metabelian, supersoluble, monomial
Aliases: C36⋊1Dic3, C12⋊1Dic9, C6.10D36, C18.10D12, C18.8Dic6, C6.8Dic18, C62.125D6, (C3×C36)⋊3C4, C4⋊(C9⋊Dic3), (C2×C36).8S3, (C6×C36).8C2, (C2×C12).8D9, (C3×C18).9Q8, (C6×C12).30S3, C3⋊2(C4⋊Dic9), C9⋊2(C4⋊Dic3), (C3×C6).57D12, (C2×C6).37D18, (C2×C18).37D6, (C3×C18).32D4, (C3×C6).25Dic6, C6.15(C2×Dic9), C6.4(C12⋊S3), C2.1(C36⋊S3), (C6×C18).39C22, C3.(C12⋊Dic3), C12.2(C3⋊Dic3), C18.15(C2×Dic3), (C3×C12).16Dic3, C6.5(C32⋊4Q8), C2.2(C12.D9), C32.4(C4⋊Dic3), (C3×C9)⋊9(C4⋊C4), (C2×C4).3(C9⋊S3), C22.5(C2×C9⋊S3), C6.9(C2×C3⋊Dic3), C2.4(C2×C9⋊Dic3), (C2×C12).7(C3⋊S3), (C3×C18).39(C2×C4), (C2×C9⋊Dic3).6C2, (C3×C6).62(C2×Dic3), (C2×C6).31(C2×C3⋊S3), SmallGroup(432,182)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C36⋊Dic3
G = < a,b,c | a12=b18=1, c2=b9, ab=ba, cac-1=a-1, cbc-1=b-1 >
Subgroups: 612 in 130 conjugacy classes, 83 normal (25 characteristic)
C1, C2, C3, C3, C4, C4, C22, C6, C6, C2×C4, C2×C4, C9, C32, Dic3, C12, C2×C6, C2×C6, C4⋊C4, C18, C3×C6, C2×Dic3, C2×C12, C2×C12, C3×C9, Dic9, C36, C2×C18, C3⋊Dic3, C3×C12, C62, C4⋊Dic3, C3×C18, C2×Dic9, C2×C36, C2×C3⋊Dic3, C6×C12, C9⋊Dic3, C3×C36, C6×C18, C4⋊Dic9, C12⋊Dic3, C2×C9⋊Dic3, C6×C36, C36⋊Dic3
Quotients: C1, C2, C4, C22, S3, C2×C4, D4, Q8, Dic3, D6, C4⋊C4, D9, C3⋊S3, Dic6, D12, C2×Dic3, Dic9, D18, C3⋊Dic3, C2×C3⋊S3, C4⋊Dic3, C9⋊S3, Dic18, D36, C2×Dic9, C32⋊4Q8, C12⋊S3, C2×C3⋊Dic3, C9⋊Dic3, C2×C9⋊S3, C4⋊Dic9, C12⋊Dic3, C12.D9, C36⋊S3, C2×C9⋊Dic3, C36⋊Dic3
►Regular action on 432 points
Generators in S432
(1 365 268 25 360 301 223 379 46 274 324 248)(2 366 269 26 343 302 224 380 47 275 307 249)(3 367 270 27 344 303 225 381 48 276 308 250)(4 368 253 28 345 304 226 382 49 277 309 251)(5 369 254 29 346 305 227 383 50 278 310 252)(6 370 255 30 347 306 228 384 51 279 311 235)(7 371 256 31 348 289 229 385 52 280 312 236)(8 372 257 32 349 290 230 386 53 281 313 237)(9 373 258 33 350 291 231 387 54 282 314 238)(10 374 259 34 351 292 232 388 37 283 315 239)(11 375 260 35 352 293 233 389 38 284 316 240)(12 376 261 36 353 294 234 390 39 285 317 241)(13 377 262 19 354 295 217 391 40 286 318 242)(14 378 263 20 355 296 218 392 41 287 319 243)(15 361 264 21 356 297 219 393 42 288 320 244)(16 362 265 22 357 298 220 394 43 271 321 245)(17 363 266 23 358 299 221 395 44 272 322 246)(18 364 267 24 359 300 222 396 45 273 323 247)(55 153 177 189 336 214 402 140 97 84 124 432)(56 154 178 190 337 215 403 141 98 85 125 415)(57 155 179 191 338 216 404 142 99 86 126 416)(58 156 180 192 339 199 405 143 100 87 109 417)(59 157 163 193 340 200 406 144 101 88 110 418)(60 158 164 194 341 201 407 127 102 89 111 419)(61 159 165 195 342 202 408 128 103 90 112 420)(62 160 166 196 325 203 409 129 104 73 113 421)(63 161 167 197 326 204 410 130 105 74 114 422)(64 162 168 198 327 205 411 131 106 75 115 423)(65 145 169 181 328 206 412 132 107 76 116 424)(66 146 170 182 329 207 413 133 108 77 117 425)(67 147 171 183 330 208 414 134 91 78 118 426)(68 148 172 184 331 209 397 135 92 79 119 427)(69 149 173 185 332 210 398 136 93 80 120 428)(70 150 174 186 333 211 399 137 94 81 121 429)(71 151 175 187 334 212 400 138 95 82 122 430)(72 152 176 188 335 213 401 139 96 83 123 431)
(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 83 10 74)(2 82 11 73)(3 81 12 90)(4 80 13 89)(5 79 14 88)(6 78 15 87)(7 77 16 86)(8 76 17 85)(9 75 18 84)(19 407 28 398)(20 406 29 397)(21 405 30 414)(22 404 31 413)(23 403 32 412)(24 402 33 411)(25 401 34 410)(26 400 35 409)(27 399 36 408)(37 161 46 152)(38 160 47 151)(39 159 48 150)(40 158 49 149)(41 157 50 148)(42 156 51 147)(43 155 52 146)(44 154 53 145)(45 153 54 162)(55 282 64 273)(56 281 65 272)(57 280 66 271)(58 279 67 288)(59 278 68 287)(60 277 69 286)(61 276 70 285)(62 275 71 284)(63 274 72 283)(91 361 100 370)(92 378 101 369)(93 377 102 368)(94 376 103 367)(95 375 104 366)(96 374 105 365)(97 373 106 364)(98 372 107 363)(99 371 108 362)(109 235 118 244)(110 252 119 243)(111 251 120 242)(112 250 121 241)(113 249 122 240)(114 248 123 239)(115 247 124 238)(116 246 125 237)(117 245 126 236)(127 253 136 262)(128 270 137 261)(129 269 138 260)(130 268 139 259)(131 267 140 258)(132 266 141 257)(133 265 142 256)(134 264 143 255)(135 263 144 254)(163 383 172 392)(164 382 173 391)(165 381 174 390)(166 380 175 389)(167 379 176 388)(168 396 177 387)(169 395 178 386)(170 394 179 385)(171 393 180 384)(181 221 190 230)(182 220 191 229)(183 219 192 228)(184 218 193 227)(185 217 194 226)(186 234 195 225)(187 233 196 224)(188 232 197 223)(189 231 198 222)(199 347 208 356)(200 346 209 355)(201 345 210 354)(202 344 211 353)(203 343 212 352)(204 360 213 351)(205 359 214 350)(206 358 215 349)(207 357 216 348)(289 329 298 338)(290 328 299 337)(291 327 300 336)(292 326 301 335)(293 325 302 334)(294 342 303 333)(295 341 304 332)(296 340 305 331)(297 339 306 330)(307 430 316 421)(308 429 317 420)(309 428 318 419)(310 427 319 418)(311 426 320 417)(312 425 321 416)(313 424 322 415)(314 423 323 432)(315 422 324 431)
G:=sub<Sym(432)| (1,365,268,25,360,301,223,379,46,274,324,248)(2,366,269,26,343,302,224,380,47,275,307,249)(3,367,270,27,344,303,225,381,48,276,308,250)(4,368,253,28,345,304,226,382,49,277,309,251)(5,369,254,29,346,305,227,383,50,278,310,252)(6,370,255,30,347,306,228,384,51,279,311,235)(7,371,256,31,348,289,229,385,52,280,312,236)(8,372,257,32,349,290,230,386,53,281,313,237)(9,373,258,33,350,291,231,387,54,282,314,238)(10,374,259,34,351,292,232,388,37,283,315,239)(11,375,260,35,352,293,233,389,38,284,316,240)(12,376,261,36,353,294,234,390,39,285,317,241)(13,377,262,19,354,295,217,391,40,286,318,242)(14,378,263,20,355,296,218,392,41,287,319,243)(15,361,264,21,356,297,219,393,42,288,320,244)(16,362,265,22,357,298,220,394,43,271,321,245)(17,363,266,23,358,299,221,395,44,272,322,246)(18,364,267,24,359,300,222,396,45,273,323,247)(55,153,177,189,336,214,402,140,97,84,124,432)(56,154,178,190,337,215,403,141,98,85,125,415)(57,155,179,191,338,216,404,142,99,86,126,416)(58,156,180,192,339,199,405,143,100,87,109,417)(59,157,163,193,340,200,406,144,101,88,110,418)(60,158,164,194,341,201,407,127,102,89,111,419)(61,159,165,195,342,202,408,128,103,90,112,420)(62,160,166,196,325,203,409,129,104,73,113,421)(63,161,167,197,326,204,410,130,105,74,114,422)(64,162,168,198,327,205,411,131,106,75,115,423)(65,145,169,181,328,206,412,132,107,76,116,424)(66,146,170,182,329,207,413,133,108,77,117,425)(67,147,171,183,330,208,414,134,91,78,118,426)(68,148,172,184,331,209,397,135,92,79,119,427)(69,149,173,185,332,210,398,136,93,80,120,428)(70,150,174,186,333,211,399,137,94,81,121,429)(71,151,175,187,334,212,400,138,95,82,122,430)(72,152,176,188,335,213,401,139,96,83,123,431), (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), (1,83,10,74)(2,82,11,73)(3,81,12,90)(4,80,13,89)(5,79,14,88)(6,78,15,87)(7,77,16,86)(8,76,17,85)(9,75,18,84)(19,407,28,398)(20,406,29,397)(21,405,30,414)(22,404,31,413)(23,403,32,412)(24,402,33,411)(25,401,34,410)(26,400,35,409)(27,399,36,408)(37,161,46,152)(38,160,47,151)(39,159,48,150)(40,158,49,149)(41,157,50,148)(42,156,51,147)(43,155,52,146)(44,154,53,145)(45,153,54,162)(55,282,64,273)(56,281,65,272)(57,280,66,271)(58,279,67,288)(59,278,68,287)(60,277,69,286)(61,276,70,285)(62,275,71,284)(63,274,72,283)(91,361,100,370)(92,378,101,369)(93,377,102,368)(94,376,103,367)(95,375,104,366)(96,374,105,365)(97,373,106,364)(98,372,107,363)(99,371,108,362)(109,235,118,244)(110,252,119,243)(111,251,120,242)(112,250,121,241)(113,249,122,240)(114,248,123,239)(115,247,124,238)(116,246,125,237)(117,245,126,236)(127,253,136,262)(128,270,137,261)(129,269,138,260)(130,268,139,259)(131,267,140,258)(132,266,141,257)(133,265,142,256)(134,264,143,255)(135,263,144,254)(163,383,172,392)(164,382,173,391)(165,381,174,390)(166,380,175,389)(167,379,176,388)(168,396,177,387)(169,395,178,386)(170,394,179,385)(171,393,180,384)(181,221,190,230)(182,220,191,229)(183,219,192,228)(184,218,193,227)(185,217,194,226)(186,234,195,225)(187,233,196,224)(188,232,197,223)(189,231,198,222)(199,347,208,356)(200,346,209,355)(201,345,210,354)(202,344,211,353)(203,343,212,352)(204,360,213,351)(205,359,214,350)(206,358,215,349)(207,357,216,348)(289,329,298,338)(290,328,299,337)(291,327,300,336)(292,326,301,335)(293,325,302,334)(294,342,303,333)(295,341,304,332)(296,340,305,331)(297,339,306,330)(307,430,316,421)(308,429,317,420)(309,428,318,419)(310,427,319,418)(311,426,320,417)(312,425,321,416)(313,424,322,415)(314,423,323,432)(315,422,324,431)>;
G:=Group( (1,365,268,25,360,301,223,379,46,274,324,248)(2,366,269,26,343,302,224,380,47,275,307,249)(3,367,270,27,344,303,225,381,48,276,308,250)(4,368,253,28,345,304,226,382,49,277,309,251)(5,369,254,29,346,305,227,383,50,278,310,252)(6,370,255,30,347,306,228,384,51,279,311,235)(7,371,256,31,348,289,229,385,52,280,312,236)(8,372,257,32,349,290,230,386,53,281,313,237)(9,373,258,33,350,291,231,387,54,282,314,238)(10,374,259,34,351,292,232,388,37,283,315,239)(11,375,260,35,352,293,233,389,38,284,316,240)(12,376,261,36,353,294,234,390,39,285,317,241)(13,377,262,19,354,295,217,391,40,286,318,242)(14,378,263,20,355,296,218,392,41,287,319,243)(15,361,264,21,356,297,219,393,42,288,320,244)(16,362,265,22,357,298,220,394,43,271,321,245)(17,363,266,23,358,299,221,395,44,272,322,246)(18,364,267,24,359,300,222,396,45,273,323,247)(55,153,177,189,336,214,402,140,97,84,124,432)(56,154,178,190,337,215,403,141,98,85,125,415)(57,155,179,191,338,216,404,142,99,86,126,416)(58,156,180,192,339,199,405,143,100,87,109,417)(59,157,163,193,340,200,406,144,101,88,110,418)(60,158,164,194,341,201,407,127,102,89,111,419)(61,159,165,195,342,202,408,128,103,90,112,420)(62,160,166,196,325,203,409,129,104,73,113,421)(63,161,167,197,326,204,410,130,105,74,114,422)(64,162,168,198,327,205,411,131,106,75,115,423)(65,145,169,181,328,206,412,132,107,76,116,424)(66,146,170,182,329,207,413,133,108,77,117,425)(67,147,171,183,330,208,414,134,91,78,118,426)(68,148,172,184,331,209,397,135,92,79,119,427)(69,149,173,185,332,210,398,136,93,80,120,428)(70,150,174,186,333,211,399,137,94,81,121,429)(71,151,175,187,334,212,400,138,95,82,122,430)(72,152,176,188,335,213,401,139,96,83,123,431), (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), (1,83,10,74)(2,82,11,73)(3,81,12,90)(4,80,13,89)(5,79,14,88)(6,78,15,87)(7,77,16,86)(8,76,17,85)(9,75,18,84)(19,407,28,398)(20,406,29,397)(21,405,30,414)(22,404,31,413)(23,403,32,412)(24,402,33,411)(25,401,34,410)(26,400,35,409)(27,399,36,408)(37,161,46,152)(38,160,47,151)(39,159,48,150)(40,158,49,149)(41,157,50,148)(42,156,51,147)(43,155,52,146)(44,154,53,145)(45,153,54,162)(55,282,64,273)(56,281,65,272)(57,280,66,271)(58,279,67,288)(59,278,68,287)(60,277,69,286)(61,276,70,285)(62,275,71,284)(63,274,72,283)(91,361,100,370)(92,378,101,369)(93,377,102,368)(94,376,103,367)(95,375,104,366)(96,374,105,365)(97,373,106,364)(98,372,107,363)(99,371,108,362)(109,235,118,244)(110,252,119,243)(111,251,120,242)(112,250,121,241)(113,249,122,240)(114,248,123,239)(115,247,124,238)(116,246,125,237)(117,245,126,236)(127,253,136,262)(128,270,137,261)(129,269,138,260)(130,268,139,259)(131,267,140,258)(132,266,141,257)(133,265,142,256)(134,264,143,255)(135,263,144,254)(163,383,172,392)(164,382,173,391)(165,381,174,390)(166,380,175,389)(167,379,176,388)(168,396,177,387)(169,395,178,386)(170,394,179,385)(171,393,180,384)(181,221,190,230)(182,220,191,229)(183,219,192,228)(184,218,193,227)(185,217,194,226)(186,234,195,225)(187,233,196,224)(188,232,197,223)(189,231,198,222)(199,347,208,356)(200,346,209,355)(201,345,210,354)(202,344,211,353)(203,343,212,352)(204,360,213,351)(205,359,214,350)(206,358,215,349)(207,357,216,348)(289,329,298,338)(290,328,299,337)(291,327,300,336)(292,326,301,335)(293,325,302,334)(294,342,303,333)(295,341,304,332)(296,340,305,331)(297,339,306,330)(307,430,316,421)(308,429,317,420)(309,428,318,419)(310,427,319,418)(311,426,320,417)(312,425,321,416)(313,424,322,415)(314,423,323,432)(315,422,324,431) );
G=PermutationGroup([[(1,365,268,25,360,301,223,379,46,274,324,248),(2,366,269,26,343,302,224,380,47,275,307,249),(3,367,270,27,344,303,225,381,48,276,308,250),(4,368,253,28,345,304,226,382,49,277,309,251),(5,369,254,29,346,305,227,383,50,278,310,252),(6,370,255,30,347,306,228,384,51,279,311,235),(7,371,256,31,348,289,229,385,52,280,312,236),(8,372,257,32,349,290,230,386,53,281,313,237),(9,373,258,33,350,291,231,387,54,282,314,238),(10,374,259,34,351,292,232,388,37,283,315,239),(11,375,260,35,352,293,233,389,38,284,316,240),(12,376,261,36,353,294,234,390,39,285,317,241),(13,377,262,19,354,295,217,391,40,286,318,242),(14,378,263,20,355,296,218,392,41,287,319,243),(15,361,264,21,356,297,219,393,42,288,320,244),(16,362,265,22,357,298,220,394,43,271,321,245),(17,363,266,23,358,299,221,395,44,272,322,246),(18,364,267,24,359,300,222,396,45,273,323,247),(55,153,177,189,336,214,402,140,97,84,124,432),(56,154,178,190,337,215,403,141,98,85,125,415),(57,155,179,191,338,216,404,142,99,86,126,416),(58,156,180,192,339,199,405,143,100,87,109,417),(59,157,163,193,340,200,406,144,101,88,110,418),(60,158,164,194,341,201,407,127,102,89,111,419),(61,159,165,195,342,202,408,128,103,90,112,420),(62,160,166,196,325,203,409,129,104,73,113,421),(63,161,167,197,326,204,410,130,105,74,114,422),(64,162,168,198,327,205,411,131,106,75,115,423),(65,145,169,181,328,206,412,132,107,76,116,424),(66,146,170,182,329,207,413,133,108,77,117,425),(67,147,171,183,330,208,414,134,91,78,118,426),(68,148,172,184,331,209,397,135,92,79,119,427),(69,149,173,185,332,210,398,136,93,80,120,428),(70,150,174,186,333,211,399,137,94,81,121,429),(71,151,175,187,334,212,400,138,95,82,122,430),(72,152,176,188,335,213,401,139,96,83,123,431)], [(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)], [(1,83,10,74),(2,82,11,73),(3,81,12,90),(4,80,13,89),(5,79,14,88),(6,78,15,87),(7,77,16,86),(8,76,17,85),(9,75,18,84),(19,407,28,398),(20,406,29,397),(21,405,30,414),(22,404,31,413),(23,403,32,412),(24,402,33,411),(25,401,34,410),(26,400,35,409),(27,399,36,408),(37,161,46,152),(38,160,47,151),(39,159,48,150),(40,158,49,149),(41,157,50,148),(42,156,51,147),(43,155,52,146),(44,154,53,145),(45,153,54,162),(55,282,64,273),(56,281,65,272),(57,280,66,271),(58,279,67,288),(59,278,68,287),(60,277,69,286),(61,276,70,285),(62,275,71,284),(63,274,72,283),(91,361,100,370),(92,378,101,369),(93,377,102,368),(94,376,103,367),(95,375,104,366),(96,374,105,365),(97,373,106,364),(98,372,107,363),(99,371,108,362),(109,235,118,244),(110,252,119,243),(111,251,120,242),(112,250,121,241),(113,249,122,240),(114,248,123,239),(115,247,124,238),(116,246,125,237),(117,245,126,236),(127,253,136,262),(128,270,137,261),(129,269,138,260),(130,268,139,259),(131,267,140,258),(132,266,141,257),(133,265,142,256),(134,264,143,255),(135,263,144,254),(163,383,172,392),(164,382,173,391),(165,381,174,390),(166,380,175,389),(167,379,176,388),(168,396,177,387),(169,395,178,386),(170,394,179,385),(171,393,180,384),(181,221,190,230),(182,220,191,229),(183,219,192,228),(184,218,193,227),(185,217,194,226),(186,234,195,225),(187,233,196,224),(188,232,197,223),(189,231,198,222),(199,347,208,356),(200,346,209,355),(201,345,210,354),(202,344,211,353),(203,343,212,352),(204,360,213,351),(205,359,214,350),(206,358,215,349),(207,357,216,348),(289,329,298,338),(290,328,299,337),(291,327,300,336),(292,326,301,335),(293,325,302,334),(294,342,303,333),(295,341,304,332),(296,340,305,331),(297,339,306,330),(307,430,316,421),(308,429,317,420),(309,428,318,419),(310,427,319,418),(311,426,320,417),(312,425,321,416),(313,424,322,415),(314,423,323,432),(315,422,324,431)]])
114 conjugacy classes
| class | 1 | 2A | 2B | 2C | 3A | 3B | 3C | 3D | 4A | 4B | 4C | 4D | 4E | 4F | 6A | ··· | 6L | 9A | ··· | 9I | 12A | ··· | 12P | 18A | ··· | 18AA | 36A | ··· | 36AJ |
| order | 1 | 2 | 2 | 2 | 3 | 3 | 3 | 3 | 4 | 4 | 4 | 4 | 4 | 4 | 6 | ··· | 6 | 9 | ··· | 9 | 12 | ··· | 12 | 18 | ··· | 18 | 36 | ··· | 36 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 54 | 54 | 54 | 54 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
114 irreducible representations
| dim | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | + | - | - | + | - | + | + | - | + | - | + | - | + | - | + | |
| image | C1 | C2 | C2 | C4 | S3 | S3 | D4 | Q8 | Dic3 | D6 | Dic3 | D6 | D9 | Dic6 | D12 | Dic6 | D12 | Dic9 | D18 | Dic18 | D36 |
| kernel | C36⋊Dic3 | C2×C9⋊Dic3 | C6×C36 | C3×C36 | C2×C36 | C6×C12 | C3×C18 | C3×C18 | C36 | C2×C18 | C3×C12 | C62 | C2×C12 | C18 | C18 | C3×C6 | C3×C6 | C12 | C2×C6 | C6 | C6 |
| # reps | 1 | 2 | 1 | 4 | 3 | 1 | 1 | 1 | 6 | 3 | 2 | 1 | 9 | 6 | 6 | 2 | 2 | 18 | 9 | 18 | 18 |
Matrix representation of C36⋊Dic3 ►in GL4(𝔽37) generated by
| 27 | 32 | 0 | 0 |
| 5 | 32 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 0 | 36 | 0 | 0 |
| 1 | 1 | 0 | 0 |
| 0 | 0 | 17 | 31 |
| 0 | 0 | 6 | 11 |
| 29 | 1 | 0 | 0 |
| 9 | 8 | 0 | 0 |
| 0 | 0 | 0 | 31 |
| 0 | 0 | 31 | 0 |
G:=sub<GL(4,GF(37))| [27,5,0,0,32,32,0,0,0,0,1,0,0,0,0,1],[0,1,0,0,36,1,0,0,0,0,17,6,0,0,31,11],[29,9,0,0,1,8,0,0,0,0,0,31,0,0,31,0] >;
C36⋊Dic3 in GAP, Magma, Sage, TeX
C_{36}\rtimes {\rm Dic}_3 % in TeX
G:=Group("C36:Dic3"); // GroupNames label
G:=SmallGroup(432,182);
// by ID
G=gap.SmallGroup(432,182);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-3,-3,-3,28,141,64,6164,662,4037,14118]);
// Polycyclic
G:=Group<a,b,c|a^12=b^18=1,c^2=b^9,a*b=b*a,c*a*c^-1=a^-1,c*b*c^-1=b^-1>;
// generators/relations