direct product, metacyclic, supersoluble, monomial, Z-group, 2-hyperelementary
Aliases: C11×Dic9, C9⋊C44, C99⋊3C4, C18.C22, C66.5S3, C22.2D9, C198.3C2, C33.2Dic3, C2.(C11×D9), C6.1(S3×C11), C3.(C11×Dic3), SmallGroup(396,1)
Series: Derived ►Chief ►Lower central ►Upper central
| C9 — C11×Dic9 |
Generators and relations for C11×Dic9
G = < a,b,c | a11=b18=1, c2=b9, ab=ba, ac=ca, cbc-1=b-1 >
Smallest permutation representation of C11×Dic9
►Regular action on 396 points
Generators in S396
(1 184 170 159 130 123 105 76 58 44 26)(2 185 171 160 131 124 106 77 59 45 27)(3 186 172 161 132 125 107 78 60 46 28)(4 187 173 162 133 126 108 79 61 47 29)(5 188 174 145 134 109 91 80 62 48 30)(6 189 175 146 135 110 92 81 63 49 31)(7 190 176 147 136 111 93 82 64 50 32)(8 191 177 148 137 112 94 83 65 51 33)(9 192 178 149 138 113 95 84 66 52 34)(10 193 179 150 139 114 96 85 67 53 35)(11 194 180 151 140 115 97 86 68 54 36)(12 195 163 152 141 116 98 87 69 37 19)(13 196 164 153 142 117 99 88 70 38 20)(14 197 165 154 143 118 100 89 71 39 21)(15 198 166 155 144 119 101 90 72 40 22)(16 181 167 156 127 120 102 73 55 41 23)(17 182 168 157 128 121 103 74 56 42 24)(18 183 169 158 129 122 104 75 57 43 25)(199 396 368 356 341 320 295 277 264 252 224)(200 379 369 357 342 321 296 278 265 235 225)(201 380 370 358 325 322 297 279 266 236 226)(202 381 371 359 326 323 298 280 267 237 227)(203 382 372 360 327 324 299 281 268 238 228)(204 383 373 343 328 307 300 282 269 239 229)(205 384 374 344 329 308 301 283 270 240 230)(206 385 375 345 330 309 302 284 253 241 231)(207 386 376 346 331 310 303 285 254 242 232)(208 387 377 347 332 311 304 286 255 243 233)(209 388 378 348 333 312 305 287 256 244 234)(210 389 361 349 334 313 306 288 257 245 217)(211 390 362 350 335 314 289 271 258 246 218)(212 391 363 351 336 315 290 272 259 247 219)(213 392 364 352 337 316 291 273 260 248 220)(214 393 365 353 338 317 292 274 261 249 221)(215 394 366 354 339 318 293 275 262 250 222)(216 395 367 355 340 319 294 276 263 251 223)
(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)
(1 208 10 199)(2 207 11 216)(3 206 12 215)(4 205 13 214)(5 204 14 213)(6 203 15 212)(7 202 16 211)(8 201 17 210)(9 200 18 209)(19 222 28 231)(20 221 29 230)(21 220 30 229)(22 219 31 228)(23 218 32 227)(24 217 33 226)(25 234 34 225)(26 233 35 224)(27 232 36 223)(37 250 46 241)(38 249 47 240)(39 248 48 239)(40 247 49 238)(41 246 50 237)(42 245 51 236)(43 244 52 235)(44 243 53 252)(45 242 54 251)(55 258 64 267)(56 257 65 266)(57 256 66 265)(58 255 67 264)(59 254 68 263)(60 253 69 262)(61 270 70 261)(62 269 71 260)(63 268 72 259)(73 271 82 280)(74 288 83 279)(75 287 84 278)(76 286 85 277)(77 285 86 276)(78 284 87 275)(79 283 88 274)(80 282 89 273)(81 281 90 272)(91 300 100 291)(92 299 101 290)(93 298 102 289)(94 297 103 306)(95 296 104 305)(96 295 105 304)(97 294 106 303)(98 293 107 302)(99 292 108 301)(109 307 118 316)(110 324 119 315)(111 323 120 314)(112 322 121 313)(113 321 122 312)(114 320 123 311)(115 319 124 310)(116 318 125 309)(117 317 126 308)(127 335 136 326)(128 334 137 325)(129 333 138 342)(130 332 139 341)(131 331 140 340)(132 330 141 339)(133 329 142 338)(134 328 143 337)(135 327 144 336)(145 343 154 352)(146 360 155 351)(147 359 156 350)(148 358 157 349)(149 357 158 348)(150 356 159 347)(151 355 160 346)(152 354 161 345)(153 353 162 344)(163 366 172 375)(164 365 173 374)(165 364 174 373)(166 363 175 372)(167 362 176 371)(168 361 177 370)(169 378 178 369)(170 377 179 368)(171 376 180 367)(181 390 190 381)(182 389 191 380)(183 388 192 379)(184 387 193 396)(185 386 194 395)(186 385 195 394)(187 384 196 393)(188 383 197 392)(189 382 198 391)
G:=sub<Sym(396)| (1,184,170,159,130,123,105,76,58,44,26)(2,185,171,160,131,124,106,77,59,45,27)(3,186,172,161,132,125,107,78,60,46,28)(4,187,173,162,133,126,108,79,61,47,29)(5,188,174,145,134,109,91,80,62,48,30)(6,189,175,146,135,110,92,81,63,49,31)(7,190,176,147,136,111,93,82,64,50,32)(8,191,177,148,137,112,94,83,65,51,33)(9,192,178,149,138,113,95,84,66,52,34)(10,193,179,150,139,114,96,85,67,53,35)(11,194,180,151,140,115,97,86,68,54,36)(12,195,163,152,141,116,98,87,69,37,19)(13,196,164,153,142,117,99,88,70,38,20)(14,197,165,154,143,118,100,89,71,39,21)(15,198,166,155,144,119,101,90,72,40,22)(16,181,167,156,127,120,102,73,55,41,23)(17,182,168,157,128,121,103,74,56,42,24)(18,183,169,158,129,122,104,75,57,43,25)(199,396,368,356,341,320,295,277,264,252,224)(200,379,369,357,342,321,296,278,265,235,225)(201,380,370,358,325,322,297,279,266,236,226)(202,381,371,359,326,323,298,280,267,237,227)(203,382,372,360,327,324,299,281,268,238,228)(204,383,373,343,328,307,300,282,269,239,229)(205,384,374,344,329,308,301,283,270,240,230)(206,385,375,345,330,309,302,284,253,241,231)(207,386,376,346,331,310,303,285,254,242,232)(208,387,377,347,332,311,304,286,255,243,233)(209,388,378,348,333,312,305,287,256,244,234)(210,389,361,349,334,313,306,288,257,245,217)(211,390,362,350,335,314,289,271,258,246,218)(212,391,363,351,336,315,290,272,259,247,219)(213,392,364,352,337,316,291,273,260,248,220)(214,393,365,353,338,317,292,274,261,249,221)(215,394,366,354,339,318,293,275,262,250,222)(216,395,367,355,340,319,294,276,263,251,223), (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), (1,208,10,199)(2,207,11,216)(3,206,12,215)(4,205,13,214)(5,204,14,213)(6,203,15,212)(7,202,16,211)(8,201,17,210)(9,200,18,209)(19,222,28,231)(20,221,29,230)(21,220,30,229)(22,219,31,228)(23,218,32,227)(24,217,33,226)(25,234,34,225)(26,233,35,224)(27,232,36,223)(37,250,46,241)(38,249,47,240)(39,248,48,239)(40,247,49,238)(41,246,50,237)(42,245,51,236)(43,244,52,235)(44,243,53,252)(45,242,54,251)(55,258,64,267)(56,257,65,266)(57,256,66,265)(58,255,67,264)(59,254,68,263)(60,253,69,262)(61,270,70,261)(62,269,71,260)(63,268,72,259)(73,271,82,280)(74,288,83,279)(75,287,84,278)(76,286,85,277)(77,285,86,276)(78,284,87,275)(79,283,88,274)(80,282,89,273)(81,281,90,272)(91,300,100,291)(92,299,101,290)(93,298,102,289)(94,297,103,306)(95,296,104,305)(96,295,105,304)(97,294,106,303)(98,293,107,302)(99,292,108,301)(109,307,118,316)(110,324,119,315)(111,323,120,314)(112,322,121,313)(113,321,122,312)(114,320,123,311)(115,319,124,310)(116,318,125,309)(117,317,126,308)(127,335,136,326)(128,334,137,325)(129,333,138,342)(130,332,139,341)(131,331,140,340)(132,330,141,339)(133,329,142,338)(134,328,143,337)(135,327,144,336)(145,343,154,352)(146,360,155,351)(147,359,156,350)(148,358,157,349)(149,357,158,348)(150,356,159,347)(151,355,160,346)(152,354,161,345)(153,353,162,344)(163,366,172,375)(164,365,173,374)(165,364,174,373)(166,363,175,372)(167,362,176,371)(168,361,177,370)(169,378,178,369)(170,377,179,368)(171,376,180,367)(181,390,190,381)(182,389,191,380)(183,388,192,379)(184,387,193,396)(185,386,194,395)(186,385,195,394)(187,384,196,393)(188,383,197,392)(189,382,198,391)>;
G:=Group( (1,184,170,159,130,123,105,76,58,44,26)(2,185,171,160,131,124,106,77,59,45,27)(3,186,172,161,132,125,107,78,60,46,28)(4,187,173,162,133,126,108,79,61,47,29)(5,188,174,145,134,109,91,80,62,48,30)(6,189,175,146,135,110,92,81,63,49,31)(7,190,176,147,136,111,93,82,64,50,32)(8,191,177,148,137,112,94,83,65,51,33)(9,192,178,149,138,113,95,84,66,52,34)(10,193,179,150,139,114,96,85,67,53,35)(11,194,180,151,140,115,97,86,68,54,36)(12,195,163,152,141,116,98,87,69,37,19)(13,196,164,153,142,117,99,88,70,38,20)(14,197,165,154,143,118,100,89,71,39,21)(15,198,166,155,144,119,101,90,72,40,22)(16,181,167,156,127,120,102,73,55,41,23)(17,182,168,157,128,121,103,74,56,42,24)(18,183,169,158,129,122,104,75,57,43,25)(199,396,368,356,341,320,295,277,264,252,224)(200,379,369,357,342,321,296,278,265,235,225)(201,380,370,358,325,322,297,279,266,236,226)(202,381,371,359,326,323,298,280,267,237,227)(203,382,372,360,327,324,299,281,268,238,228)(204,383,373,343,328,307,300,282,269,239,229)(205,384,374,344,329,308,301,283,270,240,230)(206,385,375,345,330,309,302,284,253,241,231)(207,386,376,346,331,310,303,285,254,242,232)(208,387,377,347,332,311,304,286,255,243,233)(209,388,378,348,333,312,305,287,256,244,234)(210,389,361,349,334,313,306,288,257,245,217)(211,390,362,350,335,314,289,271,258,246,218)(212,391,363,351,336,315,290,272,259,247,219)(213,392,364,352,337,316,291,273,260,248,220)(214,393,365,353,338,317,292,274,261,249,221)(215,394,366,354,339,318,293,275,262,250,222)(216,395,367,355,340,319,294,276,263,251,223), (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), (1,208,10,199)(2,207,11,216)(3,206,12,215)(4,205,13,214)(5,204,14,213)(6,203,15,212)(7,202,16,211)(8,201,17,210)(9,200,18,209)(19,222,28,231)(20,221,29,230)(21,220,30,229)(22,219,31,228)(23,218,32,227)(24,217,33,226)(25,234,34,225)(26,233,35,224)(27,232,36,223)(37,250,46,241)(38,249,47,240)(39,248,48,239)(40,247,49,238)(41,246,50,237)(42,245,51,236)(43,244,52,235)(44,243,53,252)(45,242,54,251)(55,258,64,267)(56,257,65,266)(57,256,66,265)(58,255,67,264)(59,254,68,263)(60,253,69,262)(61,270,70,261)(62,269,71,260)(63,268,72,259)(73,271,82,280)(74,288,83,279)(75,287,84,278)(76,286,85,277)(77,285,86,276)(78,284,87,275)(79,283,88,274)(80,282,89,273)(81,281,90,272)(91,300,100,291)(92,299,101,290)(93,298,102,289)(94,297,103,306)(95,296,104,305)(96,295,105,304)(97,294,106,303)(98,293,107,302)(99,292,108,301)(109,307,118,316)(110,324,119,315)(111,323,120,314)(112,322,121,313)(113,321,122,312)(114,320,123,311)(115,319,124,310)(116,318,125,309)(117,317,126,308)(127,335,136,326)(128,334,137,325)(129,333,138,342)(130,332,139,341)(131,331,140,340)(132,330,141,339)(133,329,142,338)(134,328,143,337)(135,327,144,336)(145,343,154,352)(146,360,155,351)(147,359,156,350)(148,358,157,349)(149,357,158,348)(150,356,159,347)(151,355,160,346)(152,354,161,345)(153,353,162,344)(163,366,172,375)(164,365,173,374)(165,364,174,373)(166,363,175,372)(167,362,176,371)(168,361,177,370)(169,378,178,369)(170,377,179,368)(171,376,180,367)(181,390,190,381)(182,389,191,380)(183,388,192,379)(184,387,193,396)(185,386,194,395)(186,385,195,394)(187,384,196,393)(188,383,197,392)(189,382,198,391) );
G=PermutationGroup([[(1,184,170,159,130,123,105,76,58,44,26),(2,185,171,160,131,124,106,77,59,45,27),(3,186,172,161,132,125,107,78,60,46,28),(4,187,173,162,133,126,108,79,61,47,29),(5,188,174,145,134,109,91,80,62,48,30),(6,189,175,146,135,110,92,81,63,49,31),(7,190,176,147,136,111,93,82,64,50,32),(8,191,177,148,137,112,94,83,65,51,33),(9,192,178,149,138,113,95,84,66,52,34),(10,193,179,150,139,114,96,85,67,53,35),(11,194,180,151,140,115,97,86,68,54,36),(12,195,163,152,141,116,98,87,69,37,19),(13,196,164,153,142,117,99,88,70,38,20),(14,197,165,154,143,118,100,89,71,39,21),(15,198,166,155,144,119,101,90,72,40,22),(16,181,167,156,127,120,102,73,55,41,23),(17,182,168,157,128,121,103,74,56,42,24),(18,183,169,158,129,122,104,75,57,43,25),(199,396,368,356,341,320,295,277,264,252,224),(200,379,369,357,342,321,296,278,265,235,225),(201,380,370,358,325,322,297,279,266,236,226),(202,381,371,359,326,323,298,280,267,237,227),(203,382,372,360,327,324,299,281,268,238,228),(204,383,373,343,328,307,300,282,269,239,229),(205,384,374,344,329,308,301,283,270,240,230),(206,385,375,345,330,309,302,284,253,241,231),(207,386,376,346,331,310,303,285,254,242,232),(208,387,377,347,332,311,304,286,255,243,233),(209,388,378,348,333,312,305,287,256,244,234),(210,389,361,349,334,313,306,288,257,245,217),(211,390,362,350,335,314,289,271,258,246,218),(212,391,363,351,336,315,290,272,259,247,219),(213,392,364,352,337,316,291,273,260,248,220),(214,393,365,353,338,317,292,274,261,249,221),(215,394,366,354,339,318,293,275,262,250,222),(216,395,367,355,340,319,294,276,263,251,223)], [(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)], [(1,208,10,199),(2,207,11,216),(3,206,12,215),(4,205,13,214),(5,204,14,213),(6,203,15,212),(7,202,16,211),(8,201,17,210),(9,200,18,209),(19,222,28,231),(20,221,29,230),(21,220,30,229),(22,219,31,228),(23,218,32,227),(24,217,33,226),(25,234,34,225),(26,233,35,224),(27,232,36,223),(37,250,46,241),(38,249,47,240),(39,248,48,239),(40,247,49,238),(41,246,50,237),(42,245,51,236),(43,244,52,235),(44,243,53,252),(45,242,54,251),(55,258,64,267),(56,257,65,266),(57,256,66,265),(58,255,67,264),(59,254,68,263),(60,253,69,262),(61,270,70,261),(62,269,71,260),(63,268,72,259),(73,271,82,280),(74,288,83,279),(75,287,84,278),(76,286,85,277),(77,285,86,276),(78,284,87,275),(79,283,88,274),(80,282,89,273),(81,281,90,272),(91,300,100,291),(92,299,101,290),(93,298,102,289),(94,297,103,306),(95,296,104,305),(96,295,105,304),(97,294,106,303),(98,293,107,302),(99,292,108,301),(109,307,118,316),(110,324,119,315),(111,323,120,314),(112,322,121,313),(113,321,122,312),(114,320,123,311),(115,319,124,310),(116,318,125,309),(117,317,126,308),(127,335,136,326),(128,334,137,325),(129,333,138,342),(130,332,139,341),(131,331,140,340),(132,330,141,339),(133,329,142,338),(134,328,143,337),(135,327,144,336),(145,343,154,352),(146,360,155,351),(147,359,156,350),(148,358,157,349),(149,357,158,348),(150,356,159,347),(151,355,160,346),(152,354,161,345),(153,353,162,344),(163,366,172,375),(164,365,173,374),(165,364,174,373),(166,363,175,372),(167,362,176,371),(168,361,177,370),(169,378,178,369),(170,377,179,368),(171,376,180,367),(181,390,190,381),(182,389,191,380),(183,388,192,379),(184,387,193,396),(185,386,194,395),(186,385,195,394),(187,384,196,393),(188,383,197,392),(189,382,198,391)]])
132 conjugacy classes
| class | 1 | 2 | 3 | 4A | 4B | 6 | 9A | 9B | 9C | 11A | ··· | 11J | 18A | 18B | 18C | 22A | ··· | 22J | 33A | ··· | 33J | 44A | ··· | 44T | 66A | ··· | 66J | 99A | ··· | 99AD | 198A | ··· | 198AD |
| order | 1 | 2 | 3 | 4 | 4 | 6 | 9 | 9 | 9 | 11 | ··· | 11 | 18 | 18 | 18 | 22 | ··· | 22 | 33 | ··· | 33 | 44 | ··· | 44 | 66 | ··· | 66 | 99 | ··· | 99 | 198 | ··· | 198 |
| size | 1 | 1 | 2 | 9 | 9 | 2 | 2 | 2 | 2 | 1 | ··· | 1 | 2 | 2 | 2 | 1 | ··· | 1 | 2 | ··· | 2 | 9 | ··· | 9 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
132 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | - | + | - | ||||||||
| image | C1 | C2 | C4 | C11 | C22 | C44 | S3 | Dic3 | D9 | Dic9 | S3×C11 | C11×Dic3 | C11×D9 | C11×Dic9 |
| kernel | C11×Dic9 | C198 | C99 | Dic9 | C18 | C9 | C66 | C33 | C22 | C11 | C6 | C3 | C2 | C1 |
| # reps | 1 | 1 | 2 | 10 | 10 | 20 | 1 | 1 | 3 | 3 | 10 | 10 | 30 | 30 |
Matrix representation of C11×Dic9 ►in GL2(𝔽397) generated by
| 31 | 0 |
| 0 | 31 |
| 318 | 0 |
| 184 | 201 |
| 396 | 33 |
| 24 | 1 |
G:=sub<GL(2,GF(397))| [31,0,0,31],[318,184,0,201],[396,24,33,1] >;
C11×Dic9 in GAP, Magma, Sage, TeX
C_{11}\times {\rm Dic}_9 % in TeX
G:=Group("C11xDic9"); // GroupNames label
G:=SmallGroup(396,1);
// by ID
G=gap.SmallGroup(396,1);
# by ID
G:=PCGroup([5,-2,-11,-2,-3,-3,110,4403,138,6604]);
// Polycyclic
G:=Group<a,b,c|a^11=b^18=1,c^2=b^9,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations
Export