direct product, metabelian, supersoluble, monomial, A-group
Aliases: C11×C3⋊Dic3, C66.7S3, C32⋊3C44, C33⋊3Dic3, (C3×C33)⋊7C4, C3⋊(C11×Dic3), C6.3(S3×C11), (C3×C66).5C2, (C3×C6).2C22, C22.2(C3⋊S3), C2.(C11×C3⋊S3), SmallGroup(396,14)
Series: Derived ►Chief ►Lower central ►Upper central
| C32 — C11×C3⋊Dic3 |
Generators and relations for C11×C3⋊Dic3
G = < a,b,c,d | a11=b3=c6=1, d2=c3, ab=ba, ac=ca, ad=da, bc=cb, dbd-1=b-1, dcd-1=c-1 >
Smallest permutation representation of C11×C3⋊Dic3
►Regular action on 396 points
Generators in S396
(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)
(1 365 200)(2 366 201)(3 367 202)(4 368 203)(5 369 204)(6 370 205)(7 371 206)(8 372 207)(9 373 208)(10 374 209)(11 364 199)(12 159 271)(13 160 272)(14 161 273)(15 162 274)(16 163 275)(17 164 265)(18 165 266)(19 155 267)(20 156 268)(21 157 269)(22 158 270)(23 255 63)(24 256 64)(25 257 65)(26 258 66)(27 259 56)(28 260 57)(29 261 58)(30 262 59)(31 263 60)(32 264 61)(33 254 62)(34 324 244)(35 325 245)(36 326 246)(37 327 247)(38 328 248)(39 329 249)(40 330 250)(41 320 251)(42 321 252)(43 322 253)(44 323 243)(45 353 98)(46 354 99)(47 355 89)(48 356 90)(49 357 91)(50 358 92)(51 359 93)(52 360 94)(53 361 95)(54 362 96)(55 363 97)(67 242 147)(68 232 148)(69 233 149)(70 234 150)(71 235 151)(72 236 152)(73 237 153)(74 238 154)(75 239 144)(76 240 145)(77 241 146)(78 318 171)(79 319 172)(80 309 173)(81 310 174)(82 311 175)(83 312 176)(84 313 166)(85 314 167)(86 315 168)(87 316 169)(88 317 170)(100 186 395)(101 187 396)(102 177 386)(103 178 387)(104 179 388)(105 180 389)(106 181 390)(107 182 391)(108 183 392)(109 184 393)(110 185 394)(111 220 276)(112 210 277)(113 211 278)(114 212 279)(115 213 280)(116 214 281)(117 215 282)(118 216 283)(119 217 284)(120 218 285)(121 219 286)(122 306 381)(123 307 382)(124 308 383)(125 298 384)(126 299 385)(127 300 375)(128 301 376)(129 302 377)(130 303 378)(131 304 379)(132 305 380)(133 296 336)(134 297 337)(135 287 338)(136 288 339)(137 289 340)(138 290 341)(139 291 331)(140 292 332)(141 293 333)(142 294 334)(143 295 335)(188 349 227)(189 350 228)(190 351 229)(191 352 230)(192 342 231)(193 343 221)(194 344 222)(195 345 223)(196 346 224)(197 347 225)(198 348 226)
(1 191 80 256 215 337)(2 192 81 257 216 338)(3 193 82 258 217 339)(4 194 83 259 218 340)(5 195 84 260 219 341)(6 196 85 261 220 331)(7 197 86 262 210 332)(8 198 87 263 211 333)(9 188 88 264 212 334)(10 189 78 254 213 335)(11 190 79 255 214 336)(12 69 360 322 380 103)(13 70 361 323 381 104)(14 71 362 324 382 105)(15 72 363 325 383 106)(16 73 353 326 384 107)(17 74 354 327 385 108)(18 75 355 328 375 109)(19 76 356 329 376 110)(20 77 357 330 377 100)(21 67 358 320 378 101)(22 68 359 321 379 102)(23 116 296 199 229 172)(24 117 297 200 230 173)(25 118 287 201 231 174)(26 119 288 202 221 175)(27 120 289 203 222 176)(28 121 290 204 223 166)(29 111 291 205 224 167)(30 112 292 206 225 168)(31 113 293 207 226 169)(32 114 294 208 227 170)(33 115 295 209 228 171)(34 307 389 273 151 54)(35 308 390 274 152 55)(36 298 391 275 153 45)(37 299 392 265 154 46)(38 300 393 266 144 47)(39 301 394 267 145 48)(40 302 395 268 146 49)(41 303 396 269 147 50)(42 304 386 270 148 51)(43 305 387 271 149 52)(44 306 388 272 150 53)(56 285 137 368 344 312)(57 286 138 369 345 313)(58 276 139 370 346 314)(59 277 140 371 347 315)(60 278 141 372 348 316)(61 279 142 373 349 317)(62 280 143 374 350 318)(63 281 133 364 351 319)(64 282 134 365 352 309)(65 283 135 366 342 310)(66 284 136 367 343 311)(89 248 127 184 165 239)(90 249 128 185 155 240)(91 250 129 186 156 241)(92 251 130 187 157 242)(93 252 131 177 158 232)(94 253 132 178 159 233)(95 243 122 179 160 234)(96 244 123 180 161 235)(97 245 124 181 162 236)(98 246 125 182 163 237)(99 247 126 183 164 238)
(1 34 256 273)(2 35 257 274)(3 36 258 275)(4 37 259 265)(5 38 260 266)(6 39 261 267)(7 40 262 268)(8 41 263 269)(9 42 264 270)(10 43 254 271)(11 44 255 272)(12 209 322 33)(13 199 323 23)(14 200 324 24)(15 201 325 25)(16 202 326 26)(17 203 327 27)(18 204 328 28)(19 205 329 29)(20 206 330 30)(21 207 320 31)(22 208 321 32)(45 217 391 193)(46 218 392 194)(47 219 393 195)(48 220 394 196)(49 210 395 197)(50 211 396 198)(51 212 386 188)(52 213 387 189)(53 214 388 190)(54 215 389 191)(55 216 390 192)(56 164 368 247)(57 165 369 248)(58 155 370 249)(59 156 371 250)(60 157 372 251)(61 158 373 252)(62 159 374 253)(63 160 364 243)(64 161 365 244)(65 162 366 245)(66 163 367 246)(67 293 378 169)(68 294 379 170)(69 295 380 171)(70 296 381 172)(71 297 382 173)(72 287 383 174)(73 288 384 175)(74 289 385 176)(75 290 375 166)(76 291 376 167)(77 292 377 168)(78 149 335 305)(79 150 336 306)(80 151 337 307)(81 152 338 308)(82 153 339 298)(83 154 340 299)(84 144 341 300)(85 145 331 301)(86 146 332 302)(87 147 333 303)(88 148 334 304)(89 286 184 345)(90 276 185 346)(91 277 186 347)(92 278 187 348)(93 279 177 349)(94 280 178 350)(95 281 179 351)(96 282 180 352)(97 283 181 342)(98 284 182 343)(99 285 183 344)(100 225 357 112)(101 226 358 113)(102 227 359 114)(103 228 360 115)(104 229 361 116)(105 230 362 117)(106 231 363 118)(107 221 353 119)(108 222 354 120)(109 223 355 121)(110 224 356 111)(122 319 234 133)(123 309 235 134)(124 310 236 135)(125 311 237 136)(126 312 238 137)(127 313 239 138)(128 314 240 139)(129 315 241 140)(130 316 242 141)(131 317 232 142)(132 318 233 143)
G:=sub<Sym(396)| (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), (1,365,200)(2,366,201)(3,367,202)(4,368,203)(5,369,204)(6,370,205)(7,371,206)(8,372,207)(9,373,208)(10,374,209)(11,364,199)(12,159,271)(13,160,272)(14,161,273)(15,162,274)(16,163,275)(17,164,265)(18,165,266)(19,155,267)(20,156,268)(21,157,269)(22,158,270)(23,255,63)(24,256,64)(25,257,65)(26,258,66)(27,259,56)(28,260,57)(29,261,58)(30,262,59)(31,263,60)(32,264,61)(33,254,62)(34,324,244)(35,325,245)(36,326,246)(37,327,247)(38,328,248)(39,329,249)(40,330,250)(41,320,251)(42,321,252)(43,322,253)(44,323,243)(45,353,98)(46,354,99)(47,355,89)(48,356,90)(49,357,91)(50,358,92)(51,359,93)(52,360,94)(53,361,95)(54,362,96)(55,363,97)(67,242,147)(68,232,148)(69,233,149)(70,234,150)(71,235,151)(72,236,152)(73,237,153)(74,238,154)(75,239,144)(76,240,145)(77,241,146)(78,318,171)(79,319,172)(80,309,173)(81,310,174)(82,311,175)(83,312,176)(84,313,166)(85,314,167)(86,315,168)(87,316,169)(88,317,170)(100,186,395)(101,187,396)(102,177,386)(103,178,387)(104,179,388)(105,180,389)(106,181,390)(107,182,391)(108,183,392)(109,184,393)(110,185,394)(111,220,276)(112,210,277)(113,211,278)(114,212,279)(115,213,280)(116,214,281)(117,215,282)(118,216,283)(119,217,284)(120,218,285)(121,219,286)(122,306,381)(123,307,382)(124,308,383)(125,298,384)(126,299,385)(127,300,375)(128,301,376)(129,302,377)(130,303,378)(131,304,379)(132,305,380)(133,296,336)(134,297,337)(135,287,338)(136,288,339)(137,289,340)(138,290,341)(139,291,331)(140,292,332)(141,293,333)(142,294,334)(143,295,335)(188,349,227)(189,350,228)(190,351,229)(191,352,230)(192,342,231)(193,343,221)(194,344,222)(195,345,223)(196,346,224)(197,347,225)(198,348,226), (1,191,80,256,215,337)(2,192,81,257,216,338)(3,193,82,258,217,339)(4,194,83,259,218,340)(5,195,84,260,219,341)(6,196,85,261,220,331)(7,197,86,262,210,332)(8,198,87,263,211,333)(9,188,88,264,212,334)(10,189,78,254,213,335)(11,190,79,255,214,336)(12,69,360,322,380,103)(13,70,361,323,381,104)(14,71,362,324,382,105)(15,72,363,325,383,106)(16,73,353,326,384,107)(17,74,354,327,385,108)(18,75,355,328,375,109)(19,76,356,329,376,110)(20,77,357,330,377,100)(21,67,358,320,378,101)(22,68,359,321,379,102)(23,116,296,199,229,172)(24,117,297,200,230,173)(25,118,287,201,231,174)(26,119,288,202,221,175)(27,120,289,203,222,176)(28,121,290,204,223,166)(29,111,291,205,224,167)(30,112,292,206,225,168)(31,113,293,207,226,169)(32,114,294,208,227,170)(33,115,295,209,228,171)(34,307,389,273,151,54)(35,308,390,274,152,55)(36,298,391,275,153,45)(37,299,392,265,154,46)(38,300,393,266,144,47)(39,301,394,267,145,48)(40,302,395,268,146,49)(41,303,396,269,147,50)(42,304,386,270,148,51)(43,305,387,271,149,52)(44,306,388,272,150,53)(56,285,137,368,344,312)(57,286,138,369,345,313)(58,276,139,370,346,314)(59,277,140,371,347,315)(60,278,141,372,348,316)(61,279,142,373,349,317)(62,280,143,374,350,318)(63,281,133,364,351,319)(64,282,134,365,352,309)(65,283,135,366,342,310)(66,284,136,367,343,311)(89,248,127,184,165,239)(90,249,128,185,155,240)(91,250,129,186,156,241)(92,251,130,187,157,242)(93,252,131,177,158,232)(94,253,132,178,159,233)(95,243,122,179,160,234)(96,244,123,180,161,235)(97,245,124,181,162,236)(98,246,125,182,163,237)(99,247,126,183,164,238), (1,34,256,273)(2,35,257,274)(3,36,258,275)(4,37,259,265)(5,38,260,266)(6,39,261,267)(7,40,262,268)(8,41,263,269)(9,42,264,270)(10,43,254,271)(11,44,255,272)(12,209,322,33)(13,199,323,23)(14,200,324,24)(15,201,325,25)(16,202,326,26)(17,203,327,27)(18,204,328,28)(19,205,329,29)(20,206,330,30)(21,207,320,31)(22,208,321,32)(45,217,391,193)(46,218,392,194)(47,219,393,195)(48,220,394,196)(49,210,395,197)(50,211,396,198)(51,212,386,188)(52,213,387,189)(53,214,388,190)(54,215,389,191)(55,216,390,192)(56,164,368,247)(57,165,369,248)(58,155,370,249)(59,156,371,250)(60,157,372,251)(61,158,373,252)(62,159,374,253)(63,160,364,243)(64,161,365,244)(65,162,366,245)(66,163,367,246)(67,293,378,169)(68,294,379,170)(69,295,380,171)(70,296,381,172)(71,297,382,173)(72,287,383,174)(73,288,384,175)(74,289,385,176)(75,290,375,166)(76,291,376,167)(77,292,377,168)(78,149,335,305)(79,150,336,306)(80,151,337,307)(81,152,338,308)(82,153,339,298)(83,154,340,299)(84,144,341,300)(85,145,331,301)(86,146,332,302)(87,147,333,303)(88,148,334,304)(89,286,184,345)(90,276,185,346)(91,277,186,347)(92,278,187,348)(93,279,177,349)(94,280,178,350)(95,281,179,351)(96,282,180,352)(97,283,181,342)(98,284,182,343)(99,285,183,344)(100,225,357,112)(101,226,358,113)(102,227,359,114)(103,228,360,115)(104,229,361,116)(105,230,362,117)(106,231,363,118)(107,221,353,119)(108,222,354,120)(109,223,355,121)(110,224,356,111)(122,319,234,133)(123,309,235,134)(124,310,236,135)(125,311,237,136)(126,312,238,137)(127,313,239,138)(128,314,240,139)(129,315,241,140)(130,316,242,141)(131,317,232,142)(132,318,233,143)>;
G:=Group( (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), (1,365,200)(2,366,201)(3,367,202)(4,368,203)(5,369,204)(6,370,205)(7,371,206)(8,372,207)(9,373,208)(10,374,209)(11,364,199)(12,159,271)(13,160,272)(14,161,273)(15,162,274)(16,163,275)(17,164,265)(18,165,266)(19,155,267)(20,156,268)(21,157,269)(22,158,270)(23,255,63)(24,256,64)(25,257,65)(26,258,66)(27,259,56)(28,260,57)(29,261,58)(30,262,59)(31,263,60)(32,264,61)(33,254,62)(34,324,244)(35,325,245)(36,326,246)(37,327,247)(38,328,248)(39,329,249)(40,330,250)(41,320,251)(42,321,252)(43,322,253)(44,323,243)(45,353,98)(46,354,99)(47,355,89)(48,356,90)(49,357,91)(50,358,92)(51,359,93)(52,360,94)(53,361,95)(54,362,96)(55,363,97)(67,242,147)(68,232,148)(69,233,149)(70,234,150)(71,235,151)(72,236,152)(73,237,153)(74,238,154)(75,239,144)(76,240,145)(77,241,146)(78,318,171)(79,319,172)(80,309,173)(81,310,174)(82,311,175)(83,312,176)(84,313,166)(85,314,167)(86,315,168)(87,316,169)(88,317,170)(100,186,395)(101,187,396)(102,177,386)(103,178,387)(104,179,388)(105,180,389)(106,181,390)(107,182,391)(108,183,392)(109,184,393)(110,185,394)(111,220,276)(112,210,277)(113,211,278)(114,212,279)(115,213,280)(116,214,281)(117,215,282)(118,216,283)(119,217,284)(120,218,285)(121,219,286)(122,306,381)(123,307,382)(124,308,383)(125,298,384)(126,299,385)(127,300,375)(128,301,376)(129,302,377)(130,303,378)(131,304,379)(132,305,380)(133,296,336)(134,297,337)(135,287,338)(136,288,339)(137,289,340)(138,290,341)(139,291,331)(140,292,332)(141,293,333)(142,294,334)(143,295,335)(188,349,227)(189,350,228)(190,351,229)(191,352,230)(192,342,231)(193,343,221)(194,344,222)(195,345,223)(196,346,224)(197,347,225)(198,348,226), (1,191,80,256,215,337)(2,192,81,257,216,338)(3,193,82,258,217,339)(4,194,83,259,218,340)(5,195,84,260,219,341)(6,196,85,261,220,331)(7,197,86,262,210,332)(8,198,87,263,211,333)(9,188,88,264,212,334)(10,189,78,254,213,335)(11,190,79,255,214,336)(12,69,360,322,380,103)(13,70,361,323,381,104)(14,71,362,324,382,105)(15,72,363,325,383,106)(16,73,353,326,384,107)(17,74,354,327,385,108)(18,75,355,328,375,109)(19,76,356,329,376,110)(20,77,357,330,377,100)(21,67,358,320,378,101)(22,68,359,321,379,102)(23,116,296,199,229,172)(24,117,297,200,230,173)(25,118,287,201,231,174)(26,119,288,202,221,175)(27,120,289,203,222,176)(28,121,290,204,223,166)(29,111,291,205,224,167)(30,112,292,206,225,168)(31,113,293,207,226,169)(32,114,294,208,227,170)(33,115,295,209,228,171)(34,307,389,273,151,54)(35,308,390,274,152,55)(36,298,391,275,153,45)(37,299,392,265,154,46)(38,300,393,266,144,47)(39,301,394,267,145,48)(40,302,395,268,146,49)(41,303,396,269,147,50)(42,304,386,270,148,51)(43,305,387,271,149,52)(44,306,388,272,150,53)(56,285,137,368,344,312)(57,286,138,369,345,313)(58,276,139,370,346,314)(59,277,140,371,347,315)(60,278,141,372,348,316)(61,279,142,373,349,317)(62,280,143,374,350,318)(63,281,133,364,351,319)(64,282,134,365,352,309)(65,283,135,366,342,310)(66,284,136,367,343,311)(89,248,127,184,165,239)(90,249,128,185,155,240)(91,250,129,186,156,241)(92,251,130,187,157,242)(93,252,131,177,158,232)(94,253,132,178,159,233)(95,243,122,179,160,234)(96,244,123,180,161,235)(97,245,124,181,162,236)(98,246,125,182,163,237)(99,247,126,183,164,238), (1,34,256,273)(2,35,257,274)(3,36,258,275)(4,37,259,265)(5,38,260,266)(6,39,261,267)(7,40,262,268)(8,41,263,269)(9,42,264,270)(10,43,254,271)(11,44,255,272)(12,209,322,33)(13,199,323,23)(14,200,324,24)(15,201,325,25)(16,202,326,26)(17,203,327,27)(18,204,328,28)(19,205,329,29)(20,206,330,30)(21,207,320,31)(22,208,321,32)(45,217,391,193)(46,218,392,194)(47,219,393,195)(48,220,394,196)(49,210,395,197)(50,211,396,198)(51,212,386,188)(52,213,387,189)(53,214,388,190)(54,215,389,191)(55,216,390,192)(56,164,368,247)(57,165,369,248)(58,155,370,249)(59,156,371,250)(60,157,372,251)(61,158,373,252)(62,159,374,253)(63,160,364,243)(64,161,365,244)(65,162,366,245)(66,163,367,246)(67,293,378,169)(68,294,379,170)(69,295,380,171)(70,296,381,172)(71,297,382,173)(72,287,383,174)(73,288,384,175)(74,289,385,176)(75,290,375,166)(76,291,376,167)(77,292,377,168)(78,149,335,305)(79,150,336,306)(80,151,337,307)(81,152,338,308)(82,153,339,298)(83,154,340,299)(84,144,341,300)(85,145,331,301)(86,146,332,302)(87,147,333,303)(88,148,334,304)(89,286,184,345)(90,276,185,346)(91,277,186,347)(92,278,187,348)(93,279,177,349)(94,280,178,350)(95,281,179,351)(96,282,180,352)(97,283,181,342)(98,284,182,343)(99,285,183,344)(100,225,357,112)(101,226,358,113)(102,227,359,114)(103,228,360,115)(104,229,361,116)(105,230,362,117)(106,231,363,118)(107,221,353,119)(108,222,354,120)(109,223,355,121)(110,224,356,111)(122,319,234,133)(123,309,235,134)(124,310,236,135)(125,311,237,136)(126,312,238,137)(127,313,239,138)(128,314,240,139)(129,315,241,140)(130,316,242,141)(131,317,232,142)(132,318,233,143) );
G=PermutationGroup([[(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)], [(1,365,200),(2,366,201),(3,367,202),(4,368,203),(5,369,204),(6,370,205),(7,371,206),(8,372,207),(9,373,208),(10,374,209),(11,364,199),(12,159,271),(13,160,272),(14,161,273),(15,162,274),(16,163,275),(17,164,265),(18,165,266),(19,155,267),(20,156,268),(21,157,269),(22,158,270),(23,255,63),(24,256,64),(25,257,65),(26,258,66),(27,259,56),(28,260,57),(29,261,58),(30,262,59),(31,263,60),(32,264,61),(33,254,62),(34,324,244),(35,325,245),(36,326,246),(37,327,247),(38,328,248),(39,329,249),(40,330,250),(41,320,251),(42,321,252),(43,322,253),(44,323,243),(45,353,98),(46,354,99),(47,355,89),(48,356,90),(49,357,91),(50,358,92),(51,359,93),(52,360,94),(53,361,95),(54,362,96),(55,363,97),(67,242,147),(68,232,148),(69,233,149),(70,234,150),(71,235,151),(72,236,152),(73,237,153),(74,238,154),(75,239,144),(76,240,145),(77,241,146),(78,318,171),(79,319,172),(80,309,173),(81,310,174),(82,311,175),(83,312,176),(84,313,166),(85,314,167),(86,315,168),(87,316,169),(88,317,170),(100,186,395),(101,187,396),(102,177,386),(103,178,387),(104,179,388),(105,180,389),(106,181,390),(107,182,391),(108,183,392),(109,184,393),(110,185,394),(111,220,276),(112,210,277),(113,211,278),(114,212,279),(115,213,280),(116,214,281),(117,215,282),(118,216,283),(119,217,284),(120,218,285),(121,219,286),(122,306,381),(123,307,382),(124,308,383),(125,298,384),(126,299,385),(127,300,375),(128,301,376),(129,302,377),(130,303,378),(131,304,379),(132,305,380),(133,296,336),(134,297,337),(135,287,338),(136,288,339),(137,289,340),(138,290,341),(139,291,331),(140,292,332),(141,293,333),(142,294,334),(143,295,335),(188,349,227),(189,350,228),(190,351,229),(191,352,230),(192,342,231),(193,343,221),(194,344,222),(195,345,223),(196,346,224),(197,347,225),(198,348,226)], [(1,191,80,256,215,337),(2,192,81,257,216,338),(3,193,82,258,217,339),(4,194,83,259,218,340),(5,195,84,260,219,341),(6,196,85,261,220,331),(7,197,86,262,210,332),(8,198,87,263,211,333),(9,188,88,264,212,334),(10,189,78,254,213,335),(11,190,79,255,214,336),(12,69,360,322,380,103),(13,70,361,323,381,104),(14,71,362,324,382,105),(15,72,363,325,383,106),(16,73,353,326,384,107),(17,74,354,327,385,108),(18,75,355,328,375,109),(19,76,356,329,376,110),(20,77,357,330,377,100),(21,67,358,320,378,101),(22,68,359,321,379,102),(23,116,296,199,229,172),(24,117,297,200,230,173),(25,118,287,201,231,174),(26,119,288,202,221,175),(27,120,289,203,222,176),(28,121,290,204,223,166),(29,111,291,205,224,167),(30,112,292,206,225,168),(31,113,293,207,226,169),(32,114,294,208,227,170),(33,115,295,209,228,171),(34,307,389,273,151,54),(35,308,390,274,152,55),(36,298,391,275,153,45),(37,299,392,265,154,46),(38,300,393,266,144,47),(39,301,394,267,145,48),(40,302,395,268,146,49),(41,303,396,269,147,50),(42,304,386,270,148,51),(43,305,387,271,149,52),(44,306,388,272,150,53),(56,285,137,368,344,312),(57,286,138,369,345,313),(58,276,139,370,346,314),(59,277,140,371,347,315),(60,278,141,372,348,316),(61,279,142,373,349,317),(62,280,143,374,350,318),(63,281,133,364,351,319),(64,282,134,365,352,309),(65,283,135,366,342,310),(66,284,136,367,343,311),(89,248,127,184,165,239),(90,249,128,185,155,240),(91,250,129,186,156,241),(92,251,130,187,157,242),(93,252,131,177,158,232),(94,253,132,178,159,233),(95,243,122,179,160,234),(96,244,123,180,161,235),(97,245,124,181,162,236),(98,246,125,182,163,237),(99,247,126,183,164,238)], [(1,34,256,273),(2,35,257,274),(3,36,258,275),(4,37,259,265),(5,38,260,266),(6,39,261,267),(7,40,262,268),(8,41,263,269),(9,42,264,270),(10,43,254,271),(11,44,255,272),(12,209,322,33),(13,199,323,23),(14,200,324,24),(15,201,325,25),(16,202,326,26),(17,203,327,27),(18,204,328,28),(19,205,329,29),(20,206,330,30),(21,207,320,31),(22,208,321,32),(45,217,391,193),(46,218,392,194),(47,219,393,195),(48,220,394,196),(49,210,395,197),(50,211,396,198),(51,212,386,188),(52,213,387,189),(53,214,388,190),(54,215,389,191),(55,216,390,192),(56,164,368,247),(57,165,369,248),(58,155,370,249),(59,156,371,250),(60,157,372,251),(61,158,373,252),(62,159,374,253),(63,160,364,243),(64,161,365,244),(65,162,366,245),(66,163,367,246),(67,293,378,169),(68,294,379,170),(69,295,380,171),(70,296,381,172),(71,297,382,173),(72,287,383,174),(73,288,384,175),(74,289,385,176),(75,290,375,166),(76,291,376,167),(77,292,377,168),(78,149,335,305),(79,150,336,306),(80,151,337,307),(81,152,338,308),(82,153,339,298),(83,154,340,299),(84,144,341,300),(85,145,331,301),(86,146,332,302),(87,147,333,303),(88,148,334,304),(89,286,184,345),(90,276,185,346),(91,277,186,347),(92,278,187,348),(93,279,177,349),(94,280,178,350),(95,281,179,351),(96,282,180,352),(97,283,181,342),(98,284,182,343),(99,285,183,344),(100,225,357,112),(101,226,358,113),(102,227,359,114),(103,228,360,115),(104,229,361,116),(105,230,362,117),(106,231,363,118),(107,221,353,119),(108,222,354,120),(109,223,355,121),(110,224,356,111),(122,319,234,133),(123,309,235,134),(124,310,236,135),(125,311,237,136),(126,312,238,137),(127,313,239,138),(128,314,240,139),(129,315,241,140),(130,316,242,141),(131,317,232,142),(132,318,233,143)]])
132 conjugacy classes
| class | 1 | 2 | 3A | 3B | 3C | 3D | 4A | 4B | 6A | 6B | 6C | 6D | 11A | ··· | 11J | 22A | ··· | 22J | 33A | ··· | 33AN | 44A | ··· | 44T | 66A | ··· | 66AN |
| order | 1 | 2 | 3 | 3 | 3 | 3 | 4 | 4 | 6 | 6 | 6 | 6 | 11 | ··· | 11 | 22 | ··· | 22 | 33 | ··· | 33 | 44 | ··· | 44 | 66 | ··· | 66 |
| size | 1 | 1 | 2 | 2 | 2 | 2 | 9 | 9 | 2 | 2 | 2 | 2 | 1 | ··· | 1 | 1 | ··· | 1 | 2 | ··· | 2 | 9 | ··· | 9 | 2 | ··· | 2 |
132 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 |
| type | + | + | + | - | ||||||
| image | C1 | C2 | C4 | C11 | C22 | C44 | S3 | Dic3 | S3×C11 | C11×Dic3 |
| kernel | C11×C3⋊Dic3 | C3×C66 | C3×C33 | C3⋊Dic3 | C3×C6 | C32 | C66 | C33 | C6 | C3 |
| # reps | 1 | 1 | 2 | 10 | 10 | 20 | 4 | 4 | 40 | 40 |
Matrix representation of C11×C3⋊Dic3 ►in GL4(𝔽397) generated by
| 393 | 0 | 0 | 0 |
| 0 | 393 | 0 | 0 |
| 0 | 0 | 393 | 0 |
| 0 | 0 | 0 | 393 |
| 0 | 1 | 0 | 0 |
| 396 | 396 | 0 | 0 |
| 0 | 0 | 0 | 1 |
| 0 | 0 | 396 | 396 |
| 0 | 396 | 0 | 0 |
| 1 | 1 | 0 | 0 |
| 0 | 0 | 396 | 396 |
| 0 | 0 | 1 | 0 |
| 86 | 219 | 0 | 0 |
| 133 | 311 | 0 | 0 |
| 0 | 0 | 139 | 278 |
| 0 | 0 | 139 | 258 |
G:=sub<GL(4,GF(397))| [393,0,0,0,0,393,0,0,0,0,393,0,0,0,0,393],[0,396,0,0,1,396,0,0,0,0,0,396,0,0,1,396],[0,1,0,0,396,1,0,0,0,0,396,1,0,0,396,0],[86,133,0,0,219,311,0,0,0,0,139,139,0,0,278,258] >;
C11×C3⋊Dic3 in GAP, Magma, Sage, TeX
C_{11}\times C_3\rtimes {\rm Dic}_3 % in TeX
G:=Group("C11xC3:Dic3"); // GroupNames label
G:=SmallGroup(396,14);
// by ID
G=gap.SmallGroup(396,14);
# by ID
G:=PCGroup([5,-2,-11,-2,-3,-3,110,1763,6604]);
// Polycyclic
G:=Group<a,b,c,d|a^11=b^3=c^6=1,d^2=c^3,a*b=b*a,a*c=c*a,a*d=d*a,b*c=c*b,d*b*d^-1=b^-1,d*c*d^-1=c^-1>;
// generators/relations
Export