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## G = C32×Dic11order 396 = 22·32·11

### Direct product of C32 and Dic11

Aliases: C32×Dic11, C332C12, C66.4C6, C11⋊(C3×C12), (C3×C33)⋊5C4, C22.(C3×C6), (C3×C66).3C2, C6.4(C3×D11), (C3×C6).3D11, C2.(C32×D11), SmallGroup(396,11)

Series: Derived Chief Lower central Upper central

 Derived series C1 — C11 — C32×Dic11
 Chief series C1 — C11 — C22 — C66 — C3×C66 — C32×Dic11
 Lower central C11 — C32×Dic11
 Upper central C1 — C3×C6

Generators and relations for C32×Dic11
G = < a,b,c,d | a3=b3=c22=1, d2=c11, ab=ba, ac=ca, ad=da, bc=cb, bd=db, dcd-1=c-1 >

Smallest permutation representation of C32×Dic11
Regular action on 396 points
Generators in S396
(1 180 101)(2 181 102)(3 182 103)(4 183 104)(5 184 105)(6 185 106)(7 186 107)(8 187 108)(9 188 109)(10 189 110)(11 190 89)(12 191 90)(13 192 91)(14 193 92)(15 194 93)(16 195 94)(17 196 95)(18 197 96)(19 198 97)(20 177 98)(21 178 99)(22 179 100)(23 141 128)(24 142 129)(25 143 130)(26 144 131)(27 145 132)(28 146 111)(29 147 112)(30 148 113)(31 149 114)(32 150 115)(33 151 116)(34 152 117)(35 153 118)(36 154 119)(37 133 120)(38 134 121)(39 135 122)(40 136 123)(41 137 124)(42 138 125)(43 139 126)(44 140 127)(45 159 79)(46 160 80)(47 161 81)(48 162 82)(49 163 83)(50 164 84)(51 165 85)(52 166 86)(53 167 87)(54 168 88)(55 169 67)(56 170 68)(57 171 69)(58 172 70)(59 173 71)(60 174 72)(61 175 73)(62 176 74)(63 155 75)(64 156 76)(65 157 77)(66 158 78)(199 386 287)(200 387 288)(201 388 289)(202 389 290)(203 390 291)(204 391 292)(205 392 293)(206 393 294)(207 394 295)(208 395 296)(209 396 297)(210 375 298)(211 376 299)(212 377 300)(213 378 301)(214 379 302)(215 380 303)(216 381 304)(217 382 305)(218 383 306)(219 384 307)(220 385 308)(221 342 309)(222 343 310)(223 344 311)(224 345 312)(225 346 313)(226 347 314)(227 348 315)(228 349 316)(229 350 317)(230 351 318)(231 352 319)(232 331 320)(233 332 321)(234 333 322)(235 334 323)(236 335 324)(237 336 325)(238 337 326)(239 338 327)(240 339 328)(241 340 329)(242 341 330)(243 364 265)(244 365 266)(245 366 267)(246 367 268)(247 368 269)(248 369 270)(249 370 271)(250 371 272)(251 372 273)(252 373 274)(253 374 275)(254 353 276)(255 354 277)(256 355 278)(257 356 279)(258 357 280)(259 358 281)(260 359 282)(261 360 283)(262 361 284)(263 362 285)(264 363 286)
(1 49 44)(2 50 23)(3 51 24)(4 52 25)(5 53 26)(6 54 27)(7 55 28)(8 56 29)(9 57 30)(10 58 31)(11 59 32)(12 60 33)(13 61 34)(14 62 35)(15 63 36)(16 64 37)(17 65 38)(18 66 39)(19 45 40)(20 46 41)(21 47 42)(22 48 43)(67 111 107)(68 112 108)(69 113 109)(70 114 110)(71 115 89)(72 116 90)(73 117 91)(74 118 92)(75 119 93)(76 120 94)(77 121 95)(78 122 96)(79 123 97)(80 124 98)(81 125 99)(82 126 100)(83 127 101)(84 128 102)(85 129 103)(86 130 104)(87 131 105)(88 132 106)(133 195 156)(134 196 157)(135 197 158)(136 198 159)(137 177 160)(138 178 161)(139 179 162)(140 180 163)(141 181 164)(142 182 165)(143 183 166)(144 184 167)(145 185 168)(146 186 169)(147 187 170)(148 188 171)(149 189 172)(150 190 173)(151 191 174)(152 192 175)(153 193 176)(154 194 155)(199 243 232)(200 244 233)(201 245 234)(202 246 235)(203 247 236)(204 248 237)(205 249 238)(206 250 239)(207 251 240)(208 252 241)(209 253 242)(210 254 221)(211 255 222)(212 256 223)(213 257 224)(214 258 225)(215 259 226)(216 260 227)(217 261 228)(218 262 229)(219 263 230)(220 264 231)(265 320 287)(266 321 288)(267 322 289)(268 323 290)(269 324 291)(270 325 292)(271 326 293)(272 327 294)(273 328 295)(274 329 296)(275 330 297)(276 309 298)(277 310 299)(278 311 300)(279 312 301)(280 313 302)(281 314 303)(282 315 304)(283 316 305)(284 317 306)(285 318 307)(286 319 308)(331 386 364)(332 387 365)(333 388 366)(334 389 367)(335 390 368)(336 391 369)(337 392 370)(338 393 371)(339 394 372)(340 395 373)(341 396 374)(342 375 353)(343 376 354)(344 377 355)(345 378 356)(346 379 357)(347 380 358)(348 381 359)(349 382 360)(350 383 361)(351 384 362)(352 385 363)
(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)
(1 199 12 210)(2 220 13 209)(3 219 14 208)(4 218 15 207)(5 217 16 206)(6 216 17 205)(7 215 18 204)(8 214 19 203)(9 213 20 202)(10 212 21 201)(11 211 22 200)(23 231 34 242)(24 230 35 241)(25 229 36 240)(26 228 37 239)(27 227 38 238)(28 226 39 237)(29 225 40 236)(30 224 41 235)(31 223 42 234)(32 222 43 233)(33 221 44 232)(45 247 56 258)(46 246 57 257)(47 245 58 256)(48 244 59 255)(49 243 60 254)(50 264 61 253)(51 263 62 252)(52 262 63 251)(53 261 64 250)(54 260 65 249)(55 259 66 248)(67 281 78 270)(68 280 79 269)(69 279 80 268)(70 278 81 267)(71 277 82 266)(72 276 83 265)(73 275 84 286)(74 274 85 285)(75 273 86 284)(76 272 87 283)(77 271 88 282)(89 299 100 288)(90 298 101 287)(91 297 102 308)(92 296 103 307)(93 295 104 306)(94 294 105 305)(95 293 106 304)(96 292 107 303)(97 291 108 302)(98 290 109 301)(99 289 110 300)(111 314 122 325)(112 313 123 324)(113 312 124 323)(114 311 125 322)(115 310 126 321)(116 309 127 320)(117 330 128 319)(118 329 129 318)(119 328 130 317)(120 327 131 316)(121 326 132 315)(133 338 144 349)(134 337 145 348)(135 336 146 347)(136 335 147 346)(137 334 148 345)(138 333 149 344)(139 332 150 343)(140 331 151 342)(141 352 152 341)(142 351 153 340)(143 350 154 339)(155 372 166 361)(156 371 167 360)(157 370 168 359)(158 369 169 358)(159 368 170 357)(160 367 171 356)(161 366 172 355)(162 365 173 354)(163 364 174 353)(164 363 175 374)(165 362 176 373)(177 389 188 378)(178 388 189 377)(179 387 190 376)(180 386 191 375)(181 385 192 396)(182 384 193 395)(183 383 194 394)(184 382 195 393)(185 381 196 392)(186 380 197 391)(187 379 198 390)

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

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

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

126 conjugacy classes

 class 1 2 3A ··· 3H 4A 4B 6A ··· 6H 11A ··· 11E 12A ··· 12P 22A ··· 22E 33A ··· 33AN 66A ··· 66AN order 1 2 3 ··· 3 4 4 6 ··· 6 11 ··· 11 12 ··· 12 22 ··· 22 33 ··· 33 66 ··· 66 size 1 1 1 ··· 1 11 11 1 ··· 1 2 ··· 2 11 ··· 11 2 ··· 2 2 ··· 2 2 ··· 2

126 irreducible representations

 dim 1 1 1 1 1 1 2 2 2 2 type + + + - image C1 C2 C3 C4 C6 C12 D11 Dic11 C3×D11 C3×Dic11 kernel C32×Dic11 C3×C66 C3×Dic11 C3×C33 C66 C33 C3×C6 C32 C6 C3 # reps 1 1 8 2 8 16 5 5 40 40

Matrix representation of C32×Dic11 in GL3(𝔽397) generated by

 34 0 0 0 1 0 0 0 1
,
 1 0 0 0 34 0 0 0 34
,
 1 0 0 0 0 396 0 1 108
,
 396 0 0 0 143 27 0 66 254
G:=sub<GL(3,GF(397))| [34,0,0,0,1,0,0,0,1],[1,0,0,0,34,0,0,0,34],[1,0,0,0,0,1,0,396,108],[396,0,0,0,143,66,0,27,254] >;

C32×Dic11 in GAP, Magma, Sage, TeX

C_3^2\times {\rm Dic}_{11}
% in TeX

G:=Group("C3^2xDic11");
// GroupNames label

G:=SmallGroup(396,11);
// by ID

G=gap.SmallGroup(396,11);
# by ID

G:=PCGroup([5,-2,-3,-3,-2,-11,90,9004]);
// Polycyclic

G:=Group<a,b,c,d|a^3=b^3=c^22=1,d^2=c^11,a*b=b*a,a*c=c*a,a*d=d*a,b*c=c*b,b*d=d*b,d*c*d^-1=c^-1>;
// generators/relations

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