metabelian, supersoluble, monomial, A-group
Aliases: C3⋊Dic33, C66.3S3, C6.3D33, C33⋊1Dic3, C32⋊3Dic11, (C3×C33)⋊3C4, C22.(C3⋊S3), C2.(C3⋊D33), C11⋊(C3⋊Dic3), (C3×C66).1C2, (C3×C6).2D11, SmallGroup(396,15)
Series: Derived ►Chief ►Lower central ►Upper central
| C3×C33 — C3⋊Dic33 |
Generators and relations for C3⋊Dic33
G = < a,b,c | a3=b66=1, c2=b33, ab=ba, cac-1=a-1, cbc-1=b-1 >
Smallest permutation representation of C3⋊Dic33
►Regular action on 396 points
Generators in S396
(1 95 309)(2 96 310)(3 97 311)(4 98 312)(5 99 313)(6 100 314)(7 101 315)(8 102 316)(9 103 317)(10 104 318)(11 105 319)(12 106 320)(13 107 321)(14 108 322)(15 109 323)(16 110 324)(17 111 325)(18 112 326)(19 113 327)(20 114 328)(21 115 329)(22 116 330)(23 117 265)(24 118 266)(25 119 267)(26 120 268)(27 121 269)(28 122 270)(29 123 271)(30 124 272)(31 125 273)(32 126 274)(33 127 275)(34 128 276)(35 129 277)(36 130 278)(37 131 279)(38 132 280)(39 67 281)(40 68 282)(41 69 283)(42 70 284)(43 71 285)(44 72 286)(45 73 287)(46 74 288)(47 75 289)(48 76 290)(49 77 291)(50 78 292)(51 79 293)(52 80 294)(53 81 295)(54 82 296)(55 83 297)(56 84 298)(57 85 299)(58 86 300)(59 87 301)(60 88 302)(61 89 303)(62 90 304)(63 91 305)(64 92 306)(65 93 307)(66 94 308)(133 264 388)(134 199 389)(135 200 390)(136 201 391)(137 202 392)(138 203 393)(139 204 394)(140 205 395)(141 206 396)(142 207 331)(143 208 332)(144 209 333)(145 210 334)(146 211 335)(147 212 336)(148 213 337)(149 214 338)(150 215 339)(151 216 340)(152 217 341)(153 218 342)(154 219 343)(155 220 344)(156 221 345)(157 222 346)(158 223 347)(159 224 348)(160 225 349)(161 226 350)(162 227 351)(163 228 352)(164 229 353)(165 230 354)(166 231 355)(167 232 356)(168 233 357)(169 234 358)(170 235 359)(171 236 360)(172 237 361)(173 238 362)(174 239 363)(175 240 364)(176 241 365)(177 242 366)(178 243 367)(179 244 368)(180 245 369)(181 246 370)(182 247 371)(183 248 372)(184 249 373)(185 250 374)(186 251 375)(187 252 376)(188 253 377)(189 254 378)(190 255 379)(191 256 380)(192 257 381)(193 258 382)(194 259 383)(195 260 384)(196 261 385)(197 262 386)(198 263 387)
(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)
(1 382 34 349)(2 381 35 348)(3 380 36 347)(4 379 37 346)(5 378 38 345)(6 377 39 344)(7 376 40 343)(8 375 41 342)(9 374 42 341)(10 373 43 340)(11 372 44 339)(12 371 45 338)(13 370 46 337)(14 369 47 336)(15 368 48 335)(16 367 49 334)(17 366 50 333)(18 365 51 332)(19 364 52 331)(20 363 53 396)(21 362 54 395)(22 361 55 394)(23 360 56 393)(24 359 57 392)(25 358 58 391)(26 357 59 390)(27 356 60 389)(28 355 61 388)(29 354 62 387)(30 353 63 386)(31 352 64 385)(32 351 65 384)(33 350 66 383)(67 220 100 253)(68 219 101 252)(69 218 102 251)(70 217 103 250)(71 216 104 249)(72 215 105 248)(73 214 106 247)(74 213 107 246)(75 212 108 245)(76 211 109 244)(77 210 110 243)(78 209 111 242)(79 208 112 241)(80 207 113 240)(81 206 114 239)(82 205 115 238)(83 204 116 237)(84 203 117 236)(85 202 118 235)(86 201 119 234)(87 200 120 233)(88 199 121 232)(89 264 122 231)(90 263 123 230)(91 262 124 229)(92 261 125 228)(93 260 126 227)(94 259 127 226)(95 258 128 225)(96 257 129 224)(97 256 130 223)(98 255 131 222)(99 254 132 221)(133 270 166 303)(134 269 167 302)(135 268 168 301)(136 267 169 300)(137 266 170 299)(138 265 171 298)(139 330 172 297)(140 329 173 296)(141 328 174 295)(142 327 175 294)(143 326 176 293)(144 325 177 292)(145 324 178 291)(146 323 179 290)(147 322 180 289)(148 321 181 288)(149 320 182 287)(150 319 183 286)(151 318 184 285)(152 317 185 284)(153 316 186 283)(154 315 187 282)(155 314 188 281)(156 313 189 280)(157 312 190 279)(158 311 191 278)(159 310 192 277)(160 309 193 276)(161 308 194 275)(162 307 195 274)(163 306 196 273)(164 305 197 272)(165 304 198 271)
G:=sub<Sym(396)| (1,95,309)(2,96,310)(3,97,311)(4,98,312)(5,99,313)(6,100,314)(7,101,315)(8,102,316)(9,103,317)(10,104,318)(11,105,319)(12,106,320)(13,107,321)(14,108,322)(15,109,323)(16,110,324)(17,111,325)(18,112,326)(19,113,327)(20,114,328)(21,115,329)(22,116,330)(23,117,265)(24,118,266)(25,119,267)(26,120,268)(27,121,269)(28,122,270)(29,123,271)(30,124,272)(31,125,273)(32,126,274)(33,127,275)(34,128,276)(35,129,277)(36,130,278)(37,131,279)(38,132,280)(39,67,281)(40,68,282)(41,69,283)(42,70,284)(43,71,285)(44,72,286)(45,73,287)(46,74,288)(47,75,289)(48,76,290)(49,77,291)(50,78,292)(51,79,293)(52,80,294)(53,81,295)(54,82,296)(55,83,297)(56,84,298)(57,85,299)(58,86,300)(59,87,301)(60,88,302)(61,89,303)(62,90,304)(63,91,305)(64,92,306)(65,93,307)(66,94,308)(133,264,388)(134,199,389)(135,200,390)(136,201,391)(137,202,392)(138,203,393)(139,204,394)(140,205,395)(141,206,396)(142,207,331)(143,208,332)(144,209,333)(145,210,334)(146,211,335)(147,212,336)(148,213,337)(149,214,338)(150,215,339)(151,216,340)(152,217,341)(153,218,342)(154,219,343)(155,220,344)(156,221,345)(157,222,346)(158,223,347)(159,224,348)(160,225,349)(161,226,350)(162,227,351)(163,228,352)(164,229,353)(165,230,354)(166,231,355)(167,232,356)(168,233,357)(169,234,358)(170,235,359)(171,236,360)(172,237,361)(173,238,362)(174,239,363)(175,240,364)(176,241,365)(177,242,366)(178,243,367)(179,244,368)(180,245,369)(181,246,370)(182,247,371)(183,248,372)(184,249,373)(185,250,374)(186,251,375)(187,252,376)(188,253,377)(189,254,378)(190,255,379)(191,256,380)(192,257,381)(193,258,382)(194,259,383)(195,260,384)(196,261,385)(197,262,386)(198,263,387), (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), (1,382,34,349)(2,381,35,348)(3,380,36,347)(4,379,37,346)(5,378,38,345)(6,377,39,344)(7,376,40,343)(8,375,41,342)(9,374,42,341)(10,373,43,340)(11,372,44,339)(12,371,45,338)(13,370,46,337)(14,369,47,336)(15,368,48,335)(16,367,49,334)(17,366,50,333)(18,365,51,332)(19,364,52,331)(20,363,53,396)(21,362,54,395)(22,361,55,394)(23,360,56,393)(24,359,57,392)(25,358,58,391)(26,357,59,390)(27,356,60,389)(28,355,61,388)(29,354,62,387)(30,353,63,386)(31,352,64,385)(32,351,65,384)(33,350,66,383)(67,220,100,253)(68,219,101,252)(69,218,102,251)(70,217,103,250)(71,216,104,249)(72,215,105,248)(73,214,106,247)(74,213,107,246)(75,212,108,245)(76,211,109,244)(77,210,110,243)(78,209,111,242)(79,208,112,241)(80,207,113,240)(81,206,114,239)(82,205,115,238)(83,204,116,237)(84,203,117,236)(85,202,118,235)(86,201,119,234)(87,200,120,233)(88,199,121,232)(89,264,122,231)(90,263,123,230)(91,262,124,229)(92,261,125,228)(93,260,126,227)(94,259,127,226)(95,258,128,225)(96,257,129,224)(97,256,130,223)(98,255,131,222)(99,254,132,221)(133,270,166,303)(134,269,167,302)(135,268,168,301)(136,267,169,300)(137,266,170,299)(138,265,171,298)(139,330,172,297)(140,329,173,296)(141,328,174,295)(142,327,175,294)(143,326,176,293)(144,325,177,292)(145,324,178,291)(146,323,179,290)(147,322,180,289)(148,321,181,288)(149,320,182,287)(150,319,183,286)(151,318,184,285)(152,317,185,284)(153,316,186,283)(154,315,187,282)(155,314,188,281)(156,313,189,280)(157,312,190,279)(158,311,191,278)(159,310,192,277)(160,309,193,276)(161,308,194,275)(162,307,195,274)(163,306,196,273)(164,305,197,272)(165,304,198,271)>;
G:=Group( (1,95,309)(2,96,310)(3,97,311)(4,98,312)(5,99,313)(6,100,314)(7,101,315)(8,102,316)(9,103,317)(10,104,318)(11,105,319)(12,106,320)(13,107,321)(14,108,322)(15,109,323)(16,110,324)(17,111,325)(18,112,326)(19,113,327)(20,114,328)(21,115,329)(22,116,330)(23,117,265)(24,118,266)(25,119,267)(26,120,268)(27,121,269)(28,122,270)(29,123,271)(30,124,272)(31,125,273)(32,126,274)(33,127,275)(34,128,276)(35,129,277)(36,130,278)(37,131,279)(38,132,280)(39,67,281)(40,68,282)(41,69,283)(42,70,284)(43,71,285)(44,72,286)(45,73,287)(46,74,288)(47,75,289)(48,76,290)(49,77,291)(50,78,292)(51,79,293)(52,80,294)(53,81,295)(54,82,296)(55,83,297)(56,84,298)(57,85,299)(58,86,300)(59,87,301)(60,88,302)(61,89,303)(62,90,304)(63,91,305)(64,92,306)(65,93,307)(66,94,308)(133,264,388)(134,199,389)(135,200,390)(136,201,391)(137,202,392)(138,203,393)(139,204,394)(140,205,395)(141,206,396)(142,207,331)(143,208,332)(144,209,333)(145,210,334)(146,211,335)(147,212,336)(148,213,337)(149,214,338)(150,215,339)(151,216,340)(152,217,341)(153,218,342)(154,219,343)(155,220,344)(156,221,345)(157,222,346)(158,223,347)(159,224,348)(160,225,349)(161,226,350)(162,227,351)(163,228,352)(164,229,353)(165,230,354)(166,231,355)(167,232,356)(168,233,357)(169,234,358)(170,235,359)(171,236,360)(172,237,361)(173,238,362)(174,239,363)(175,240,364)(176,241,365)(177,242,366)(178,243,367)(179,244,368)(180,245,369)(181,246,370)(182,247,371)(183,248,372)(184,249,373)(185,250,374)(186,251,375)(187,252,376)(188,253,377)(189,254,378)(190,255,379)(191,256,380)(192,257,381)(193,258,382)(194,259,383)(195,260,384)(196,261,385)(197,262,386)(198,263,387), (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), (1,382,34,349)(2,381,35,348)(3,380,36,347)(4,379,37,346)(5,378,38,345)(6,377,39,344)(7,376,40,343)(8,375,41,342)(9,374,42,341)(10,373,43,340)(11,372,44,339)(12,371,45,338)(13,370,46,337)(14,369,47,336)(15,368,48,335)(16,367,49,334)(17,366,50,333)(18,365,51,332)(19,364,52,331)(20,363,53,396)(21,362,54,395)(22,361,55,394)(23,360,56,393)(24,359,57,392)(25,358,58,391)(26,357,59,390)(27,356,60,389)(28,355,61,388)(29,354,62,387)(30,353,63,386)(31,352,64,385)(32,351,65,384)(33,350,66,383)(67,220,100,253)(68,219,101,252)(69,218,102,251)(70,217,103,250)(71,216,104,249)(72,215,105,248)(73,214,106,247)(74,213,107,246)(75,212,108,245)(76,211,109,244)(77,210,110,243)(78,209,111,242)(79,208,112,241)(80,207,113,240)(81,206,114,239)(82,205,115,238)(83,204,116,237)(84,203,117,236)(85,202,118,235)(86,201,119,234)(87,200,120,233)(88,199,121,232)(89,264,122,231)(90,263,123,230)(91,262,124,229)(92,261,125,228)(93,260,126,227)(94,259,127,226)(95,258,128,225)(96,257,129,224)(97,256,130,223)(98,255,131,222)(99,254,132,221)(133,270,166,303)(134,269,167,302)(135,268,168,301)(136,267,169,300)(137,266,170,299)(138,265,171,298)(139,330,172,297)(140,329,173,296)(141,328,174,295)(142,327,175,294)(143,326,176,293)(144,325,177,292)(145,324,178,291)(146,323,179,290)(147,322,180,289)(148,321,181,288)(149,320,182,287)(150,319,183,286)(151,318,184,285)(152,317,185,284)(153,316,186,283)(154,315,187,282)(155,314,188,281)(156,313,189,280)(157,312,190,279)(158,311,191,278)(159,310,192,277)(160,309,193,276)(161,308,194,275)(162,307,195,274)(163,306,196,273)(164,305,197,272)(165,304,198,271) );
G=PermutationGroup([[(1,95,309),(2,96,310),(3,97,311),(4,98,312),(5,99,313),(6,100,314),(7,101,315),(8,102,316),(9,103,317),(10,104,318),(11,105,319),(12,106,320),(13,107,321),(14,108,322),(15,109,323),(16,110,324),(17,111,325),(18,112,326),(19,113,327),(20,114,328),(21,115,329),(22,116,330),(23,117,265),(24,118,266),(25,119,267),(26,120,268),(27,121,269),(28,122,270),(29,123,271),(30,124,272),(31,125,273),(32,126,274),(33,127,275),(34,128,276),(35,129,277),(36,130,278),(37,131,279),(38,132,280),(39,67,281),(40,68,282),(41,69,283),(42,70,284),(43,71,285),(44,72,286),(45,73,287),(46,74,288),(47,75,289),(48,76,290),(49,77,291),(50,78,292),(51,79,293),(52,80,294),(53,81,295),(54,82,296),(55,83,297),(56,84,298),(57,85,299),(58,86,300),(59,87,301),(60,88,302),(61,89,303),(62,90,304),(63,91,305),(64,92,306),(65,93,307),(66,94,308),(133,264,388),(134,199,389),(135,200,390),(136,201,391),(137,202,392),(138,203,393),(139,204,394),(140,205,395),(141,206,396),(142,207,331),(143,208,332),(144,209,333),(145,210,334),(146,211,335),(147,212,336),(148,213,337),(149,214,338),(150,215,339),(151,216,340),(152,217,341),(153,218,342),(154,219,343),(155,220,344),(156,221,345),(157,222,346),(158,223,347),(159,224,348),(160,225,349),(161,226,350),(162,227,351),(163,228,352),(164,229,353),(165,230,354),(166,231,355),(167,232,356),(168,233,357),(169,234,358),(170,235,359),(171,236,360),(172,237,361),(173,238,362),(174,239,363),(175,240,364),(176,241,365),(177,242,366),(178,243,367),(179,244,368),(180,245,369),(181,246,370),(182,247,371),(183,248,372),(184,249,373),(185,250,374),(186,251,375),(187,252,376),(188,253,377),(189,254,378),(190,255,379),(191,256,380),(192,257,381),(193,258,382),(194,259,383),(195,260,384),(196,261,385),(197,262,386),(198,263,387)], [(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)], [(1,382,34,349),(2,381,35,348),(3,380,36,347),(4,379,37,346),(5,378,38,345),(6,377,39,344),(7,376,40,343),(8,375,41,342),(9,374,42,341),(10,373,43,340),(11,372,44,339),(12,371,45,338),(13,370,46,337),(14,369,47,336),(15,368,48,335),(16,367,49,334),(17,366,50,333),(18,365,51,332),(19,364,52,331),(20,363,53,396),(21,362,54,395),(22,361,55,394),(23,360,56,393),(24,359,57,392),(25,358,58,391),(26,357,59,390),(27,356,60,389),(28,355,61,388),(29,354,62,387),(30,353,63,386),(31,352,64,385),(32,351,65,384),(33,350,66,383),(67,220,100,253),(68,219,101,252),(69,218,102,251),(70,217,103,250),(71,216,104,249),(72,215,105,248),(73,214,106,247),(74,213,107,246),(75,212,108,245),(76,211,109,244),(77,210,110,243),(78,209,111,242),(79,208,112,241),(80,207,113,240),(81,206,114,239),(82,205,115,238),(83,204,116,237),(84,203,117,236),(85,202,118,235),(86,201,119,234),(87,200,120,233),(88,199,121,232),(89,264,122,231),(90,263,123,230),(91,262,124,229),(92,261,125,228),(93,260,126,227),(94,259,127,226),(95,258,128,225),(96,257,129,224),(97,256,130,223),(98,255,131,222),(99,254,132,221),(133,270,166,303),(134,269,167,302),(135,268,168,301),(136,267,169,300),(137,266,170,299),(138,265,171,298),(139,330,172,297),(140,329,173,296),(141,328,174,295),(142,327,175,294),(143,326,176,293),(144,325,177,292),(145,324,178,291),(146,323,179,290),(147,322,180,289),(148,321,181,288),(149,320,182,287),(150,319,183,286),(151,318,184,285),(152,317,185,284),(153,316,186,283),(154,315,187,282),(155,314,188,281),(156,313,189,280),(157,312,190,279),(158,311,191,278),(159,310,192,277),(160,309,193,276),(161,308,194,275),(162,307,195,274),(163,306,196,273),(164,305,197,272),(165,304,198,271)]])
102 conjugacy classes
| class | 1 | 2 | 3A | 3B | 3C | 3D | 4A | 4B | 6A | 6B | 6C | 6D | 11A | ··· | 11E | 22A | ··· | 22E | 33A | ··· | 33AN | 66A | ··· | 66AN |
| order | 1 | 2 | 3 | 3 | 3 | 3 | 4 | 4 | 6 | 6 | 6 | 6 | 11 | ··· | 11 | 22 | ··· | 22 | 33 | ··· | 33 | 66 | ··· | 66 |
| size | 1 | 1 | 2 | 2 | 2 | 2 | 99 | 99 | 2 | 2 | 2 | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
102 irreducible representations
| dim | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | - | + | - | + | - | |
| image | C1 | C2 | C4 | S3 | Dic3 | D11 | Dic11 | D33 | Dic33 |
| kernel | C3⋊Dic33 | C3×C66 | C3×C33 | C66 | C33 | C3×C6 | C32 | C6 | C3 |
| # reps | 1 | 1 | 2 | 4 | 4 | 5 | 5 | 40 | 40 |
Matrix representation of C3⋊Dic33 ►in GL4(𝔽397) generated by
| 109 | 388 | 0 | 0 |
| 9 | 287 | 0 | 0 |
| 0 | 0 | 115 | 264 |
| 0 | 0 | 360 | 281 |
| 9 | 287 | 0 | 0 |
| 110 | 376 | 0 | 0 |
| 0 | 0 | 289 | 396 |
| 0 | 0 | 143 | 141 |
| 269 | 277 | 0 | 0 |
| 206 | 128 | 0 | 0 |
| 0 | 0 | 275 | 388 |
| 0 | 0 | 110 | 122 |
G:=sub<GL(4,GF(397))| [109,9,0,0,388,287,0,0,0,0,115,360,0,0,264,281],[9,110,0,0,287,376,0,0,0,0,289,143,0,0,396,141],[269,206,0,0,277,128,0,0,0,0,275,110,0,0,388,122] >;
C3⋊Dic33 in GAP, Magma, Sage, TeX
C_3\rtimes {\rm Dic}_{33} % in TeX
G:=Group("C3:Dic33"); // GroupNames label
G:=SmallGroup(396,15);
// by ID
G=gap.SmallGroup(396,15);
# by ID
G:=PCGroup([5,-2,-2,-3,-3,-11,10,122,483,9004]);
// Polycyclic
G:=Group<a,b,c|a^3=b^66=1,c^2=b^33,a*b=b*a,c*a*c^-1=a^-1,c*b*c^-1=b^-1>;
// generators/relations
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