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G = C9×Dic11order 396 = 22·32·11

Direct product of C9 and Dic11

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

Aliases: C9×Dic11, C11⋊C36, C992C4, C33.C12, C22.C18, C66.2C6, C198.2C2, C18.2D11, C2.(C9×D11), C6.2(C3×D11), C3.(C3×Dic11), (C3×Dic11).C3, SmallGroup(396,2)

Series: Derived Chief Lower central Upper central

C1C11 — C9×Dic11
C1C11C33C66C198 — C9×Dic11
C11 — C9×Dic11
C1C18

Generators and relations for C9×Dic11
 G = < a,b,c | a9=b22=1, c2=b11, ab=ba, ac=ca, cbc-1=b-1 >

11C4
11C12
11C36

Smallest permutation representation of C9×Dic11
Regular action on 396 points
Generators in S396
(1 126 140 328 58 371 332 230 246)(2 127 141 329 59 372 333 231 247)(3 128 142 330 60 373 334 232 248)(4 129 143 309 61 374 335 233 249)(5 130 144 310 62 353 336 234 250)(6 131 145 311 63 354 337 235 251)(7 132 146 312 64 355 338 236 252)(8 111 147 313 65 356 339 237 253)(9 112 148 314 66 357 340 238 254)(10 113 149 315 45 358 341 239 255)(11 114 150 316 46 359 342 240 256)(12 115 151 317 47 360 343 241 257)(13 116 152 318 48 361 344 242 258)(14 117 153 319 49 362 345 221 259)(15 118 154 320 50 363 346 222 260)(16 119 133 321 51 364 347 223 261)(17 120 134 322 52 365 348 224 262)(18 121 135 323 53 366 349 225 263)(19 122 136 324 54 367 350 226 264)(20 123 137 325 55 368 351 227 243)(21 124 138 326 56 369 352 228 244)(22 125 139 327 57 370 331 229 245)(23 103 306 191 381 272 206 71 165)(24 104 307 192 382 273 207 72 166)(25 105 308 193 383 274 208 73 167)(26 106 287 194 384 275 209 74 168)(27 107 288 195 385 276 210 75 169)(28 108 289 196 386 277 211 76 170)(29 109 290 197 387 278 212 77 171)(30 110 291 198 388 279 213 78 172)(31 89 292 177 389 280 214 79 173)(32 90 293 178 390 281 215 80 174)(33 91 294 179 391 282 216 81 175)(34 92 295 180 392 283 217 82 176)(35 93 296 181 393 284 218 83 155)(36 94 297 182 394 285 219 84 156)(37 95 298 183 395 286 220 85 157)(38 96 299 184 396 265 199 86 158)(39 97 300 185 375 266 200 87 159)(40 98 301 186 376 267 201 88 160)(41 99 302 187 377 268 202 67 161)(42 100 303 188 378 269 203 68 162)(43 101 304 189 379 270 204 69 163)(44 102 305 190 380 271 205 70 164)
(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)
(1 204 12 215)(2 203 13 214)(3 202 14 213)(4 201 15 212)(5 200 16 211)(6 199 17 210)(7 220 18 209)(8 219 19 208)(9 218 20 207)(10 217 21 206)(11 216 22 205)(23 315 34 326)(24 314 35 325)(25 313 36 324)(26 312 37 323)(27 311 38 322)(28 310 39 321)(29 309 40 320)(30 330 41 319)(31 329 42 318)(32 328 43 317)(33 327 44 316)(45 92 56 103)(46 91 57 102)(47 90 58 101)(48 89 59 100)(49 110 60 99)(50 109 61 98)(51 108 62 97)(52 107 63 96)(53 106 64 95)(54 105 65 94)(55 104 66 93)(67 117 78 128)(68 116 79 127)(69 115 80 126)(70 114 81 125)(71 113 82 124)(72 112 83 123)(73 111 84 122)(74 132 85 121)(75 131 86 120)(76 130 87 119)(77 129 88 118)(133 170 144 159)(134 169 145 158)(135 168 146 157)(136 167 147 156)(137 166 148 155)(138 165 149 176)(139 164 150 175)(140 163 151 174)(141 162 152 173)(142 161 153 172)(143 160 154 171)(177 333 188 344)(178 332 189 343)(179 331 190 342)(180 352 191 341)(181 351 192 340)(182 350 193 339)(183 349 194 338)(184 348 195 337)(185 347 196 336)(186 346 197 335)(187 345 198 334)(221 388 232 377)(222 387 233 376)(223 386 234 375)(224 385 235 396)(225 384 236 395)(226 383 237 394)(227 382 238 393)(228 381 239 392)(229 380 240 391)(230 379 241 390)(231 378 242 389)(243 273 254 284)(244 272 255 283)(245 271 256 282)(246 270 257 281)(247 269 258 280)(248 268 259 279)(249 267 260 278)(250 266 261 277)(251 265 262 276)(252 286 263 275)(253 285 264 274)(287 355 298 366)(288 354 299 365)(289 353 300 364)(290 374 301 363)(291 373 302 362)(292 372 303 361)(293 371 304 360)(294 370 305 359)(295 369 306 358)(296 368 307 357)(297 367 308 356)

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

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

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

126 conjugacy classes

class 1  2 3A3B4A4B6A6B9A···9F11A···11E12A12B12C12D18A···18F22A···22E33A···33J36A···36L66A···66J99A···99AD198A···198AD
order123344669···911···111212121218···1822···2233···3336···3666···6699···99198···198
size11111111111···12···2111111111···12···22···211···112···22···22···2

126 irreducible representations

dim111111111222222
type+++-
imageC1C2C3C4C6C9C12C18C36D11Dic11C3×D11C3×Dic11C9×D11C9×Dic11
kernelC9×Dic11C198C3×Dic11C99C66Dic11C33C22C11C18C9C6C3C2C1
# reps11222646125510103030

Matrix representation of C9×Dic11 in GL2(𝔽397) generated by

2860
0286
,
1396
151247
,
17190
291380
G:=sub<GL(2,GF(397))| [286,0,0,286],[1,151,396,247],[17,291,190,380] >;

C9×Dic11 in GAP, Magma, Sage, TeX

C_9\times {\rm Dic}_{11}
% in TeX

G:=Group("C9xDic11");
// GroupNames label

G:=SmallGroup(396,2);
// by ID

G=gap.SmallGroup(396,2);
# by ID

G:=PCGroup([5,-2,-3,-2,-3,-11,30,66,9004]);
// Polycyclic

G:=Group<a,b,c|a^9=b^22=1,c^2=b^11,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations

Export

Subgroup lattice of C9×Dic11 in TeX

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