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G = C32.3CSU2(𝔽3)  order 432 = 24·33

2nd non-split extension by C32 of CSU2(𝔽3) acting via CSU2(𝔽3)/SL2(𝔽3)=C2

non-abelian, soluble

Aliases: C32.3CSU2(𝔽3), C3⋊(Q8.D9), Q8⋊C9.2S3, C6.4(C3⋊S4), (C3×C6).14S4, (C3×Q8).3D9, C6.5(C3.S4), Q8.2(C9⋊S3), C3.2(C6.5S4), (Q8×C32).10S3, C2.2(C32.3S4), (C3×Q8⋊C9).2C2, (C3×Q8).3(C3⋊S3), SmallGroup(432,255)

Series: Derived ►Chief ►Lower central ►Upper central

Derived series
C1 — C2 — Q8 — C3×Q8⋊C9 — C32.3CSU2(𝔽3)
Chief series
C1 — C2 — Q8 — C3×Q8 — Q8×C32 — C3×Q8⋊C9 — C32.3CSU2(𝔽3)
Lower central
C3×Q8⋊C9 — C32.3CSU2(𝔽3)
Upper central
C1 — C2

Generators and relations for C32.3CSU2(𝔽3)
 G = < a,b,c,d,e,f | a3=b3=c4=1, d2=f2=c2, e3=fbf-1=b-1, ab=ba, ac=ca, ad=da, ae=ea, faf-1=a-1, bc=cb, bd=db, be=eb, dcd-1=fdf-1=c-1, ece-1=cd, fcf-1=c2d, ede-1=c, fef-1=be2 >

Subgroups: 452 in 68 conjugacy classes, 23 normal (11 characteristic)
C1, C2, C3, C3, C4, C6, C6, C8, Q8, Q8, C9, C32, Dic3, C12, Q16, C18, C3×C6, C3⋊C8, Dic6, C3×Q8, C3×Q8, C3×C9, Dic9, C3⋊Dic3, C3×C12, C3⋊Q16, C3×C18, Q8⋊C9, C32⋊4C8, C32⋊4Q8, Q8×C32, C9⋊Dic3, Q8.D9, C32⋊7Q16, C3×Q8⋊C9, C32.3CSU2(𝔽3)
Quotients: C1, C2, S3, D9, C3⋊S3, S4, CSU2(𝔽3), C9⋊S3, C3.S4, C3⋊S4, Q8.D9, C6.5S4, C32.3S4, C32.3CSU2(𝔽3)

Smallest permutation representation of C32.3CSU2(𝔽3)
►Regular action on 432 points
Generators in S432
(1 94 194)(2 95 195)(3 96 196)(4 97 197)(5 98 198)(6 99 190)(7 91 191)(8 92 192)(9 93 193)(10 392 353)(11 393 354)(12 394 355)(13 395 356)(14 396 357)(15 388 358)(16 389 359)(17 390 360)(18 391 352)(19 128 306)(20 129 298)(21 130 299)(22 131 300)(23 132 301)(24 133 302)(25 134 303)(26 135 304)(27 127 305)(28 218 40)(29 219 41)(30 220 42)(31 221 43)(32 222 44)(33 223 45)(34 224 37)(35 225 38)(36 217 39)(46 363 63)(47 364 55)(48 365 56)(49 366 57)(50 367 58)(51 368 59)(52 369 60)(53 361 61)(54 362 62)(64 216 165)(65 208 166)(66 209 167)(67 210 168)(68 211 169)(69 212 170)(70 213 171)(71 214 163)(72 215 164)(73 314 342)(74 315 334)(75 307 335)(76 308 336)(77 309 337)(78 310 338)(79 311 339)(80 312 340)(81 313 341)(82 242 407)(83 243 408)(84 235 409)(85 236 410)(86 237 411)(87 238 412)(88 239 413)(89 240 414)(90 241 406)(100 185 295)(101 186 296)(102 187 297)(103 188 289)(104 189 290)(105 181 291)(106 182 292)(107 183 293)(108 184 294)(109 123 231)(110 124 232)(111 125 233)(112 126 234)(113 118 226)(114 119 227)(115 120 228)(116 121 229)(117 122 230)(136 176 200)(137 177 201)(138 178 202)(139 179 203)(140 180 204)(141 172 205)(142 173 206)(143 174 207)(144 175 199)(145 330 272)(146 331 273)(147 332 274)(148 333 275)(149 325 276)(150 326 277)(151 327 278)(152 328 279)(153 329 271)(154 322 263)(155 323 264)(156 324 265)(157 316 266)(158 317 267)(159 318 268)(160 319 269)(161 320 270)(162 321 262)(244 346 418)(245 347 419)(246 348 420)(247 349 421)(248 350 422)(249 351 423)(250 343 415)(251 344 416)(252 345 417)(253 285 387)(254 286 379)(255 287 380)(256 288 381)(257 280 382)(258 281 383)(259 282 384)(260 283 385)(261 284 386)(370 403 430)(371 404 431)(372 405 432)(373 397 424)(374 398 425)(375 399 426)(376 400 427)(377 401 428)(378 402 429)

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

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

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

(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)

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

36 conjugacy classes

class 1  2 3A3B3C3D4A4B6A6B6C6D8A8B9A···9I12A12B12C12D18A···18I
order123333446666889···91212121218···18
size1122226108222254548···8121212128···8

36 irreducible representations

dim112222344466
type+++++-+---++
imageC1C2S3S3D9CSU2(𝔽3)S4CSU2(𝔽3)Q8.D9C6.5S4C3.S4C3⋊S4
kernelC32.3CSU2(𝔽3)C3×Q8⋊C9Q8⋊C9Q8×C32C3×Q8C32C3×C6C32C3C3C6C6
# reps113192219331

Matrix representation of C32.3CSU2(𝔽3) ►in GL6(𝔽73)

010000
72720000
001000
000100
000010
000001
,
010000
72720000
001000
000100
000014
00005471
,
100000
010000
00215400
00545200
000010
000001
,
100000
010000
0007200
001000
000010
000001
,
42450000
28700000
00563700
00381600
00003451
00006814
,
100000
72720000
00296900
00284400
0000045
0000130

G:=sub<GL(6,GF(73))| [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],[0,72,0,0,0,0,1,72,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,54,0,0,0,0,4,71],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,21,54,0,0,0,0,54,52,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,72,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[42,28,0,0,0,0,45,70,0,0,0,0,0,0,56,38,0,0,0,0,37,16,0,0,0,0,0,0,34,68,0,0,0,0,51,14],[1,72,0,0,0,0,0,72,0,0,0,0,0,0,29,28,0,0,0,0,69,44,0,0,0,0,0,0,0,13,0,0,0,0,45,0] >;
 

C32.3CSU2(𝔽3) in GAP, Magma, Sage, TeX 

C_3^2._3{\rm CSU}_2({\mathbb F}_3)
 
% in TeX
 
G:=Group("C3^2.3CSU(2,3)");
 
// GroupNames label
 
G:=SmallGroup(432,255);
 
// by ID
 
G=gap.SmallGroup(432,255);
 
# by ID
 
G:=PCGroup([7,-2,-3,-3,-3,-2,2,-2,1512,309,260,254,1011,3784,5681,172,2273,3414,285,124]);
 
// Polycyclic
 
G:=Group<a,b,c,d,e,f|a^3=b^3=c^4=1,d^2=f^2=c^2,e^3=f*b*f^-1=b^-1,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,f*a*f^-1=a^-1,b*c=c*b,b*d=d*b,b*e=e*b,d*c*d^-1=f*d*f^-1=c^-1,e*c*e^-1=c*d,f*c*f^-1=c^2*d,e*d*e^-1=c,f*e*f^-1=b*e^2>;
 
// generators/relations
 

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