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## G = C2×Dic11⋊C4order 352 = 25·11

### Direct product of C2 and Dic11⋊C4

Series: Derived Chief Lower central Upper central

 Derived series C1 — C22 — C2×Dic11⋊C4
 Chief series C1 — C11 — C22 — C2×C22 — C2×Dic11 — C22×Dic11 — C2×Dic11⋊C4
 Lower central C11 — C22 — C2×Dic11⋊C4
 Upper central C1 — C23 — C22×C4

Generators and relations for C2×Dic11⋊C4
G = < a,b,c,d | a2=b22=d4=1, c2=b11, ab=ba, ac=ca, ad=da, cbc-1=b-1, bd=db, dcd-1=b11c >

Subgroups: 378 in 92 conjugacy classes, 57 normal (17 characteristic)
C1, C2, C2, C4, C22, C22, C2×C4, C2×C4, C23, C11, C4⋊C4, C22×C4, C22×C4, C22, C22, C2×C4⋊C4, Dic11, Dic11, C44, C2×C22, C2×C22, C2×Dic11, C2×Dic11, C2×C44, C2×C44, C22×C22, Dic11⋊C4, C22×Dic11, C22×C44, C2×Dic11⋊C4
Quotients: C1, C2, C4, C22, C2×C4, D4, Q8, C23, C4⋊C4, C22×C4, C2×D4, C2×Q8, D11, C2×C4⋊C4, D22, Dic22, C4×D11, C11⋊D4, C22×D11, Dic11⋊C4, C2×Dic22, C2×C4×D11, C2×C11⋊D4, C2×Dic11⋊C4

Smallest permutation representation of C2×Dic11⋊C4
Regular action on 352 points
Generators in S352
(1 122)(2 123)(3 124)(4 125)(5 126)(6 127)(7 128)(8 129)(9 130)(10 131)(11 132)(12 111)(13 112)(14 113)(15 114)(16 115)(17 116)(18 117)(19 118)(20 119)(21 120)(22 121)(23 89)(24 90)(25 91)(26 92)(27 93)(28 94)(29 95)(30 96)(31 97)(32 98)(33 99)(34 100)(35 101)(36 102)(37 103)(38 104)(39 105)(40 106)(41 107)(42 108)(43 109)(44 110)(45 155)(46 156)(47 157)(48 158)(49 159)(50 160)(51 161)(52 162)(53 163)(54 164)(55 165)(56 166)(57 167)(58 168)(59 169)(60 170)(61 171)(62 172)(63 173)(64 174)(65 175)(66 176)(67 133)(68 134)(69 135)(70 136)(71 137)(72 138)(73 139)(74 140)(75 141)(76 142)(77 143)(78 144)(79 145)(80 146)(81 147)(82 148)(83 149)(84 150)(85 151)(86 152)(87 153)(88 154)(177 303)(178 304)(179 305)(180 306)(181 307)(182 308)(183 287)(184 288)(185 289)(186 290)(187 291)(188 292)(189 293)(190 294)(191 295)(192 296)(193 297)(194 298)(195 299)(196 300)(197 301)(198 302)(199 270)(200 271)(201 272)(202 273)(203 274)(204 275)(205 276)(206 277)(207 278)(208 279)(209 280)(210 281)(211 282)(212 283)(213 284)(214 285)(215 286)(216 265)(217 266)(218 267)(219 268)(220 269)(221 345)(222 346)(223 347)(224 348)(225 349)(226 350)(227 351)(228 352)(229 331)(230 332)(231 333)(232 334)(233 335)(234 336)(235 337)(236 338)(237 339)(238 340)(239 341)(240 342)(241 343)(242 344)(243 315)(244 316)(245 317)(246 318)(247 319)(248 320)(249 321)(250 322)(251 323)(252 324)(253 325)(254 326)(255 327)(256 328)(257 329)(258 330)(259 309)(260 310)(261 311)(262 312)(263 313)(264 314)
(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)
(1 201 12 212)(2 200 13 211)(3 199 14 210)(4 220 15 209)(5 219 16 208)(6 218 17 207)(7 217 18 206)(8 216 19 205)(9 215 20 204)(10 214 21 203)(11 213 22 202)(23 194 34 183)(24 193 35 182)(25 192 36 181)(26 191 37 180)(27 190 38 179)(28 189 39 178)(29 188 40 177)(30 187 41 198)(31 186 42 197)(32 185 43 196)(33 184 44 195)(45 251 56 262)(46 250 57 261)(47 249 58 260)(48 248 59 259)(49 247 60 258)(50 246 61 257)(51 245 62 256)(52 244 63 255)(53 243 64 254)(54 264 65 253)(55 263 66 252)(67 238 78 227)(68 237 79 226)(69 236 80 225)(70 235 81 224)(71 234 82 223)(72 233 83 222)(73 232 84 221)(74 231 85 242)(75 230 86 241)(76 229 87 240)(77 228 88 239)(89 298 100 287)(90 297 101 308)(91 296 102 307)(92 295 103 306)(93 294 104 305)(94 293 105 304)(95 292 106 303)(96 291 107 302)(97 290 108 301)(98 289 109 300)(99 288 110 299)(111 283 122 272)(112 282 123 271)(113 281 124 270)(114 280 125 269)(115 279 126 268)(116 278 127 267)(117 277 128 266)(118 276 129 265)(119 275 130 286)(120 274 131 285)(121 273 132 284)(133 340 144 351)(134 339 145 350)(135 338 146 349)(136 337 147 348)(137 336 148 347)(138 335 149 346)(139 334 150 345)(140 333 151 344)(141 332 152 343)(142 331 153 342)(143 352 154 341)(155 323 166 312)(156 322 167 311)(157 321 168 310)(158 320 169 309)(159 319 170 330)(160 318 171 329)(161 317 172 328)(162 316 173 327)(163 315 174 326)(164 314 175 325)(165 313 176 324)
(1 78 34 56)(2 79 35 57)(3 80 36 58)(4 81 37 59)(5 82 38 60)(6 83 39 61)(7 84 40 62)(8 85 41 63)(9 86 42 64)(10 87 43 65)(11 88 44 66)(12 67 23 45)(13 68 24 46)(14 69 25 47)(15 70 26 48)(16 71 27 49)(17 72 28 50)(18 73 29 51)(19 74 30 52)(20 75 31 53)(21 76 32 54)(22 77 33 55)(89 155 111 133)(90 156 112 134)(91 157 113 135)(92 158 114 136)(93 159 115 137)(94 160 116 138)(95 161 117 139)(96 162 118 140)(97 163 119 141)(98 164 120 142)(99 165 121 143)(100 166 122 144)(101 167 123 145)(102 168 124 146)(103 169 125 147)(104 170 126 148)(105 171 127 149)(106 172 128 150)(107 173 129 151)(108 174 130 152)(109 175 131 153)(110 176 132 154)(177 245 217 232)(178 246 218 233)(179 247 219 234)(180 248 220 235)(181 249 199 236)(182 250 200 237)(183 251 201 238)(184 252 202 239)(185 253 203 240)(186 254 204 241)(187 255 205 242)(188 256 206 221)(189 257 207 222)(190 258 208 223)(191 259 209 224)(192 260 210 225)(193 261 211 226)(194 262 212 227)(195 263 213 228)(196 264 214 229)(197 243 215 230)(198 244 216 231)(265 333 302 316)(266 334 303 317)(267 335 304 318)(268 336 305 319)(269 337 306 320)(270 338 307 321)(271 339 308 322)(272 340 287 323)(273 341 288 324)(274 342 289 325)(275 343 290 326)(276 344 291 327)(277 345 292 328)(278 346 293 329)(279 347 294 330)(280 348 295 309)(281 349 296 310)(282 350 297 311)(283 351 298 312)(284 352 299 313)(285 331 300 314)(286 332 301 315)

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

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

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

100 conjugacy classes

 class 1 2A ··· 2G 4A 4B 4C 4D 4E ··· 4L 11A ··· 11E 22A ··· 22AI 44A ··· 44AN order 1 2 ··· 2 4 4 4 4 4 ··· 4 11 ··· 11 22 ··· 22 44 ··· 44 size 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 2 2 type + + + + + - + + + - image C1 C2 C2 C2 C4 D4 Q8 D11 D22 D22 Dic22 C4×D11 C11⋊D4 kernel C2×Dic11⋊C4 Dic11⋊C4 C22×Dic11 C22×C44 C2×Dic11 C2×C22 C2×C22 C22×C4 C2×C4 C23 C22 C22 C22 # reps 1 4 2 1 8 2 2 5 10 5 20 20 20

Matrix representation of C2×Dic11⋊C4 in GL5(𝔽89)

 1 0 0 0 0 0 88 0 0 0 0 0 88 0 0 0 0 0 88 0 0 0 0 0 88
,
 1 0 0 0 0 0 62 88 0 0 0 79 82 0 0 0 0 0 45 1 0 0 0 30 62
,
 88 0 0 0 0 0 39 81 0 0 0 12 50 0 0 0 0 0 73 35 0 0 0 13 16
,
 55 0 0 0 0 0 88 0 0 0 0 0 88 0 0 0 0 0 77 59 0 0 0 79 12

G:=sub<GL(5,GF(89))| [1,0,0,0,0,0,88,0,0,0,0,0,88,0,0,0,0,0,88,0,0,0,0,0,88],[1,0,0,0,0,0,62,79,0,0,0,88,82,0,0,0,0,0,45,30,0,0,0,1,62],[88,0,0,0,0,0,39,12,0,0,0,81,50,0,0,0,0,0,73,13,0,0,0,35,16],[55,0,0,0,0,0,88,0,0,0,0,0,88,0,0,0,0,0,77,79,0,0,0,59,12] >;

C2×Dic11⋊C4 in GAP, Magma, Sage, TeX

C_2\times {\rm Dic}_{11}\rtimes C_4
% in TeX

G:=Group("C2xDic11:C4");
// GroupNames label

G:=SmallGroup(352,118);
// by ID

G=gap.SmallGroup(352,118);
# by ID

G:=PCGroup([6,-2,-2,-2,-2,-2,-11,96,362,50,11525]);
// Polycyclic

G:=Group<a,b,c,d|a^2=b^22=d^4=1,c^2=b^11,a*b=b*a,a*c=c*a,a*d=d*a,c*b*c^-1=b^-1,b*d=d*b,d*c*d^-1=b^11*c>;
// generators/relations

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