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G = C36⋊Dic3order 432 = 24·33

1st semidirect product of C36 and Dic3 acting via Dic3/C6=C2

metabelian, supersoluble, monomial

Aliases: C361Dic3, C121Dic9, 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, C32(C4⋊Dic9), C92(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(C324Q8), 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

C1C3×C18 — C36⋊Dic3
C1C3C32C3×C9C3×C18C6×C18C2×C9⋊Dic3 — C36⋊Dic3
C3×C9C3×C18 — C36⋊Dic3
C1C22C2×C4

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 [×3], C3, C3 [×3], C4 [×2], C4 [×2], C22, C6 [×3], C6 [×9], C2×C4, C2×C4 [×2], C9 [×3], C32, Dic3 [×8], C12 [×8], C2×C6, C2×C6 [×3], C4⋊C4, C18 [×9], C3×C6 [×3], C2×Dic3 [×8], C2×C12, C2×C12 [×3], C3×C9, Dic9 [×6], C36 [×6], C2×C18 [×3], C3⋊Dic3 [×2], C3×C12 [×2], C62, C4⋊Dic3 [×4], C3×C18 [×3], C2×Dic9 [×6], C2×C36 [×3], C2×C3⋊Dic3 [×2], C6×C12, C9⋊Dic3 [×2], C3×C36 [×2], C6×C18, C4⋊Dic9 [×3], C12⋊Dic3, C2×C9⋊Dic3 [×2], C6×C36, C36⋊Dic3
Quotients: C1, C2 [×3], C4 [×2], C22, S3 [×4], C2×C4, D4, Q8, Dic3 [×8], D6 [×4], C4⋊C4, D9 [×3], C3⋊S3, Dic6 [×4], D12 [×4], C2×Dic3 [×4], Dic9 [×6], D18 [×3], C3⋊Dic3 [×2], C2×C3⋊S3, C4⋊Dic3 [×4], C9⋊S3, Dic18 [×3], D36 [×3], C2×Dic9 [×3], C324Q8, C12⋊S3, C2×C3⋊Dic3, C9⋊Dic3 [×2], C2×C9⋊S3, C4⋊Dic9 [×3], C12⋊Dic3, C12.D9, C36⋊S3, C2×C9⋊Dic3, C36⋊Dic3

Smallest permutation representation of C36⋊Dic3
Regular action on 432 points
Generators in S432
(1 206 315 374 188 120 221 263 284 325 133 242)(2 207 316 375 189 121 222 264 285 326 134 243)(3 208 317 376 190 122 223 265 286 327 135 244)(4 209 318 377 191 123 224 266 287 328 136 245)(5 210 319 378 192 124 225 267 288 329 137 246)(6 211 320 361 193 125 226 268 271 330 138 247)(7 212 321 362 194 126 227 269 272 331 139 248)(8 213 322 363 195 109 228 270 273 332 140 249)(9 214 323 364 196 110 229 253 274 333 141 250)(10 215 324 365 197 111 230 254 275 334 142 251)(11 216 307 366 198 112 231 255 276 335 143 252)(12 199 308 367 181 113 232 256 277 336 144 235)(13 200 309 368 182 114 233 257 278 337 127 236)(14 201 310 369 183 115 234 258 279 338 128 237)(15 202 311 370 184 116 217 259 280 339 129 238)(16 203 312 371 185 117 218 260 281 340 130 239)(17 204 313 372 186 118 219 261 282 341 131 240)(18 205 314 373 187 119 220 262 283 342 132 241)(19 104 393 52 56 149 302 344 428 409 177 87)(20 105 394 53 57 150 303 345 429 410 178 88)(21 106 395 54 58 151 304 346 430 411 179 89)(22 107 396 37 59 152 305 347 431 412 180 90)(23 108 379 38 60 153 306 348 432 413 163 73)(24 91 380 39 61 154 289 349 415 414 164 74)(25 92 381 40 62 155 290 350 416 397 165 75)(26 93 382 41 63 156 291 351 417 398 166 76)(27 94 383 42 64 157 292 352 418 399 167 77)(28 95 384 43 65 158 293 353 419 400 168 78)(29 96 385 44 66 159 294 354 420 401 169 79)(30 97 386 45 67 160 295 355 421 402 170 80)(31 98 387 46 68 161 296 356 422 403 171 81)(32 99 388 47 69 162 297 357 423 404 172 82)(33 100 389 48 70 145 298 358 424 405 173 83)(34 101 390 49 71 146 299 359 425 406 174 84)(35 102 391 50 72 147 300 360 426 407 175 85)(36 103 392 51 55 148 301 343 427 408 176 86)
(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)
(1 301 10 292)(2 300 11 291)(3 299 12 290)(4 298 13 289)(5 297 14 306)(6 296 15 305)(7 295 16 304)(8 294 17 303)(9 293 18 302)(19 229 28 220)(20 228 29 219)(21 227 30 218)(22 226 31 217)(23 225 32 234)(24 224 33 233)(25 223 34 232)(26 222 35 231)(27 221 36 230)(37 361 46 370)(38 378 47 369)(39 377 48 368)(40 376 49 367)(41 375 50 366)(42 374 51 365)(43 373 52 364)(44 372 53 363)(45 371 54 362)(55 324 64 315)(56 323 65 314)(57 322 66 313)(58 321 67 312)(59 320 68 311)(60 319 69 310)(61 318 70 309)(62 317 71 308)(63 316 72 307)(73 267 82 258)(74 266 83 257)(75 265 84 256)(76 264 85 255)(77 263 86 254)(78 262 87 253)(79 261 88 270)(80 260 89 269)(81 259 90 268)(91 123 100 114)(92 122 101 113)(93 121 102 112)(94 120 103 111)(95 119 104 110)(96 118 105 109)(97 117 106 126)(98 116 107 125)(99 115 108 124)(127 415 136 424)(128 432 137 423)(129 431 138 422)(130 430 139 421)(131 429 140 420)(132 428 141 419)(133 427 142 418)(134 426 143 417)(135 425 144 416)(145 200 154 209)(146 199 155 208)(147 216 156 207)(148 215 157 206)(149 214 158 205)(150 213 159 204)(151 212 160 203)(152 211 161 202)(153 210 162 201)(163 288 172 279)(164 287 173 278)(165 286 174 277)(166 285 175 276)(167 284 176 275)(168 283 177 274)(169 282 178 273)(170 281 179 272)(171 280 180 271)(181 381 190 390)(182 380 191 389)(183 379 192 388)(184 396 193 387)(185 395 194 386)(186 394 195 385)(187 393 196 384)(188 392 197 383)(189 391 198 382)(235 350 244 359)(236 349 245 358)(237 348 246 357)(238 347 247 356)(239 346 248 355)(240 345 249 354)(241 344 250 353)(242 343 251 352)(243 360 252 351)(325 408 334 399)(326 407 335 398)(327 406 336 397)(328 405 337 414)(329 404 338 413)(330 403 339 412)(331 402 340 411)(332 401 341 410)(333 400 342 409)

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

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

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

114 conjugacy classes

class 1 2A2B2C3A3B3C3D4A4B4C4D4E4F6A···6L9A···9I12A···12P18A···18AA36A···36AJ
order122233334444446···69···912···1218···1836···36
size1111222222545454542···22···22···22···22···2

114 irreducible representations

dim111122222222222222222
type++++++--+-++-+-+-+-+
imageC1C2C2C4S3S3D4Q8Dic3D6Dic3D6D9Dic6D12Dic6D12Dic9D18Dic18D36
kernelC36⋊Dic3C2×C9⋊Dic3C6×C36C3×C36C2×C36C6×C12C3×C18C3×C18C36C2×C18C3×C12C62C2×C12C18C18C3×C6C3×C6C12C2×C6C6C6
# reps121431116321966221891818

Matrix representation of C36⋊Dic3 in GL4(𝔽37) generated by

273200
53200
0010
0001
,
03600
1100
001731
00611
,
29100
9800
00031
00310
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

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