direct product, metabelian, supersoluble, monomial, A-group
Aliases: C22×C9⋊Dic3, C62.138D6, C62.22Dic3, (C6×C18)⋊7C4, C6⋊2(C2×Dic9), (C2×C6)⋊5Dic9, (C2×C18)⋊5Dic3, C18⋊2(C2×Dic3), (C2×C18).45D6, (C2×C6).45D18, C23.4(C9⋊S3), (C2×C62).25S3, C9⋊2(C22×Dic3), C3⋊2(C22×Dic9), C6.47(C22×D9), (C22×C6).11D9, (C6×C18).51C22, C18.47(C22×S3), (C3×C18).56C23, (C22×C18).11S3, C32.4(C22×Dic3), (C2×C6×C18).7C2, (C3×C18)⋊9(C2×C4), (C3×C9)⋊10(C22×C4), C2.2(C22×C9⋊S3), C3.(C22×C3⋊Dic3), C22.11(C2×C9⋊S3), C6.36(C22×C3⋊S3), C6.11(C2×C3⋊Dic3), (C3×C6).65(C2×Dic3), (C22×C6).13(C3⋊S3), (C3×C6).170(C22×S3), (C2×C6).10(C3⋊Dic3), (C2×C6).38(C2×C3⋊S3), SmallGroup(432,396)
Series: Derived ►Chief ►Lower central ►Upper central
| C3×C9 — C22×C9⋊Dic3 |
Generators and relations for C22×C9⋊Dic3
G = < a,b,c,d,e | a2=b2=c9=d6=1, e2=d3, ab=ba, ac=ca, ad=da, ae=ea, bc=cb, bd=db, be=eb, cd=dc, ece-1=c-1, ede-1=d-1 >
Subgroups: 996 in 270 conjugacy classes, 171 normal (13 characteristic)
C1, C2, C2, C3, C3, C4, C22, C6, C6, C2×C4, C23, C9, C32, Dic3, C2×C6, C22×C4, C18, C3×C6, C3×C6, C2×Dic3, C22×C6, C22×C6, C3×C9, Dic9, C2×C18, C3⋊Dic3, C62, C22×Dic3, C3×C18, C3×C18, C2×Dic9, C22×C18, C2×C3⋊Dic3, C2×C62, C9⋊Dic3, C6×C18, C22×Dic9, C22×C3⋊Dic3, C2×C9⋊Dic3, C2×C6×C18, C22×C9⋊Dic3
Quotients: C1, C2, C4, C22, S3, C2×C4, C23, Dic3, D6, C22×C4, D9, C3⋊S3, C2×Dic3, C22×S3, Dic9, D18, C3⋊Dic3, C2×C3⋊S3, C22×Dic3, C9⋊S3, C2×Dic9, C22×D9, C2×C3⋊Dic3, C22×C3⋊S3, C9⋊Dic3, C2×C9⋊S3, C22×Dic9, C22×C3⋊Dic3, C2×C9⋊Dic3, C22×C9⋊S3, C22×C9⋊Dic3
►Regular action on 432 points
Generators in S432
(1 178)(2 179)(3 180)(4 172)(5 173)(6 174)(7 175)(8 176)(9 177)(10 314)(11 315)(12 307)(13 308)(14 309)(15 310)(16 311)(17 312)(18 313)(19 303)(20 304)(21 305)(22 306)(23 298)(24 299)(25 300)(26 301)(27 302)(28 163)(29 164)(30 165)(31 166)(32 167)(33 168)(34 169)(35 170)(36 171)(37 156)(38 157)(39 158)(40 159)(41 160)(42 161)(43 162)(44 154)(45 155)(46 127)(47 128)(48 129)(49 130)(50 131)(51 132)(52 133)(53 134)(54 135)(55 136)(56 137)(57 138)(58 139)(59 140)(60 141)(61 142)(62 143)(63 144)(64 145)(65 146)(66 147)(67 148)(68 149)(69 150)(70 151)(71 152)(72 153)(73 208)(74 209)(75 210)(76 211)(77 212)(78 213)(79 214)(80 215)(81 216)(82 229)(83 230)(84 231)(85 232)(86 233)(87 234)(88 226)(89 227)(90 228)(91 224)(92 225)(93 217)(94 218)(95 219)(96 220)(97 221)(98 222)(99 223)(100 181)(101 182)(102 183)(103 184)(104 185)(105 186)(106 187)(107 188)(108 189)(109 190)(110 191)(111 192)(112 193)(113 194)(114 195)(115 196)(116 197)(117 198)(118 199)(119 200)(120 201)(121 202)(122 203)(123 204)(124 205)(125 206)(126 207)(235 370)(236 371)(237 372)(238 373)(239 374)(240 375)(241 376)(242 377)(243 378)(244 379)(245 380)(246 381)(247 382)(248 383)(249 384)(250 385)(251 386)(252 387)(253 388)(254 389)(255 390)(256 391)(257 392)(258 393)(259 394)(260 395)(261 396)(262 343)(263 344)(264 345)(265 346)(266 347)(267 348)(268 349)(269 350)(270 351)(271 352)(272 353)(273 354)(274 355)(275 356)(276 357)(277 358)(278 359)(279 360)(280 361)(281 362)(282 363)(283 364)(284 365)(285 366)(286 367)(287 368)(288 369)(289 424)(290 425)(291 426)(292 427)(293 428)(294 429)(295 430)(296 431)(297 432)(316 397)(317 398)(318 399)(319 400)(320 401)(321 402)(322 403)(323 404)(324 405)(325 406)(326 407)(327 408)(328 409)(329 410)(330 411)(331 412)(332 413)(333 414)(334 415)(335 416)(336 417)(337 418)(338 419)(339 420)(340 421)(341 422)(342 423)
(1 124)(2 125)(3 126)(4 118)(5 119)(6 120)(7 121)(8 122)(9 123)(10 368)(11 369)(12 361)(13 362)(14 363)(15 364)(16 365)(17 366)(18 367)(19 357)(20 358)(21 359)(22 360)(23 352)(24 353)(25 354)(26 355)(27 356)(28 109)(29 110)(30 111)(31 112)(32 113)(33 114)(34 115)(35 116)(36 117)(37 102)(38 103)(39 104)(40 105)(41 106)(42 107)(43 108)(44 100)(45 101)(46 73)(47 74)(48 75)(49 76)(50 77)(51 78)(52 79)(53 80)(54 81)(55 82)(56 83)(57 84)(58 85)(59 86)(60 87)(61 88)(62 89)(63 90)(64 91)(65 92)(66 93)(67 94)(68 95)(69 96)(70 97)(71 98)(72 99)(127 208)(128 209)(129 210)(130 211)(131 212)(132 213)(133 214)(134 215)(135 216)(136 229)(137 230)(138 231)(139 232)(140 233)(141 234)(142 226)(143 227)(144 228)(145 224)(146 225)(147 217)(148 218)(149 219)(150 220)(151 221)(152 222)(153 223)(154 181)(155 182)(156 183)(157 184)(158 185)(159 186)(160 187)(161 188)(162 189)(163 190)(164 191)(165 192)(166 193)(167 194)(168 195)(169 196)(170 197)(171 198)(172 199)(173 200)(174 201)(175 202)(176 203)(177 204)(178 205)(179 206)(180 207)(235 316)(236 317)(237 318)(238 319)(239 320)(240 321)(241 322)(242 323)(243 324)(244 325)(245 326)(246 327)(247 328)(248 329)(249 330)(250 331)(251 332)(252 333)(253 334)(254 335)(255 336)(256 337)(257 338)(258 339)(259 340)(260 341)(261 342)(262 289)(263 290)(264 291)(265 292)(266 293)(267 294)(268 295)(269 296)(270 297)(271 298)(272 299)(273 300)(274 301)(275 302)(276 303)(277 304)(278 305)(279 306)(280 307)(281 308)(282 309)(283 310)(284 311)(285 312)(286 313)(287 314)(288 315)(343 424)(344 425)(345 426)(346 427)(347 428)(348 429)(349 430)(350 431)(351 432)(370 397)(371 398)(372 399)(373 400)(374 401)(375 402)(376 403)(377 404)(378 405)(379 406)(380 407)(381 408)(382 409)(383 410)(384 411)(385 412)(386 413)(387 414)(388 415)(389 416)(390 417)(391 418)(392 419)(393 420)(394 421)(395 422)(396 423)
(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 48 35 70 37 62)(2 49 36 71 38 63)(3 50 28 72 39 55)(4 51 29 64 40 56)(5 52 30 65 41 57)(6 53 31 66 42 58)(7 54 32 67 43 59)(8 46 33 68 44 60)(9 47 34 69 45 61)(10 404 25 422 431 408)(11 405 26 423 432 409)(12 397 27 415 424 410)(13 398 19 416 425 411)(14 399 20 417 426 412)(15 400 21 418 427 413)(16 401 22 419 428 414)(17 402 23 420 429 406)(18 403 24 421 430 407)(73 114 95 100 87 122)(74 115 96 101 88 123)(75 116 97 102 89 124)(76 117 98 103 90 125)(77 109 99 104 82 126)(78 110 91 105 83 118)(79 111 92 106 84 119)(80 112 93 107 85 120)(81 113 94 108 86 121)(127 168 149 154 141 176)(128 169 150 155 142 177)(129 170 151 156 143 178)(130 171 152 157 144 179)(131 163 153 158 136 180)(132 164 145 159 137 172)(133 165 146 160 138 173)(134 166 147 161 139 174)(135 167 148 162 140 175)(181 234 203 208 195 219)(182 226 204 209 196 220)(183 227 205 210 197 221)(184 228 206 211 198 222)(185 229 207 212 190 223)(186 230 199 213 191 224)(187 231 200 214 192 225)(188 232 201 215 193 217)(189 233 202 216 194 218)(235 275 253 262 248 280)(236 276 254 263 249 281)(237 277 255 264 250 282)(238 278 256 265 251 283)(239 279 257 266 252 284)(240 271 258 267 244 285)(241 272 259 268 245 286)(242 273 260 269 246 287)(243 274 261 270 247 288)(289 329 307 316 302 334)(290 330 308 317 303 335)(291 331 309 318 304 336)(292 332 310 319 305 337)(293 333 311 320 306 338)(294 325 312 321 298 339)(295 326 313 322 299 340)(296 327 314 323 300 341)(297 328 315 324 301 342)(343 383 361 370 356 388)(344 384 362 371 357 389)(345 385 363 372 358 390)(346 386 364 373 359 391)(347 387 365 374 360 392)(348 379 366 375 352 393)(349 380 367 376 353 394)(350 381 368 377 354 395)(351 382 369 378 355 396)
(1 23 70 406)(2 22 71 414)(3 21 72 413)(4 20 64 412)(5 19 65 411)(6 27 66 410)(7 26 67 409)(8 25 68 408)(9 24 69 407)(10 60 422 33)(11 59 423 32)(12 58 415 31)(13 57 416 30)(14 56 417 29)(15 55 418 28)(16 63 419 36)(17 62 420 35)(18 61 421 34)(37 429 48 402)(38 428 49 401)(39 427 50 400)(40 426 51 399)(41 425 52 398)(42 424 53 397)(43 432 54 405)(44 431 46 404)(45 430 47 403)(73 377 100 350)(74 376 101 349)(75 375 102 348)(76 374 103 347)(77 373 104 346)(78 372 105 345)(79 371 106 344)(80 370 107 343)(81 378 108 351)(82 391 109 364)(83 390 110 363)(84 389 111 362)(85 388 112 361)(86 396 113 369)(87 395 114 368)(88 394 115 367)(89 393 116 366)(90 392 117 365)(91 385 118 358)(92 384 119 357)(93 383 120 356)(94 382 121 355)(95 381 122 354)(96 380 123 353)(97 379 124 352)(98 387 125 360)(99 386 126 359)(127 323 154 296)(128 322 155 295)(129 321 156 294)(130 320 157 293)(131 319 158 292)(132 318 159 291)(133 317 160 290)(134 316 161 289)(135 324 162 297)(136 337 163 310)(137 336 164 309)(138 335 165 308)(139 334 166 307)(140 342 167 315)(141 341 168 314)(142 340 169 313)(143 339 170 312)(144 338 171 311)(145 331 172 304)(146 330 173 303)(147 329 174 302)(148 328 175 301)(149 327 176 300)(150 326 177 299)(151 325 178 298)(152 333 179 306)(153 332 180 305)(181 269 208 242)(182 268 209 241)(183 267 210 240)(184 266 211 239)(185 265 212 238)(186 264 213 237)(187 263 214 236)(188 262 215 235)(189 270 216 243)(190 283 229 256)(191 282 230 255)(192 281 231 254)(193 280 232 253)(194 288 233 261)(195 287 234 260)(196 286 226 259)(197 285 227 258)(198 284 228 257)(199 277 224 250)(200 276 225 249)(201 275 217 248)(202 274 218 247)(203 273 219 246)(204 272 220 245)(205 271 221 244)(206 279 222 252)(207 278 223 251)
G:=sub<Sym(432)| (1,178)(2,179)(3,180)(4,172)(5,173)(6,174)(7,175)(8,176)(9,177)(10,314)(11,315)(12,307)(13,308)(14,309)(15,310)(16,311)(17,312)(18,313)(19,303)(20,304)(21,305)(22,306)(23,298)(24,299)(25,300)(26,301)(27,302)(28,163)(29,164)(30,165)(31,166)(32,167)(33,168)(34,169)(35,170)(36,171)(37,156)(38,157)(39,158)(40,159)(41,160)(42,161)(43,162)(44,154)(45,155)(46,127)(47,128)(48,129)(49,130)(50,131)(51,132)(52,133)(53,134)(54,135)(55,136)(56,137)(57,138)(58,139)(59,140)(60,141)(61,142)(62,143)(63,144)(64,145)(65,146)(66,147)(67,148)(68,149)(69,150)(70,151)(71,152)(72,153)(73,208)(74,209)(75,210)(76,211)(77,212)(78,213)(79,214)(80,215)(81,216)(82,229)(83,230)(84,231)(85,232)(86,233)(87,234)(88,226)(89,227)(90,228)(91,224)(92,225)(93,217)(94,218)(95,219)(96,220)(97,221)(98,222)(99,223)(100,181)(101,182)(102,183)(103,184)(104,185)(105,186)(106,187)(107,188)(108,189)(109,190)(110,191)(111,192)(112,193)(113,194)(114,195)(115,196)(116,197)(117,198)(118,199)(119,200)(120,201)(121,202)(122,203)(123,204)(124,205)(125,206)(126,207)(235,370)(236,371)(237,372)(238,373)(239,374)(240,375)(241,376)(242,377)(243,378)(244,379)(245,380)(246,381)(247,382)(248,383)(249,384)(250,385)(251,386)(252,387)(253,388)(254,389)(255,390)(256,391)(257,392)(258,393)(259,394)(260,395)(261,396)(262,343)(263,344)(264,345)(265,346)(266,347)(267,348)(268,349)(269,350)(270,351)(271,352)(272,353)(273,354)(274,355)(275,356)(276,357)(277,358)(278,359)(279,360)(280,361)(281,362)(282,363)(283,364)(284,365)(285,366)(286,367)(287,368)(288,369)(289,424)(290,425)(291,426)(292,427)(293,428)(294,429)(295,430)(296,431)(297,432)(316,397)(317,398)(318,399)(319,400)(320,401)(321,402)(322,403)(323,404)(324,405)(325,406)(326,407)(327,408)(328,409)(329,410)(330,411)(331,412)(332,413)(333,414)(334,415)(335,416)(336,417)(337,418)(338,419)(339,420)(340,421)(341,422)(342,423), (1,124)(2,125)(3,126)(4,118)(5,119)(6,120)(7,121)(8,122)(9,123)(10,368)(11,369)(12,361)(13,362)(14,363)(15,364)(16,365)(17,366)(18,367)(19,357)(20,358)(21,359)(22,360)(23,352)(24,353)(25,354)(26,355)(27,356)(28,109)(29,110)(30,111)(31,112)(32,113)(33,114)(34,115)(35,116)(36,117)(37,102)(38,103)(39,104)(40,105)(41,106)(42,107)(43,108)(44,100)(45,101)(46,73)(47,74)(48,75)(49,76)(50,77)(51,78)(52,79)(53,80)(54,81)(55,82)(56,83)(57,84)(58,85)(59,86)(60,87)(61,88)(62,89)(63,90)(64,91)(65,92)(66,93)(67,94)(68,95)(69,96)(70,97)(71,98)(72,99)(127,208)(128,209)(129,210)(130,211)(131,212)(132,213)(133,214)(134,215)(135,216)(136,229)(137,230)(138,231)(139,232)(140,233)(141,234)(142,226)(143,227)(144,228)(145,224)(146,225)(147,217)(148,218)(149,219)(150,220)(151,221)(152,222)(153,223)(154,181)(155,182)(156,183)(157,184)(158,185)(159,186)(160,187)(161,188)(162,189)(163,190)(164,191)(165,192)(166,193)(167,194)(168,195)(169,196)(170,197)(171,198)(172,199)(173,200)(174,201)(175,202)(176,203)(177,204)(178,205)(179,206)(180,207)(235,316)(236,317)(237,318)(238,319)(239,320)(240,321)(241,322)(242,323)(243,324)(244,325)(245,326)(246,327)(247,328)(248,329)(249,330)(250,331)(251,332)(252,333)(253,334)(254,335)(255,336)(256,337)(257,338)(258,339)(259,340)(260,341)(261,342)(262,289)(263,290)(264,291)(265,292)(266,293)(267,294)(268,295)(269,296)(270,297)(271,298)(272,299)(273,300)(274,301)(275,302)(276,303)(277,304)(278,305)(279,306)(280,307)(281,308)(282,309)(283,310)(284,311)(285,312)(286,313)(287,314)(288,315)(343,424)(344,425)(345,426)(346,427)(347,428)(348,429)(349,430)(350,431)(351,432)(370,397)(371,398)(372,399)(373,400)(374,401)(375,402)(376,403)(377,404)(378,405)(379,406)(380,407)(381,408)(382,409)(383,410)(384,411)(385,412)(386,413)(387,414)(388,415)(389,416)(390,417)(391,418)(392,419)(393,420)(394,421)(395,422)(396,423), (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), (1,48,35,70,37,62)(2,49,36,71,38,63)(3,50,28,72,39,55)(4,51,29,64,40,56)(5,52,30,65,41,57)(6,53,31,66,42,58)(7,54,32,67,43,59)(8,46,33,68,44,60)(9,47,34,69,45,61)(10,404,25,422,431,408)(11,405,26,423,432,409)(12,397,27,415,424,410)(13,398,19,416,425,411)(14,399,20,417,426,412)(15,400,21,418,427,413)(16,401,22,419,428,414)(17,402,23,420,429,406)(18,403,24,421,430,407)(73,114,95,100,87,122)(74,115,96,101,88,123)(75,116,97,102,89,124)(76,117,98,103,90,125)(77,109,99,104,82,126)(78,110,91,105,83,118)(79,111,92,106,84,119)(80,112,93,107,85,120)(81,113,94,108,86,121)(127,168,149,154,141,176)(128,169,150,155,142,177)(129,170,151,156,143,178)(130,171,152,157,144,179)(131,163,153,158,136,180)(132,164,145,159,137,172)(133,165,146,160,138,173)(134,166,147,161,139,174)(135,167,148,162,140,175)(181,234,203,208,195,219)(182,226,204,209,196,220)(183,227,205,210,197,221)(184,228,206,211,198,222)(185,229,207,212,190,223)(186,230,199,213,191,224)(187,231,200,214,192,225)(188,232,201,215,193,217)(189,233,202,216,194,218)(235,275,253,262,248,280)(236,276,254,263,249,281)(237,277,255,264,250,282)(238,278,256,265,251,283)(239,279,257,266,252,284)(240,271,258,267,244,285)(241,272,259,268,245,286)(242,273,260,269,246,287)(243,274,261,270,247,288)(289,329,307,316,302,334)(290,330,308,317,303,335)(291,331,309,318,304,336)(292,332,310,319,305,337)(293,333,311,320,306,338)(294,325,312,321,298,339)(295,326,313,322,299,340)(296,327,314,323,300,341)(297,328,315,324,301,342)(343,383,361,370,356,388)(344,384,362,371,357,389)(345,385,363,372,358,390)(346,386,364,373,359,391)(347,387,365,374,360,392)(348,379,366,375,352,393)(349,380,367,376,353,394)(350,381,368,377,354,395)(351,382,369,378,355,396), (1,23,70,406)(2,22,71,414)(3,21,72,413)(4,20,64,412)(5,19,65,411)(6,27,66,410)(7,26,67,409)(8,25,68,408)(9,24,69,407)(10,60,422,33)(11,59,423,32)(12,58,415,31)(13,57,416,30)(14,56,417,29)(15,55,418,28)(16,63,419,36)(17,62,420,35)(18,61,421,34)(37,429,48,402)(38,428,49,401)(39,427,50,400)(40,426,51,399)(41,425,52,398)(42,424,53,397)(43,432,54,405)(44,431,46,404)(45,430,47,403)(73,377,100,350)(74,376,101,349)(75,375,102,348)(76,374,103,347)(77,373,104,346)(78,372,105,345)(79,371,106,344)(80,370,107,343)(81,378,108,351)(82,391,109,364)(83,390,110,363)(84,389,111,362)(85,388,112,361)(86,396,113,369)(87,395,114,368)(88,394,115,367)(89,393,116,366)(90,392,117,365)(91,385,118,358)(92,384,119,357)(93,383,120,356)(94,382,121,355)(95,381,122,354)(96,380,123,353)(97,379,124,352)(98,387,125,360)(99,386,126,359)(127,323,154,296)(128,322,155,295)(129,321,156,294)(130,320,157,293)(131,319,158,292)(132,318,159,291)(133,317,160,290)(134,316,161,289)(135,324,162,297)(136,337,163,310)(137,336,164,309)(138,335,165,308)(139,334,166,307)(140,342,167,315)(141,341,168,314)(142,340,169,313)(143,339,170,312)(144,338,171,311)(145,331,172,304)(146,330,173,303)(147,329,174,302)(148,328,175,301)(149,327,176,300)(150,326,177,299)(151,325,178,298)(152,333,179,306)(153,332,180,305)(181,269,208,242)(182,268,209,241)(183,267,210,240)(184,266,211,239)(185,265,212,238)(186,264,213,237)(187,263,214,236)(188,262,215,235)(189,270,216,243)(190,283,229,256)(191,282,230,255)(192,281,231,254)(193,280,232,253)(194,288,233,261)(195,287,234,260)(196,286,226,259)(197,285,227,258)(198,284,228,257)(199,277,224,250)(200,276,225,249)(201,275,217,248)(202,274,218,247)(203,273,219,246)(204,272,220,245)(205,271,221,244)(206,279,222,252)(207,278,223,251)>;
G:=Group( (1,178)(2,179)(3,180)(4,172)(5,173)(6,174)(7,175)(8,176)(9,177)(10,314)(11,315)(12,307)(13,308)(14,309)(15,310)(16,311)(17,312)(18,313)(19,303)(20,304)(21,305)(22,306)(23,298)(24,299)(25,300)(26,301)(27,302)(28,163)(29,164)(30,165)(31,166)(32,167)(33,168)(34,169)(35,170)(36,171)(37,156)(38,157)(39,158)(40,159)(41,160)(42,161)(43,162)(44,154)(45,155)(46,127)(47,128)(48,129)(49,130)(50,131)(51,132)(52,133)(53,134)(54,135)(55,136)(56,137)(57,138)(58,139)(59,140)(60,141)(61,142)(62,143)(63,144)(64,145)(65,146)(66,147)(67,148)(68,149)(69,150)(70,151)(71,152)(72,153)(73,208)(74,209)(75,210)(76,211)(77,212)(78,213)(79,214)(80,215)(81,216)(82,229)(83,230)(84,231)(85,232)(86,233)(87,234)(88,226)(89,227)(90,228)(91,224)(92,225)(93,217)(94,218)(95,219)(96,220)(97,221)(98,222)(99,223)(100,181)(101,182)(102,183)(103,184)(104,185)(105,186)(106,187)(107,188)(108,189)(109,190)(110,191)(111,192)(112,193)(113,194)(114,195)(115,196)(116,197)(117,198)(118,199)(119,200)(120,201)(121,202)(122,203)(123,204)(124,205)(125,206)(126,207)(235,370)(236,371)(237,372)(238,373)(239,374)(240,375)(241,376)(242,377)(243,378)(244,379)(245,380)(246,381)(247,382)(248,383)(249,384)(250,385)(251,386)(252,387)(253,388)(254,389)(255,390)(256,391)(257,392)(258,393)(259,394)(260,395)(261,396)(262,343)(263,344)(264,345)(265,346)(266,347)(267,348)(268,349)(269,350)(270,351)(271,352)(272,353)(273,354)(274,355)(275,356)(276,357)(277,358)(278,359)(279,360)(280,361)(281,362)(282,363)(283,364)(284,365)(285,366)(286,367)(287,368)(288,369)(289,424)(290,425)(291,426)(292,427)(293,428)(294,429)(295,430)(296,431)(297,432)(316,397)(317,398)(318,399)(319,400)(320,401)(321,402)(322,403)(323,404)(324,405)(325,406)(326,407)(327,408)(328,409)(329,410)(330,411)(331,412)(332,413)(333,414)(334,415)(335,416)(336,417)(337,418)(338,419)(339,420)(340,421)(341,422)(342,423), (1,124)(2,125)(3,126)(4,118)(5,119)(6,120)(7,121)(8,122)(9,123)(10,368)(11,369)(12,361)(13,362)(14,363)(15,364)(16,365)(17,366)(18,367)(19,357)(20,358)(21,359)(22,360)(23,352)(24,353)(25,354)(26,355)(27,356)(28,109)(29,110)(30,111)(31,112)(32,113)(33,114)(34,115)(35,116)(36,117)(37,102)(38,103)(39,104)(40,105)(41,106)(42,107)(43,108)(44,100)(45,101)(46,73)(47,74)(48,75)(49,76)(50,77)(51,78)(52,79)(53,80)(54,81)(55,82)(56,83)(57,84)(58,85)(59,86)(60,87)(61,88)(62,89)(63,90)(64,91)(65,92)(66,93)(67,94)(68,95)(69,96)(70,97)(71,98)(72,99)(127,208)(128,209)(129,210)(130,211)(131,212)(132,213)(133,214)(134,215)(135,216)(136,229)(137,230)(138,231)(139,232)(140,233)(141,234)(142,226)(143,227)(144,228)(145,224)(146,225)(147,217)(148,218)(149,219)(150,220)(151,221)(152,222)(153,223)(154,181)(155,182)(156,183)(157,184)(158,185)(159,186)(160,187)(161,188)(162,189)(163,190)(164,191)(165,192)(166,193)(167,194)(168,195)(169,196)(170,197)(171,198)(172,199)(173,200)(174,201)(175,202)(176,203)(177,204)(178,205)(179,206)(180,207)(235,316)(236,317)(237,318)(238,319)(239,320)(240,321)(241,322)(242,323)(243,324)(244,325)(245,326)(246,327)(247,328)(248,329)(249,330)(250,331)(251,332)(252,333)(253,334)(254,335)(255,336)(256,337)(257,338)(258,339)(259,340)(260,341)(261,342)(262,289)(263,290)(264,291)(265,292)(266,293)(267,294)(268,295)(269,296)(270,297)(271,298)(272,299)(273,300)(274,301)(275,302)(276,303)(277,304)(278,305)(279,306)(280,307)(281,308)(282,309)(283,310)(284,311)(285,312)(286,313)(287,314)(288,315)(343,424)(344,425)(345,426)(346,427)(347,428)(348,429)(349,430)(350,431)(351,432)(370,397)(371,398)(372,399)(373,400)(374,401)(375,402)(376,403)(377,404)(378,405)(379,406)(380,407)(381,408)(382,409)(383,410)(384,411)(385,412)(386,413)(387,414)(388,415)(389,416)(390,417)(391,418)(392,419)(393,420)(394,421)(395,422)(396,423), (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), (1,48,35,70,37,62)(2,49,36,71,38,63)(3,50,28,72,39,55)(4,51,29,64,40,56)(5,52,30,65,41,57)(6,53,31,66,42,58)(7,54,32,67,43,59)(8,46,33,68,44,60)(9,47,34,69,45,61)(10,404,25,422,431,408)(11,405,26,423,432,409)(12,397,27,415,424,410)(13,398,19,416,425,411)(14,399,20,417,426,412)(15,400,21,418,427,413)(16,401,22,419,428,414)(17,402,23,420,429,406)(18,403,24,421,430,407)(73,114,95,100,87,122)(74,115,96,101,88,123)(75,116,97,102,89,124)(76,117,98,103,90,125)(77,109,99,104,82,126)(78,110,91,105,83,118)(79,111,92,106,84,119)(80,112,93,107,85,120)(81,113,94,108,86,121)(127,168,149,154,141,176)(128,169,150,155,142,177)(129,170,151,156,143,178)(130,171,152,157,144,179)(131,163,153,158,136,180)(132,164,145,159,137,172)(133,165,146,160,138,173)(134,166,147,161,139,174)(135,167,148,162,140,175)(181,234,203,208,195,219)(182,226,204,209,196,220)(183,227,205,210,197,221)(184,228,206,211,198,222)(185,229,207,212,190,223)(186,230,199,213,191,224)(187,231,200,214,192,225)(188,232,201,215,193,217)(189,233,202,216,194,218)(235,275,253,262,248,280)(236,276,254,263,249,281)(237,277,255,264,250,282)(238,278,256,265,251,283)(239,279,257,266,252,284)(240,271,258,267,244,285)(241,272,259,268,245,286)(242,273,260,269,246,287)(243,274,261,270,247,288)(289,329,307,316,302,334)(290,330,308,317,303,335)(291,331,309,318,304,336)(292,332,310,319,305,337)(293,333,311,320,306,338)(294,325,312,321,298,339)(295,326,313,322,299,340)(296,327,314,323,300,341)(297,328,315,324,301,342)(343,383,361,370,356,388)(344,384,362,371,357,389)(345,385,363,372,358,390)(346,386,364,373,359,391)(347,387,365,374,360,392)(348,379,366,375,352,393)(349,380,367,376,353,394)(350,381,368,377,354,395)(351,382,369,378,355,396), (1,23,70,406)(2,22,71,414)(3,21,72,413)(4,20,64,412)(5,19,65,411)(6,27,66,410)(7,26,67,409)(8,25,68,408)(9,24,69,407)(10,60,422,33)(11,59,423,32)(12,58,415,31)(13,57,416,30)(14,56,417,29)(15,55,418,28)(16,63,419,36)(17,62,420,35)(18,61,421,34)(37,429,48,402)(38,428,49,401)(39,427,50,400)(40,426,51,399)(41,425,52,398)(42,424,53,397)(43,432,54,405)(44,431,46,404)(45,430,47,403)(73,377,100,350)(74,376,101,349)(75,375,102,348)(76,374,103,347)(77,373,104,346)(78,372,105,345)(79,371,106,344)(80,370,107,343)(81,378,108,351)(82,391,109,364)(83,390,110,363)(84,389,111,362)(85,388,112,361)(86,396,113,369)(87,395,114,368)(88,394,115,367)(89,393,116,366)(90,392,117,365)(91,385,118,358)(92,384,119,357)(93,383,120,356)(94,382,121,355)(95,381,122,354)(96,380,123,353)(97,379,124,352)(98,387,125,360)(99,386,126,359)(127,323,154,296)(128,322,155,295)(129,321,156,294)(130,320,157,293)(131,319,158,292)(132,318,159,291)(133,317,160,290)(134,316,161,289)(135,324,162,297)(136,337,163,310)(137,336,164,309)(138,335,165,308)(139,334,166,307)(140,342,167,315)(141,341,168,314)(142,340,169,313)(143,339,170,312)(144,338,171,311)(145,331,172,304)(146,330,173,303)(147,329,174,302)(148,328,175,301)(149,327,176,300)(150,326,177,299)(151,325,178,298)(152,333,179,306)(153,332,180,305)(181,269,208,242)(182,268,209,241)(183,267,210,240)(184,266,211,239)(185,265,212,238)(186,264,213,237)(187,263,214,236)(188,262,215,235)(189,270,216,243)(190,283,229,256)(191,282,230,255)(192,281,231,254)(193,280,232,253)(194,288,233,261)(195,287,234,260)(196,286,226,259)(197,285,227,258)(198,284,228,257)(199,277,224,250)(200,276,225,249)(201,275,217,248)(202,274,218,247)(203,273,219,246)(204,272,220,245)(205,271,221,244)(206,279,222,252)(207,278,223,251) );
G=PermutationGroup([[(1,178),(2,179),(3,180),(4,172),(5,173),(6,174),(7,175),(8,176),(9,177),(10,314),(11,315),(12,307),(13,308),(14,309),(15,310),(16,311),(17,312),(18,313),(19,303),(20,304),(21,305),(22,306),(23,298),(24,299),(25,300),(26,301),(27,302),(28,163),(29,164),(30,165),(31,166),(32,167),(33,168),(34,169),(35,170),(36,171),(37,156),(38,157),(39,158),(40,159),(41,160),(42,161),(43,162),(44,154),(45,155),(46,127),(47,128),(48,129),(49,130),(50,131),(51,132),(52,133),(53,134),(54,135),(55,136),(56,137),(57,138),(58,139),(59,140),(60,141),(61,142),(62,143),(63,144),(64,145),(65,146),(66,147),(67,148),(68,149),(69,150),(70,151),(71,152),(72,153),(73,208),(74,209),(75,210),(76,211),(77,212),(78,213),(79,214),(80,215),(81,216),(82,229),(83,230),(84,231),(85,232),(86,233),(87,234),(88,226),(89,227),(90,228),(91,224),(92,225),(93,217),(94,218),(95,219),(96,220),(97,221),(98,222),(99,223),(100,181),(101,182),(102,183),(103,184),(104,185),(105,186),(106,187),(107,188),(108,189),(109,190),(110,191),(111,192),(112,193),(113,194),(114,195),(115,196),(116,197),(117,198),(118,199),(119,200),(120,201),(121,202),(122,203),(123,204),(124,205),(125,206),(126,207),(235,370),(236,371),(237,372),(238,373),(239,374),(240,375),(241,376),(242,377),(243,378),(244,379),(245,380),(246,381),(247,382),(248,383),(249,384),(250,385),(251,386),(252,387),(253,388),(254,389),(255,390),(256,391),(257,392),(258,393),(259,394),(260,395),(261,396),(262,343),(263,344),(264,345),(265,346),(266,347),(267,348),(268,349),(269,350),(270,351),(271,352),(272,353),(273,354),(274,355),(275,356),(276,357),(277,358),(278,359),(279,360),(280,361),(281,362),(282,363),(283,364),(284,365),(285,366),(286,367),(287,368),(288,369),(289,424),(290,425),(291,426),(292,427),(293,428),(294,429),(295,430),(296,431),(297,432),(316,397),(317,398),(318,399),(319,400),(320,401),(321,402),(322,403),(323,404),(324,405),(325,406),(326,407),(327,408),(328,409),(329,410),(330,411),(331,412),(332,413),(333,414),(334,415),(335,416),(336,417),(337,418),(338,419),(339,420),(340,421),(341,422),(342,423)], [(1,124),(2,125),(3,126),(4,118),(5,119),(6,120),(7,121),(8,122),(9,123),(10,368),(11,369),(12,361),(13,362),(14,363),(15,364),(16,365),(17,366),(18,367),(19,357),(20,358),(21,359),(22,360),(23,352),(24,353),(25,354),(26,355),(27,356),(28,109),(29,110),(30,111),(31,112),(32,113),(33,114),(34,115),(35,116),(36,117),(37,102),(38,103),(39,104),(40,105),(41,106),(42,107),(43,108),(44,100),(45,101),(46,73),(47,74),(48,75),(49,76),(50,77),(51,78),(52,79),(53,80),(54,81),(55,82),(56,83),(57,84),(58,85),(59,86),(60,87),(61,88),(62,89),(63,90),(64,91),(65,92),(66,93),(67,94),(68,95),(69,96),(70,97),(71,98),(72,99),(127,208),(128,209),(129,210),(130,211),(131,212),(132,213),(133,214),(134,215),(135,216),(136,229),(137,230),(138,231),(139,232),(140,233),(141,234),(142,226),(143,227),(144,228),(145,224),(146,225),(147,217),(148,218),(149,219),(150,220),(151,221),(152,222),(153,223),(154,181),(155,182),(156,183),(157,184),(158,185),(159,186),(160,187),(161,188),(162,189),(163,190),(164,191),(165,192),(166,193),(167,194),(168,195),(169,196),(170,197),(171,198),(172,199),(173,200),(174,201),(175,202),(176,203),(177,204),(178,205),(179,206),(180,207),(235,316),(236,317),(237,318),(238,319),(239,320),(240,321),(241,322),(242,323),(243,324),(244,325),(245,326),(246,327),(247,328),(248,329),(249,330),(250,331),(251,332),(252,333),(253,334),(254,335),(255,336),(256,337),(257,338),(258,339),(259,340),(260,341),(261,342),(262,289),(263,290),(264,291),(265,292),(266,293),(267,294),(268,295),(269,296),(270,297),(271,298),(272,299),(273,300),(274,301),(275,302),(276,303),(277,304),(278,305),(279,306),(280,307),(281,308),(282,309),(283,310),(284,311),(285,312),(286,313),(287,314),(288,315),(343,424),(344,425),(345,426),(346,427),(347,428),(348,429),(349,430),(350,431),(351,432),(370,397),(371,398),(372,399),(373,400),(374,401),(375,402),(376,403),(377,404),(378,405),(379,406),(380,407),(381,408),(382,409),(383,410),(384,411),(385,412),(386,413),(387,414),(388,415),(389,416),(390,417),(391,418),(392,419),(393,420),(394,421),(395,422),(396,423)], [(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)], [(1,48,35,70,37,62),(2,49,36,71,38,63),(3,50,28,72,39,55),(4,51,29,64,40,56),(5,52,30,65,41,57),(6,53,31,66,42,58),(7,54,32,67,43,59),(8,46,33,68,44,60),(9,47,34,69,45,61),(10,404,25,422,431,408),(11,405,26,423,432,409),(12,397,27,415,424,410),(13,398,19,416,425,411),(14,399,20,417,426,412),(15,400,21,418,427,413),(16,401,22,419,428,414),(17,402,23,420,429,406),(18,403,24,421,430,407),(73,114,95,100,87,122),(74,115,96,101,88,123),(75,116,97,102,89,124),(76,117,98,103,90,125),(77,109,99,104,82,126),(78,110,91,105,83,118),(79,111,92,106,84,119),(80,112,93,107,85,120),(81,113,94,108,86,121),(127,168,149,154,141,176),(128,169,150,155,142,177),(129,170,151,156,143,178),(130,171,152,157,144,179),(131,163,153,158,136,180),(132,164,145,159,137,172),(133,165,146,160,138,173),(134,166,147,161,139,174),(135,167,148,162,140,175),(181,234,203,208,195,219),(182,226,204,209,196,220),(183,227,205,210,197,221),(184,228,206,211,198,222),(185,229,207,212,190,223),(186,230,199,213,191,224),(187,231,200,214,192,225),(188,232,201,215,193,217),(189,233,202,216,194,218),(235,275,253,262,248,280),(236,276,254,263,249,281),(237,277,255,264,250,282),(238,278,256,265,251,283),(239,279,257,266,252,284),(240,271,258,267,244,285),(241,272,259,268,245,286),(242,273,260,269,246,287),(243,274,261,270,247,288),(289,329,307,316,302,334),(290,330,308,317,303,335),(291,331,309,318,304,336),(292,332,310,319,305,337),(293,333,311,320,306,338),(294,325,312,321,298,339),(295,326,313,322,299,340),(296,327,314,323,300,341),(297,328,315,324,301,342),(343,383,361,370,356,388),(344,384,362,371,357,389),(345,385,363,372,358,390),(346,386,364,373,359,391),(347,387,365,374,360,392),(348,379,366,375,352,393),(349,380,367,376,353,394),(350,381,368,377,354,395),(351,382,369,378,355,396)], [(1,23,70,406),(2,22,71,414),(3,21,72,413),(4,20,64,412),(5,19,65,411),(6,27,66,410),(7,26,67,409),(8,25,68,408),(9,24,69,407),(10,60,422,33),(11,59,423,32),(12,58,415,31),(13,57,416,30),(14,56,417,29),(15,55,418,28),(16,63,419,36),(17,62,420,35),(18,61,421,34),(37,429,48,402),(38,428,49,401),(39,427,50,400),(40,426,51,399),(41,425,52,398),(42,424,53,397),(43,432,54,405),(44,431,46,404),(45,430,47,403),(73,377,100,350),(74,376,101,349),(75,375,102,348),(76,374,103,347),(77,373,104,346),(78,372,105,345),(79,371,106,344),(80,370,107,343),(81,378,108,351),(82,391,109,364),(83,390,110,363),(84,389,111,362),(85,388,112,361),(86,396,113,369),(87,395,114,368),(88,394,115,367),(89,393,116,366),(90,392,117,365),(91,385,118,358),(92,384,119,357),(93,383,120,356),(94,382,121,355),(95,381,122,354),(96,380,123,353),(97,379,124,352),(98,387,125,360),(99,386,126,359),(127,323,154,296),(128,322,155,295),(129,321,156,294),(130,320,157,293),(131,319,158,292),(132,318,159,291),(133,317,160,290),(134,316,161,289),(135,324,162,297),(136,337,163,310),(137,336,164,309),(138,335,165,308),(139,334,166,307),(140,342,167,315),(141,341,168,314),(142,340,169,313),(143,339,170,312),(144,338,171,311),(145,331,172,304),(146,330,173,303),(147,329,174,302),(148,328,175,301),(149,327,176,300),(150,326,177,299),(151,325,178,298),(152,333,179,306),(153,332,180,305),(181,269,208,242),(182,268,209,241),(183,267,210,240),(184,266,211,239),(185,265,212,238),(186,264,213,237),(187,263,214,236),(188,262,215,235),(189,270,216,243),(190,283,229,256),(191,282,230,255),(192,281,231,254),(193,280,232,253),(194,288,233,261),(195,287,234,260),(196,286,226,259),(197,285,227,258),(198,284,228,257),(199,277,224,250),(200,276,225,249),(201,275,217,248),(202,274,218,247),(203,273,219,246),(204,272,220,245),(205,271,221,244),(206,279,222,252),(207,278,223,251)]])
120 conjugacy classes
| class | 1 | 2A | ··· | 2G | 3A | 3B | 3C | 3D | 4A | ··· | 4H | 6A | ··· | 6AB | 9A | ··· | 9I | 18A | ··· | 18BK |
| order | 1 | 2 | ··· | 2 | 3 | 3 | 3 | 3 | 4 | ··· | 4 | 6 | ··· | 6 | 9 | ··· | 9 | 18 | ··· | 18 |
| size | 1 | 1 | ··· | 1 | 2 | 2 | 2 | 2 | 27 | ··· | 27 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
120 irreducible representations
| dim | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | - | + | - | + | + | - | + | |
| image | C1 | C2 | C2 | C4 | S3 | S3 | Dic3 | D6 | Dic3 | D6 | D9 | Dic9 | D18 |
| kernel | C22×C9⋊Dic3 | C2×C9⋊Dic3 | C2×C6×C18 | C6×C18 | C22×C18 | C2×C62 | C2×C18 | C2×C18 | C62 | C62 | C22×C6 | C2×C6 | C2×C6 |
| # reps | 1 | 6 | 1 | 8 | 3 | 1 | 12 | 9 | 4 | 3 | 9 | 36 | 27 |
Matrix representation of C22×C9⋊Dic3 ►in GL6(𝔽37)
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 36 | 0 | 0 | 0 | 0 |
| 0 | 0 | 36 | 0 | 0 | 0 |
| 0 | 0 | 0 | 36 | 0 | 0 |
| 0 | 0 | 0 | 0 | 36 | 0 |
| 0 | 0 | 0 | 0 | 0 | 36 |
| 36 | 0 | 0 | 0 | 0 | 0 |
| 0 | 36 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 16 | 0 | 0 | 0 |
| 0 | 0 | 0 | 7 | 0 | 0 |
| 0 | 0 | 0 | 0 | 36 | 1 |
| 0 | 0 | 0 | 0 | 36 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 36 | 0 | 0 | 0 |
| 0 | 0 | 0 | 36 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 36 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 36 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 36 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 8 | 1 |
| 0 | 0 | 0 | 0 | 9 | 29 |
G:=sub<GL(6,GF(37))| [1,0,0,0,0,0,0,36,0,0,0,0,0,0,36,0,0,0,0,0,0,36,0,0,0,0,0,0,36,0,0,0,0,0,0,36],[36,0,0,0,0,0,0,36,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,16,0,0,0,0,0,0,7,0,0,0,0,0,0,36,36,0,0,0,0,1,0],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,36,0,0,0,0,0,0,36,0,0,0,0,0,0,1,1,0,0,0,0,36,0],[36,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,36,0,0,0,0,0,0,0,8,9,0,0,0,0,1,29] >;
C22×C9⋊Dic3 in GAP, Magma, Sage, TeX
C_2^2\times C_9\rtimes {\rm Dic}_3 % in TeX
G:=Group("C2^2xC9:Dic3"); // GroupNames label
G:=SmallGroup(432,396);
// by ID
G=gap.SmallGroup(432,396);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-3,-3,-3,56,6164,662,4037,14118]);
// Polycyclic
G:=Group<a,b,c,d,e|a^2=b^2=c^9=d^6=1,e^2=d^3,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,e*c*e^-1=c^-1,e*d*e^-1=d^-1>;
// generators/relations