metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C22.2C42, C42.1D11, C22.4M4(2), C11⋊C8⋊3C4, (C2×C44).3C4, (C4×C44).7C2, C11⋊1(C8⋊C4), C44.24(C2×C4), (C2×C4).88D22, C4.19(C4×D11), (C2×C4).2Dic11, C2.3(C4×Dic11), C2.1(C44.C4), (C2×C44).102C22, C22.7(C2×Dic11), (C2×C11⋊C8).7C2, (C2×C22).25(C2×C4), SmallGroup(352,9)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.D11
G = < a,b,c,d | a4=b4=c11=1, d2=b, ab=ba, ac=ca, dad-1=ab2, bc=cb, bd=db, dcd-1=c-1 >
Smallest permutation representation of C42.D11
►Regular action on 352 points
Generators in S352
(1 120 32 98)(2 121 33 99)(3 111 23 89)(4 112 24 90)(5 113 25 91)(6 114 26 92)(7 115 27 93)(8 116 28 94)(9 117 29 95)(10 118 30 96)(11 119 31 97)(12 122 34 100)(13 123 35 101)(14 124 36 102)(15 125 37 103)(16 126 38 104)(17 127 39 105)(18 128 40 106)(19 129 41 107)(20 130 42 108)(21 131 43 109)(22 132 44 110)(45 155 67 133)(46 156 68 134)(47 157 69 135)(48 158 70 136)(49 159 71 137)(50 160 72 138)(51 161 73 139)(52 162 74 140)(53 163 75 141)(54 164 76 142)(55 165 77 143)(56 166 78 144)(57 167 79 145)(58 168 80 146)(59 169 81 147)(60 170 82 148)(61 171 83 149)(62 172 84 150)(63 173 85 151)(64 174 86 152)(65 175 87 153)(66 176 88 154)(177 298 199 276)(178 299 200 277)(179 300 201 278)(180 301 202 279)(181 302 203 280)(182 303 204 281)(183 304 205 282)(184 305 206 283)(185 306 207 284)(186 307 208 285)(187 308 209 286)(188 287 210 265)(189 288 211 266)(190 289 212 267)(191 290 213 268)(192 291 214 269)(193 292 215 270)(194 293 216 271)(195 294 217 272)(196 295 218 273)(197 296 219 274)(198 297 220 275)(221 342 243 320)(222 343 244 321)(223 344 245 322)(224 345 246 323)(225 346 247 324)(226 347 248 325)(227 348 249 326)(228 349 250 327)(229 350 251 328)(230 351 252 329)(231 352 253 330)(232 331 254 309)(233 332 255 310)(234 333 256 311)(235 334 257 312)(236 335 258 313)(237 336 259 314)(238 337 260 315)(239 338 261 316)(240 339 262 317)(241 340 263 318)(242 341 264 319)
(1 65 21 54)(2 66 22 55)(3 56 12 45)(4 57 13 46)(5 58 14 47)(6 59 15 48)(7 60 16 49)(8 61 17 50)(9 62 18 51)(10 63 19 52)(11 64 20 53)(23 78 34 67)(24 79 35 68)(25 80 36 69)(26 81 37 70)(27 82 38 71)(28 83 39 72)(29 84 40 73)(30 85 41 74)(31 86 42 75)(32 87 43 76)(33 88 44 77)(89 144 100 133)(90 145 101 134)(91 146 102 135)(92 147 103 136)(93 148 104 137)(94 149 105 138)(95 150 106 139)(96 151 107 140)(97 152 108 141)(98 153 109 142)(99 154 110 143)(111 166 122 155)(112 167 123 156)(113 168 124 157)(114 169 125 158)(115 170 126 159)(116 171 127 160)(117 172 128 161)(118 173 129 162)(119 174 130 163)(120 175 131 164)(121 176 132 165)(177 232 188 221)(178 233 189 222)(179 234 190 223)(180 235 191 224)(181 236 192 225)(182 237 193 226)(183 238 194 227)(184 239 195 228)(185 240 196 229)(186 241 197 230)(187 242 198 231)(199 254 210 243)(200 255 211 244)(201 256 212 245)(202 257 213 246)(203 258 214 247)(204 259 215 248)(205 260 216 249)(206 261 217 250)(207 262 218 251)(208 263 219 252)(209 264 220 253)(265 320 276 309)(266 321 277 310)(267 322 278 311)(268 323 279 312)(269 324 280 313)(270 325 281 314)(271 326 282 315)(272 327 283 316)(273 328 284 317)(274 329 285 318)(275 330 286 319)(287 342 298 331)(288 343 299 332)(289 344 300 333)(290 345 301 334)(291 346 302 335)(292 347 303 336)(293 348 304 337)(294 349 305 338)(295 350 306 339)(296 351 307 340)(297 352 308 341)
(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)
(1 242 65 198 21 231 54 187)(2 241 66 197 22 230 55 186)(3 240 56 196 12 229 45 185)(4 239 57 195 13 228 46 184)(5 238 58 194 14 227 47 183)(6 237 59 193 15 226 48 182)(7 236 60 192 16 225 49 181)(8 235 61 191 17 224 50 180)(9 234 62 190 18 223 51 179)(10 233 63 189 19 222 52 178)(11 232 64 188 20 221 53 177)(23 262 78 218 34 251 67 207)(24 261 79 217 35 250 68 206)(25 260 80 216 36 249 69 205)(26 259 81 215 37 248 70 204)(27 258 82 214 38 247 71 203)(28 257 83 213 39 246 72 202)(29 256 84 212 40 245 73 201)(30 255 85 211 41 244 74 200)(31 254 86 210 42 243 75 199)(32 264 87 220 43 253 76 209)(33 263 88 219 44 252 77 208)(89 328 144 284 100 317 133 273)(90 327 145 283 101 316 134 272)(91 326 146 282 102 315 135 271)(92 325 147 281 103 314 136 270)(93 324 148 280 104 313 137 269)(94 323 149 279 105 312 138 268)(95 322 150 278 106 311 139 267)(96 321 151 277 107 310 140 266)(97 320 152 276 108 309 141 265)(98 330 153 286 109 319 142 275)(99 329 154 285 110 318 143 274)(111 350 166 306 122 339 155 295)(112 349 167 305 123 338 156 294)(113 348 168 304 124 337 157 293)(114 347 169 303 125 336 158 292)(115 346 170 302 126 335 159 291)(116 345 171 301 127 334 160 290)(117 344 172 300 128 333 161 289)(118 343 173 299 129 332 162 288)(119 342 174 298 130 331 163 287)(120 352 175 308 131 341 164 297)(121 351 176 307 132 340 165 296)
G:=sub<Sym(352)| (1,120,32,98)(2,121,33,99)(3,111,23,89)(4,112,24,90)(5,113,25,91)(6,114,26,92)(7,115,27,93)(8,116,28,94)(9,117,29,95)(10,118,30,96)(11,119,31,97)(12,122,34,100)(13,123,35,101)(14,124,36,102)(15,125,37,103)(16,126,38,104)(17,127,39,105)(18,128,40,106)(19,129,41,107)(20,130,42,108)(21,131,43,109)(22,132,44,110)(45,155,67,133)(46,156,68,134)(47,157,69,135)(48,158,70,136)(49,159,71,137)(50,160,72,138)(51,161,73,139)(52,162,74,140)(53,163,75,141)(54,164,76,142)(55,165,77,143)(56,166,78,144)(57,167,79,145)(58,168,80,146)(59,169,81,147)(60,170,82,148)(61,171,83,149)(62,172,84,150)(63,173,85,151)(64,174,86,152)(65,175,87,153)(66,176,88,154)(177,298,199,276)(178,299,200,277)(179,300,201,278)(180,301,202,279)(181,302,203,280)(182,303,204,281)(183,304,205,282)(184,305,206,283)(185,306,207,284)(186,307,208,285)(187,308,209,286)(188,287,210,265)(189,288,211,266)(190,289,212,267)(191,290,213,268)(192,291,214,269)(193,292,215,270)(194,293,216,271)(195,294,217,272)(196,295,218,273)(197,296,219,274)(198,297,220,275)(221,342,243,320)(222,343,244,321)(223,344,245,322)(224,345,246,323)(225,346,247,324)(226,347,248,325)(227,348,249,326)(228,349,250,327)(229,350,251,328)(230,351,252,329)(231,352,253,330)(232,331,254,309)(233,332,255,310)(234,333,256,311)(235,334,257,312)(236,335,258,313)(237,336,259,314)(238,337,260,315)(239,338,261,316)(240,339,262,317)(241,340,263,318)(242,341,264,319), (1,65,21,54)(2,66,22,55)(3,56,12,45)(4,57,13,46)(5,58,14,47)(6,59,15,48)(7,60,16,49)(8,61,17,50)(9,62,18,51)(10,63,19,52)(11,64,20,53)(23,78,34,67)(24,79,35,68)(25,80,36,69)(26,81,37,70)(27,82,38,71)(28,83,39,72)(29,84,40,73)(30,85,41,74)(31,86,42,75)(32,87,43,76)(33,88,44,77)(89,144,100,133)(90,145,101,134)(91,146,102,135)(92,147,103,136)(93,148,104,137)(94,149,105,138)(95,150,106,139)(96,151,107,140)(97,152,108,141)(98,153,109,142)(99,154,110,143)(111,166,122,155)(112,167,123,156)(113,168,124,157)(114,169,125,158)(115,170,126,159)(116,171,127,160)(117,172,128,161)(118,173,129,162)(119,174,130,163)(120,175,131,164)(121,176,132,165)(177,232,188,221)(178,233,189,222)(179,234,190,223)(180,235,191,224)(181,236,192,225)(182,237,193,226)(183,238,194,227)(184,239,195,228)(185,240,196,229)(186,241,197,230)(187,242,198,231)(199,254,210,243)(200,255,211,244)(201,256,212,245)(202,257,213,246)(203,258,214,247)(204,259,215,248)(205,260,216,249)(206,261,217,250)(207,262,218,251)(208,263,219,252)(209,264,220,253)(265,320,276,309)(266,321,277,310)(267,322,278,311)(268,323,279,312)(269,324,280,313)(270,325,281,314)(271,326,282,315)(272,327,283,316)(273,328,284,317)(274,329,285,318)(275,330,286,319)(287,342,298,331)(288,343,299,332)(289,344,300,333)(290,345,301,334)(291,346,302,335)(292,347,303,336)(293,348,304,337)(294,349,305,338)(295,350,306,339)(296,351,307,340)(297,352,308,341), (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), (1,242,65,198,21,231,54,187)(2,241,66,197,22,230,55,186)(3,240,56,196,12,229,45,185)(4,239,57,195,13,228,46,184)(5,238,58,194,14,227,47,183)(6,237,59,193,15,226,48,182)(7,236,60,192,16,225,49,181)(8,235,61,191,17,224,50,180)(9,234,62,190,18,223,51,179)(10,233,63,189,19,222,52,178)(11,232,64,188,20,221,53,177)(23,262,78,218,34,251,67,207)(24,261,79,217,35,250,68,206)(25,260,80,216,36,249,69,205)(26,259,81,215,37,248,70,204)(27,258,82,214,38,247,71,203)(28,257,83,213,39,246,72,202)(29,256,84,212,40,245,73,201)(30,255,85,211,41,244,74,200)(31,254,86,210,42,243,75,199)(32,264,87,220,43,253,76,209)(33,263,88,219,44,252,77,208)(89,328,144,284,100,317,133,273)(90,327,145,283,101,316,134,272)(91,326,146,282,102,315,135,271)(92,325,147,281,103,314,136,270)(93,324,148,280,104,313,137,269)(94,323,149,279,105,312,138,268)(95,322,150,278,106,311,139,267)(96,321,151,277,107,310,140,266)(97,320,152,276,108,309,141,265)(98,330,153,286,109,319,142,275)(99,329,154,285,110,318,143,274)(111,350,166,306,122,339,155,295)(112,349,167,305,123,338,156,294)(113,348,168,304,124,337,157,293)(114,347,169,303,125,336,158,292)(115,346,170,302,126,335,159,291)(116,345,171,301,127,334,160,290)(117,344,172,300,128,333,161,289)(118,343,173,299,129,332,162,288)(119,342,174,298,130,331,163,287)(120,352,175,308,131,341,164,297)(121,351,176,307,132,340,165,296)>;
G:=Group( (1,120,32,98)(2,121,33,99)(3,111,23,89)(4,112,24,90)(5,113,25,91)(6,114,26,92)(7,115,27,93)(8,116,28,94)(9,117,29,95)(10,118,30,96)(11,119,31,97)(12,122,34,100)(13,123,35,101)(14,124,36,102)(15,125,37,103)(16,126,38,104)(17,127,39,105)(18,128,40,106)(19,129,41,107)(20,130,42,108)(21,131,43,109)(22,132,44,110)(45,155,67,133)(46,156,68,134)(47,157,69,135)(48,158,70,136)(49,159,71,137)(50,160,72,138)(51,161,73,139)(52,162,74,140)(53,163,75,141)(54,164,76,142)(55,165,77,143)(56,166,78,144)(57,167,79,145)(58,168,80,146)(59,169,81,147)(60,170,82,148)(61,171,83,149)(62,172,84,150)(63,173,85,151)(64,174,86,152)(65,175,87,153)(66,176,88,154)(177,298,199,276)(178,299,200,277)(179,300,201,278)(180,301,202,279)(181,302,203,280)(182,303,204,281)(183,304,205,282)(184,305,206,283)(185,306,207,284)(186,307,208,285)(187,308,209,286)(188,287,210,265)(189,288,211,266)(190,289,212,267)(191,290,213,268)(192,291,214,269)(193,292,215,270)(194,293,216,271)(195,294,217,272)(196,295,218,273)(197,296,219,274)(198,297,220,275)(221,342,243,320)(222,343,244,321)(223,344,245,322)(224,345,246,323)(225,346,247,324)(226,347,248,325)(227,348,249,326)(228,349,250,327)(229,350,251,328)(230,351,252,329)(231,352,253,330)(232,331,254,309)(233,332,255,310)(234,333,256,311)(235,334,257,312)(236,335,258,313)(237,336,259,314)(238,337,260,315)(239,338,261,316)(240,339,262,317)(241,340,263,318)(242,341,264,319), (1,65,21,54)(2,66,22,55)(3,56,12,45)(4,57,13,46)(5,58,14,47)(6,59,15,48)(7,60,16,49)(8,61,17,50)(9,62,18,51)(10,63,19,52)(11,64,20,53)(23,78,34,67)(24,79,35,68)(25,80,36,69)(26,81,37,70)(27,82,38,71)(28,83,39,72)(29,84,40,73)(30,85,41,74)(31,86,42,75)(32,87,43,76)(33,88,44,77)(89,144,100,133)(90,145,101,134)(91,146,102,135)(92,147,103,136)(93,148,104,137)(94,149,105,138)(95,150,106,139)(96,151,107,140)(97,152,108,141)(98,153,109,142)(99,154,110,143)(111,166,122,155)(112,167,123,156)(113,168,124,157)(114,169,125,158)(115,170,126,159)(116,171,127,160)(117,172,128,161)(118,173,129,162)(119,174,130,163)(120,175,131,164)(121,176,132,165)(177,232,188,221)(178,233,189,222)(179,234,190,223)(180,235,191,224)(181,236,192,225)(182,237,193,226)(183,238,194,227)(184,239,195,228)(185,240,196,229)(186,241,197,230)(187,242,198,231)(199,254,210,243)(200,255,211,244)(201,256,212,245)(202,257,213,246)(203,258,214,247)(204,259,215,248)(205,260,216,249)(206,261,217,250)(207,262,218,251)(208,263,219,252)(209,264,220,253)(265,320,276,309)(266,321,277,310)(267,322,278,311)(268,323,279,312)(269,324,280,313)(270,325,281,314)(271,326,282,315)(272,327,283,316)(273,328,284,317)(274,329,285,318)(275,330,286,319)(287,342,298,331)(288,343,299,332)(289,344,300,333)(290,345,301,334)(291,346,302,335)(292,347,303,336)(293,348,304,337)(294,349,305,338)(295,350,306,339)(296,351,307,340)(297,352,308,341), (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), (1,242,65,198,21,231,54,187)(2,241,66,197,22,230,55,186)(3,240,56,196,12,229,45,185)(4,239,57,195,13,228,46,184)(5,238,58,194,14,227,47,183)(6,237,59,193,15,226,48,182)(7,236,60,192,16,225,49,181)(8,235,61,191,17,224,50,180)(9,234,62,190,18,223,51,179)(10,233,63,189,19,222,52,178)(11,232,64,188,20,221,53,177)(23,262,78,218,34,251,67,207)(24,261,79,217,35,250,68,206)(25,260,80,216,36,249,69,205)(26,259,81,215,37,248,70,204)(27,258,82,214,38,247,71,203)(28,257,83,213,39,246,72,202)(29,256,84,212,40,245,73,201)(30,255,85,211,41,244,74,200)(31,254,86,210,42,243,75,199)(32,264,87,220,43,253,76,209)(33,263,88,219,44,252,77,208)(89,328,144,284,100,317,133,273)(90,327,145,283,101,316,134,272)(91,326,146,282,102,315,135,271)(92,325,147,281,103,314,136,270)(93,324,148,280,104,313,137,269)(94,323,149,279,105,312,138,268)(95,322,150,278,106,311,139,267)(96,321,151,277,107,310,140,266)(97,320,152,276,108,309,141,265)(98,330,153,286,109,319,142,275)(99,329,154,285,110,318,143,274)(111,350,166,306,122,339,155,295)(112,349,167,305,123,338,156,294)(113,348,168,304,124,337,157,293)(114,347,169,303,125,336,158,292)(115,346,170,302,126,335,159,291)(116,345,171,301,127,334,160,290)(117,344,172,300,128,333,161,289)(118,343,173,299,129,332,162,288)(119,342,174,298,130,331,163,287)(120,352,175,308,131,341,164,297)(121,351,176,307,132,340,165,296) );
G=PermutationGroup([[(1,120,32,98),(2,121,33,99),(3,111,23,89),(4,112,24,90),(5,113,25,91),(6,114,26,92),(7,115,27,93),(8,116,28,94),(9,117,29,95),(10,118,30,96),(11,119,31,97),(12,122,34,100),(13,123,35,101),(14,124,36,102),(15,125,37,103),(16,126,38,104),(17,127,39,105),(18,128,40,106),(19,129,41,107),(20,130,42,108),(21,131,43,109),(22,132,44,110),(45,155,67,133),(46,156,68,134),(47,157,69,135),(48,158,70,136),(49,159,71,137),(50,160,72,138),(51,161,73,139),(52,162,74,140),(53,163,75,141),(54,164,76,142),(55,165,77,143),(56,166,78,144),(57,167,79,145),(58,168,80,146),(59,169,81,147),(60,170,82,148),(61,171,83,149),(62,172,84,150),(63,173,85,151),(64,174,86,152),(65,175,87,153),(66,176,88,154),(177,298,199,276),(178,299,200,277),(179,300,201,278),(180,301,202,279),(181,302,203,280),(182,303,204,281),(183,304,205,282),(184,305,206,283),(185,306,207,284),(186,307,208,285),(187,308,209,286),(188,287,210,265),(189,288,211,266),(190,289,212,267),(191,290,213,268),(192,291,214,269),(193,292,215,270),(194,293,216,271),(195,294,217,272),(196,295,218,273),(197,296,219,274),(198,297,220,275),(221,342,243,320),(222,343,244,321),(223,344,245,322),(224,345,246,323),(225,346,247,324),(226,347,248,325),(227,348,249,326),(228,349,250,327),(229,350,251,328),(230,351,252,329),(231,352,253,330),(232,331,254,309),(233,332,255,310),(234,333,256,311),(235,334,257,312),(236,335,258,313),(237,336,259,314),(238,337,260,315),(239,338,261,316),(240,339,262,317),(241,340,263,318),(242,341,264,319)], [(1,65,21,54),(2,66,22,55),(3,56,12,45),(4,57,13,46),(5,58,14,47),(6,59,15,48),(7,60,16,49),(8,61,17,50),(9,62,18,51),(10,63,19,52),(11,64,20,53),(23,78,34,67),(24,79,35,68),(25,80,36,69),(26,81,37,70),(27,82,38,71),(28,83,39,72),(29,84,40,73),(30,85,41,74),(31,86,42,75),(32,87,43,76),(33,88,44,77),(89,144,100,133),(90,145,101,134),(91,146,102,135),(92,147,103,136),(93,148,104,137),(94,149,105,138),(95,150,106,139),(96,151,107,140),(97,152,108,141),(98,153,109,142),(99,154,110,143),(111,166,122,155),(112,167,123,156),(113,168,124,157),(114,169,125,158),(115,170,126,159),(116,171,127,160),(117,172,128,161),(118,173,129,162),(119,174,130,163),(120,175,131,164),(121,176,132,165),(177,232,188,221),(178,233,189,222),(179,234,190,223),(180,235,191,224),(181,236,192,225),(182,237,193,226),(183,238,194,227),(184,239,195,228),(185,240,196,229),(186,241,197,230),(187,242,198,231),(199,254,210,243),(200,255,211,244),(201,256,212,245),(202,257,213,246),(203,258,214,247),(204,259,215,248),(205,260,216,249),(206,261,217,250),(207,262,218,251),(208,263,219,252),(209,264,220,253),(265,320,276,309),(266,321,277,310),(267,322,278,311),(268,323,279,312),(269,324,280,313),(270,325,281,314),(271,326,282,315),(272,327,283,316),(273,328,284,317),(274,329,285,318),(275,330,286,319),(287,342,298,331),(288,343,299,332),(289,344,300,333),(290,345,301,334),(291,346,302,335),(292,347,303,336),(293,348,304,337),(294,349,305,338),(295,350,306,339),(296,351,307,340),(297,352,308,341)], [(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)], [(1,242,65,198,21,231,54,187),(2,241,66,197,22,230,55,186),(3,240,56,196,12,229,45,185),(4,239,57,195,13,228,46,184),(5,238,58,194,14,227,47,183),(6,237,59,193,15,226,48,182),(7,236,60,192,16,225,49,181),(8,235,61,191,17,224,50,180),(9,234,62,190,18,223,51,179),(10,233,63,189,19,222,52,178),(11,232,64,188,20,221,53,177),(23,262,78,218,34,251,67,207),(24,261,79,217,35,250,68,206),(25,260,80,216,36,249,69,205),(26,259,81,215,37,248,70,204),(27,258,82,214,38,247,71,203),(28,257,83,213,39,246,72,202),(29,256,84,212,40,245,73,201),(30,255,85,211,41,244,74,200),(31,254,86,210,42,243,75,199),(32,264,87,220,43,253,76,209),(33,263,88,219,44,252,77,208),(89,328,144,284,100,317,133,273),(90,327,145,283,101,316,134,272),(91,326,146,282,102,315,135,271),(92,325,147,281,103,314,136,270),(93,324,148,280,104,313,137,269),(94,323,149,279,105,312,138,268),(95,322,150,278,106,311,139,267),(96,321,151,277,107,310,140,266),(97,320,152,276,108,309,141,265),(98,330,153,286,109,319,142,275),(99,329,154,285,110,318,143,274),(111,350,166,306,122,339,155,295),(112,349,167,305,123,338,156,294),(113,348,168,304,124,337,157,293),(114,347,169,303,125,336,158,292),(115,346,170,302,126,335,159,291),(116,345,171,301,127,334,160,290),(117,344,172,300,128,333,161,289),(118,343,173,299,129,332,162,288),(119,342,174,298,130,331,163,287),(120,352,175,308,131,341,164,297),(121,351,176,307,132,340,165,296)]])
100 conjugacy classes
| class | 1 | 2A | 2B | 2C | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 8A | ··· | 8H | 11A | ··· | 11E | 22A | ··· | 22O | 44A | ··· | 44BH |
| order | 1 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 8 | ··· | 8 | 11 | ··· | 11 | 22 | ··· | 22 | 44 | ··· | 44 |
| size | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 22 | ··· | 22 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
100 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | - | + | |||||
| image | C1 | C2 | C2 | C4 | C4 | M4(2) | D11 | Dic11 | D22 | C4×D11 | C44.C4 |
| kernel | C42.D11 | C2×C11⋊C8 | C4×C44 | C11⋊C8 | C2×C44 | C22 | C42 | C2×C4 | C2×C4 | C4 | C2 |
| # reps | 1 | 2 | 1 | 8 | 4 | 4 | 5 | 10 | 5 | 20 | 40 |
Matrix representation of C42.D11 ►in GL3(𝔽89) generated by
| 34 | 0 | 0 |
| 0 | 58 | 61 |
| 0 | 28 | 31 |
| 1 | 0 | 0 |
| 0 | 34 | 0 |
| 0 | 0 | 34 |
| 1 | 0 | 0 |
| 0 | 0 | 1 |
| 0 | 88 | 55 |
| 88 | 0 | 0 |
| 0 | 38 | 20 |
| 0 | 63 | 51 |
G:=sub<GL(3,GF(89))| [34,0,0,0,58,28,0,61,31],[1,0,0,0,34,0,0,0,34],[1,0,0,0,0,88,0,1,55],[88,0,0,0,38,63,0,20,51] >;
C42.D11 in GAP, Magma, Sage, TeX
C_4^2.D_{11} % in TeX
G:=Group("C4^2.D11"); // GroupNames label
G:=SmallGroup(352,9);
// by ID
G=gap.SmallGroup(352,9);
# by ID
G:=PCGroup([6,-2,-2,-2,-2,-2,-11,24,217,55,86,11525]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=c^11=1,d^2=b,a*b=b*a,a*c=c*a,d*a*d^-1=a*b^2,b*c=c*b,b*d=d*b,d*c*d^-1=c^-1>;
// generators/relations
Export