 272)(58 188 265)(59 189 266)(60 190 267)(61 191 268)(62 192 269)(63 185 270)(64 186 271)(65 381 405)(66 382 406)(67 383 407)(68 384 408)(69 377 401)(70 378 402)(71 379 403)(72 380 404)(73 159 81)(74 160 82)(75 153 83)(76 154 84)(77 155 85)(78 156 86)(79 157 87)(80 158 88)(89 120 429)(90 113 430)(91 114 431)(92 115 432)(93 116 425)(94 117 426)(95 118 427)(96 119 428)(97 263 389)(98 264 390)(99 257 391)(100 258 392)(101 259 385)(102 260 386)(103 261 387)(104 262 388)(105 228 397)(106 229 398)(107 230 399)(108 231 400)(109 232 393)(110 225 394)(111 226 395)(112 227 396)(121 420 412)(122 421 413)(123 422 414)(124 423 415)(125 424 416)(126 417 409)(127 418 410)(128 419 411)(129 233 254)(130 234 255)(131 235 256)(132 236 249)(133 237 250)(134 238 251)(135 239 252)(136 240 253)(137 222 145)(138 223 146)(139 224 147)(140 217 148)(141 218 149)(142 219 150)(143 220 151)(144 221 152)(193 331 201)(194 332 202)(195 333 203)(196 334 204)(197 335 205)(198 336 206)(199 329 207)(200 330 208)(273 374 281)(274 375 282)(275 376 283)(276 369 284)(277 370 285)(278 371 286)(279 372 287)(280 373 288)

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

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

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

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

189 conjugacy classes

class 1  2 3A···3Z4A4B4C6A···6Z8A8B12A···12Z12AA···12BZ24A···24AZ
order123···34446···68812···1212···1224···24
size111···12441···1222···24···42···2

189 irreducible representations

dim1111112222
type++++-
imageC1C2C2C3C6C6D4Q16C3×D4C3×Q16
kernelQ16×C33C32×C24Q8×C33C32×Q16C3×C24Q8×C32C32×C6C33C3×C6C32
# reps112262652122652

Matrix representation of Q16×C33 ►in GL4(𝔽73) generated by

64000
06400
00640
00064
,
8000
06400
00640
00064
,
64000
0100
00640
00064
,
72000
07200
005716
005757
,
1000
0100
002328
002850
G:=sub<GL(4,GF(73))| [64,0,0,0,0,64,0,0,0,0,64,0,0,0,0,64],[8,0,0,0,0,64,0,0,0,0,64,0,0,0,0,64],[64,0,0,0,0,1,0,0,0,0,64,0,0,0,0,64],[72,0,0,0,0,72,0,0,0,0,57,57,0,0,16,57],[1,0,0,0,0,1,0,0,0,0,23,28,0,0,28,50] >;
 

Q16×C33 in GAP, Magma, Sage, TeX 

Q_{16}\times C_3^3
 
% in TeX
 
G:=Group("Q16xC3^3");
 
// GroupNames label
 
G:=SmallGroup(432,519);
 
// by ID
 
G=gap.SmallGroup(432,519);
 
# by ID
 
G:=PCGroup([7,-2,-2,-3,-3,-3,-2,-2,1512,1541,1520,13613,6816,124]);
 
// 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,a*e=e*a,b*c=c*b,b*d=d*b,b*e=e*b,c*d=d*c,c*e=e*c,e*d*e^-1=d^-1>;
 
// generators/relations
 

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