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G = C11×Dic9order 396 = 22·32·11

Direct product of C11 and Dic9

direct product, metacyclic, supersoluble, monomial, Z-group, 2-hyperelementary

Aliases: C11×Dic9, C9⋊C44, C993C4, 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

C1C9 — C11×Dic9
C1C3C9C18C198 — C11×Dic9
C9 — C11×Dic9
C1C22

Generators and relations for C11×Dic9
 G = < a,b,c | a11=b18=1, c2=b9, ab=ba, ac=ca, cbc-1=b-1 >

9C4
3Dic3
9C44
3C11×Dic3

Smallest permutation representation of C11×Dic9
Regular action on 396 points
Generators in S396
(1 195 170 159 134 112 101 76 58 44 22)(2 196 171 160 135 113 102 77 59 45 23)(3 197 172 161 136 114 103 78 60 46 24)(4 198 173 162 137 115 104 79 61 47 25)(5 181 174 145 138 116 105 80 62 48 26)(6 182 175 146 139 117 106 81 63 49 27)(7 183 176 147 140 118 107 82 64 50 28)(8 184 177 148 141 119 108 83 65 51 29)(9 185 178 149 142 120 91 84 66 52 30)(10 186 179 150 143 121 92 85 67 53 31)(11 187 180 151 144 122 93 86 68 54 32)(12 188 163 152 127 123 94 87 69 37 33)(13 189 164 153 128 124 95 88 70 38 34)(14 190 165 154 129 125 96 89 71 39 35)(15 191 166 155 130 126 97 90 72 40 36)(16 192 167 156 131 109 98 73 55 41 19)(17 193 168 157 132 110 99 74 56 42 20)(18 194 169 158 133 111 100 75 57 43 21)(199 390 372 359 330 324 293 284 270 248 221)(200 391 373 360 331 307 294 285 253 249 222)(201 392 374 343 332 308 295 286 254 250 223)(202 393 375 344 333 309 296 287 255 251 224)(203 394 376 345 334 310 297 288 256 252 225)(204 395 377 346 335 311 298 271 257 235 226)(205 396 378 347 336 312 299 272 258 236 227)(206 379 361 348 337 313 300 273 259 237 228)(207 380 362 349 338 314 301 274 260 238 229)(208 381 363 350 339 315 302 275 261 239 230)(209 382 364 351 340 316 303 276 262 240 231)(210 383 365 352 341 317 304 277 263 241 232)(211 384 366 353 342 318 305 278 264 242 233)(212 385 367 354 325 319 306 279 265 243 234)(213 386 368 355 326 320 289 280 266 244 217)(214 387 369 356 327 321 290 281 267 245 218)(215 388 370 357 328 322 291 282 268 246 219)(216 389 371 358 329 323 292 283 269 247 220)
(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)
(1 203 10 212)(2 202 11 211)(3 201 12 210)(4 200 13 209)(5 199 14 208)(6 216 15 207)(7 215 16 206)(8 214 17 205)(9 213 18 204)(19 228 28 219)(20 227 29 218)(21 226 30 217)(22 225 31 234)(23 224 32 233)(24 223 33 232)(25 222 34 231)(26 221 35 230)(27 220 36 229)(37 241 46 250)(38 240 47 249)(39 239 48 248)(40 238 49 247)(41 237 50 246)(42 236 51 245)(43 235 52 244)(44 252 53 243)(45 251 54 242)(55 259 64 268)(56 258 65 267)(57 257 66 266)(58 256 67 265)(59 255 68 264)(60 254 69 263)(61 253 70 262)(62 270 71 261)(63 269 72 260)(73 273 82 282)(74 272 83 281)(75 271 84 280)(76 288 85 279)(77 287 86 278)(78 286 87 277)(79 285 88 276)(80 284 89 275)(81 283 90 274)(91 289 100 298)(92 306 101 297)(93 305 102 296)(94 304 103 295)(95 303 104 294)(96 302 105 293)(97 301 106 292)(98 300 107 291)(99 299 108 290)(109 313 118 322)(110 312 119 321)(111 311 120 320)(112 310 121 319)(113 309 122 318)(114 308 123 317)(115 307 124 316)(116 324 125 315)(117 323 126 314)(127 341 136 332)(128 340 137 331)(129 339 138 330)(130 338 139 329)(131 337 140 328)(132 336 141 327)(133 335 142 326)(134 334 143 325)(135 333 144 342)(145 359 154 350)(146 358 155 349)(147 357 156 348)(148 356 157 347)(149 355 158 346)(150 354 159 345)(151 353 160 344)(152 352 161 343)(153 351 162 360)(163 365 172 374)(164 364 173 373)(165 363 174 372)(166 362 175 371)(167 361 176 370)(168 378 177 369)(169 377 178 368)(170 376 179 367)(171 375 180 366)(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)| (1,195,170,159,134,112,101,76,58,44,22)(2,196,171,160,135,113,102,77,59,45,23)(3,197,172,161,136,114,103,78,60,46,24)(4,198,173,162,137,115,104,79,61,47,25)(5,181,174,145,138,116,105,80,62,48,26)(6,182,175,146,139,117,106,81,63,49,27)(7,183,176,147,140,118,107,82,64,50,28)(8,184,177,148,141,119,108,83,65,51,29)(9,185,178,149,142,120,91,84,66,52,30)(10,186,179,150,143,121,92,85,67,53,31)(11,187,180,151,144,122,93,86,68,54,32)(12,188,163,152,127,123,94,87,69,37,33)(13,189,164,153,128,124,95,88,70,38,34)(14,190,165,154,129,125,96,89,71,39,35)(15,191,166,155,130,126,97,90,72,40,36)(16,192,167,156,131,109,98,73,55,41,19)(17,193,168,157,132,110,99,74,56,42,20)(18,194,169,158,133,111,100,75,57,43,21)(199,390,372,359,330,324,293,284,270,248,221)(200,391,373,360,331,307,294,285,253,249,222)(201,392,374,343,332,308,295,286,254,250,223)(202,393,375,344,333,309,296,287,255,251,224)(203,394,376,345,334,310,297,288,256,252,225)(204,395,377,346,335,311,298,271,257,235,226)(205,396,378,347,336,312,299,272,258,236,227)(206,379,361,348,337,313,300,273,259,237,228)(207,380,362,349,338,314,301,274,260,238,229)(208,381,363,350,339,315,302,275,261,239,230)(209,382,364,351,340,316,303,276,262,240,231)(210,383,365,352,341,317,304,277,263,241,232)(211,384,366,353,342,318,305,278,264,242,233)(212,385,367,354,325,319,306,279,265,243,234)(213,386,368,355,326,320,289,280,266,244,217)(214,387,369,356,327,321,290,281,267,245,218)(215,388,370,357,328,322,291,282,268,246,219)(216,389,371,358,329,323,292,283,269,247,220), (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), (1,203,10,212)(2,202,11,211)(3,201,12,210)(4,200,13,209)(5,199,14,208)(6,216,15,207)(7,215,16,206)(8,214,17,205)(9,213,18,204)(19,228,28,219)(20,227,29,218)(21,226,30,217)(22,225,31,234)(23,224,32,233)(24,223,33,232)(25,222,34,231)(26,221,35,230)(27,220,36,229)(37,241,46,250)(38,240,47,249)(39,239,48,248)(40,238,49,247)(41,237,50,246)(42,236,51,245)(43,235,52,244)(44,252,53,243)(45,251,54,242)(55,259,64,268)(56,258,65,267)(57,257,66,266)(58,256,67,265)(59,255,68,264)(60,254,69,263)(61,253,70,262)(62,270,71,261)(63,269,72,260)(73,273,82,282)(74,272,83,281)(75,271,84,280)(76,288,85,279)(77,287,86,278)(78,286,87,277)(79,285,88,276)(80,284,89,275)(81,283,90,274)(91,289,100,298)(92,306,101,297)(93,305,102,296)(94,304,103,295)(95,303,104,294)(96,302,105,293)(97,301,106,292)(98,300,107,291)(99,299,108,290)(109,313,118,322)(110,312,119,321)(111,311,120,320)(112,310,121,319)(113,309,122,318)(114,308,123,317)(115,307,124,316)(116,324,125,315)(117,323,126,314)(127,341,136,332)(128,340,137,331)(129,339,138,330)(130,338,139,329)(131,337,140,328)(132,336,141,327)(133,335,142,326)(134,334,143,325)(135,333,144,342)(145,359,154,350)(146,358,155,349)(147,357,156,348)(148,356,157,347)(149,355,158,346)(150,354,159,345)(151,353,160,344)(152,352,161,343)(153,351,162,360)(163,365,172,374)(164,364,173,373)(165,363,174,372)(166,362,175,371)(167,361,176,370)(168,378,177,369)(169,377,178,368)(170,376,179,367)(171,375,180,366)(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( (1,195,170,159,134,112,101,76,58,44,22)(2,196,171,160,135,113,102,77,59,45,23)(3,197,172,161,136,114,103,78,60,46,24)(4,198,173,162,137,115,104,79,61,47,25)(5,181,174,145,138,116,105,80,62,48,26)(6,182,175,146,139,117,106,81,63,49,27)(7,183,176,147,140,118,107,82,64,50,28)(8,184,177,148,141,119,108,83,65,51,29)(9,185,178,149,142,120,91,84,66,52,30)(10,186,179,150,143,121,92,85,67,53,31)(11,187,180,151,144,122,93,86,68,54,32)(12,188,163,152,127,123,94,87,69,37,33)(13,189,164,153,128,124,95,88,70,38,34)(14,190,165,154,129,125,96,89,71,39,35)(15,191,166,155,130,126,97,90,72,40,36)(16,192,167,156,131,109,98,73,55,41,19)(17,193,168,157,132,110,99,74,56,42,20)(18,194,169,158,133,111,100,75,57,43,21)(199,390,372,359,330,324,293,284,270,248,221)(200,391,373,360,331,307,294,285,253,249,222)(201,392,374,343,332,308,295,286,254,250,223)(202,393,375,344,333,309,296,287,255,251,224)(203,394,376,345,334,310,297,288,256,252,225)(204,395,377,346,335,311,298,271,257,235,226)(205,396,378,347,336,312,299,272,258,236,227)(206,379,361,348,337,313,300,273,259,237,228)(207,380,362,349,338,314,301,274,260,238,229)(208,381,363,350,339,315,302,275,261,239,230)(209,382,364,351,340,316,303,276,262,240,231)(210,383,365,352,341,317,304,277,263,241,232)(211,384,366,353,342,318,305,278,264,242,233)(212,385,367,354,325,319,306,279,265,243,234)(213,386,368,355,326,320,289,280,266,244,217)(214,387,369,356,327,321,290,281,267,245,218)(215,388,370,357,328,322,291,282,268,246,219)(216,389,371,358,329,323,292,283,269,247,220), (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), (1,203,10,212)(2,202,11,211)(3,201,12,210)(4,200,13,209)(5,199,14,208)(6,216,15,207)(7,215,16,206)(8,214,17,205)(9,213,18,204)(19,228,28,219)(20,227,29,218)(21,226,30,217)(22,225,31,234)(23,224,32,233)(24,223,33,232)(25,222,34,231)(26,221,35,230)(27,220,36,229)(37,241,46,250)(38,240,47,249)(39,239,48,248)(40,238,49,247)(41,237,50,246)(42,236,51,245)(43,235,52,244)(44,252,53,243)(45,251,54,242)(55,259,64,268)(56,258,65,267)(57,257,66,266)(58,256,67,265)(59,255,68,264)(60,254,69,263)(61,253,70,262)(62,270,71,261)(63,269,72,260)(73,273,82,282)(74,272,83,281)(75,271,84,280)(76,288,85,279)(77,287,86,278)(78,286,87,277)(79,285,88,276)(80,284,89,275)(81,283,90,274)(91,289,100,298)(92,306,101,297)(93,305,102,296)(94,304,103,295)(95,303,104,294)(96,302,105,293)(97,301,106,292)(98,300,107,291)(99,299,108,290)(109,313,118,322)(110,312,119,321)(111,311,120,320)(112,310,121,319)(113,309,122,318)(114,308,123,317)(115,307,124,316)(116,324,125,315)(117,323,126,314)(127,341,136,332)(128,340,137,331)(129,339,138,330)(130,338,139,329)(131,337,140,328)(132,336,141,327)(133,335,142,326)(134,334,143,325)(135,333,144,342)(145,359,154,350)(146,358,155,349)(147,357,156,348)(148,356,157,347)(149,355,158,346)(150,354,159,345)(151,353,160,344)(152,352,161,343)(153,351,162,360)(163,365,172,374)(164,364,173,373)(165,363,174,372)(166,362,175,371)(167,361,176,370)(168,378,177,369)(169,377,178,368)(170,376,179,367)(171,375,180,366)(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([(1,195,170,159,134,112,101,76,58,44,22),(2,196,171,160,135,113,102,77,59,45,23),(3,197,172,161,136,114,103,78,60,46,24),(4,198,173,162,137,115,104,79,61,47,25),(5,181,174,145,138,116,105,80,62,48,26),(6,182,175,146,139,117,106,81,63,49,27),(7,183,176,147,140,118,107,82,64,50,28),(8,184,177,148,141,119,108,83,65,51,29),(9,185,178,149,142,120,91,84,66,52,30),(10,186,179,150,143,121,92,85,67,53,31),(11,187,180,151,144,122,93,86,68,54,32),(12,188,163,152,127,123,94,87,69,37,33),(13,189,164,153,128,124,95,88,70,38,34),(14,190,165,154,129,125,96,89,71,39,35),(15,191,166,155,130,126,97,90,72,40,36),(16,192,167,156,131,109,98,73,55,41,19),(17,193,168,157,132,110,99,74,56,42,20),(18,194,169,158,133,111,100,75,57,43,21),(199,390,372,359,330,324,293,284,270,248,221),(200,391,373,360,331,307,294,285,253,249,222),(201,392,374,343,332,308,295,286,254,250,223),(202,393,375,344,333,309,296,287,255,251,224),(203,394,376,345,334,310,297,288,256,252,225),(204,395,377,346,335,311,298,271,257,235,226),(205,396,378,347,336,312,299,272,258,236,227),(206,379,361,348,337,313,300,273,259,237,228),(207,380,362,349,338,314,301,274,260,238,229),(208,381,363,350,339,315,302,275,261,239,230),(209,382,364,351,340,316,303,276,262,240,231),(210,383,365,352,341,317,304,277,263,241,232),(211,384,366,353,342,318,305,278,264,242,233),(212,385,367,354,325,319,306,279,265,243,234),(213,386,368,355,326,320,289,280,266,244,217),(214,387,369,356,327,321,290,281,267,245,218),(215,388,370,357,328,322,291,282,268,246,219),(216,389,371,358,329,323,292,283,269,247,220)], [(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)], [(1,203,10,212),(2,202,11,211),(3,201,12,210),(4,200,13,209),(5,199,14,208),(6,216,15,207),(7,215,16,206),(8,214,17,205),(9,213,18,204),(19,228,28,219),(20,227,29,218),(21,226,30,217),(22,225,31,234),(23,224,32,233),(24,223,33,232),(25,222,34,231),(26,221,35,230),(27,220,36,229),(37,241,46,250),(38,240,47,249),(39,239,48,248),(40,238,49,247),(41,237,50,246),(42,236,51,245),(43,235,52,244),(44,252,53,243),(45,251,54,242),(55,259,64,268),(56,258,65,267),(57,257,66,266),(58,256,67,265),(59,255,68,264),(60,254,69,263),(61,253,70,262),(62,270,71,261),(63,269,72,260),(73,273,82,282),(74,272,83,281),(75,271,84,280),(76,288,85,279),(77,287,86,278),(78,286,87,277),(79,285,88,276),(80,284,89,275),(81,283,90,274),(91,289,100,298),(92,306,101,297),(93,305,102,296),(94,304,103,295),(95,303,104,294),(96,302,105,293),(97,301,106,292),(98,300,107,291),(99,299,108,290),(109,313,118,322),(110,312,119,321),(111,311,120,320),(112,310,121,319),(113,309,122,318),(114,308,123,317),(115,307,124,316),(116,324,125,315),(117,323,126,314),(127,341,136,332),(128,340,137,331),(129,339,138,330),(130,338,139,329),(131,337,140,328),(132,336,141,327),(133,335,142,326),(134,334,143,325),(135,333,144,342),(145,359,154,350),(146,358,155,349),(147,357,156,348),(148,356,157,347),(149,355,158,346),(150,354,159,345),(151,353,160,344),(152,352,161,343),(153,351,162,360),(163,365,172,374),(164,364,173,373),(165,363,174,372),(166,362,175,371),(167,361,176,370),(168,378,177,369),(169,377,178,368),(170,376,179,367),(171,375,180,366),(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 4A4B 6 9A9B9C11A···11J18A18B18C22A···22J33A···33J44A···44T66A···66J99A···99AD198A···198AD
order12344699911···1118181822···2233···3344···4466···6699···99198···198
size1129922221···12221···12···29···92···22···22···2

132 irreducible representations

dim11111122222222
type+++-+-
imageC1C2C4C11C22C44S3Dic3D9Dic9S3×C11C11×Dic3C11×D9C11×Dic9
kernelC11×Dic9C198C99Dic9C18C9C66C33C22C11C6C3C2C1
# reps112101020113310103030

Matrix representation of C11×Dic9 in GL2(𝔽397) generated by

310
031
,
3180
184201
,
39633
241
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

Subgroup lattice of C11×Dic9 in TeX

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