metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: Dic11⋊C8, C44.8Q8, C44.51D4, C4.8Dic22, C22.1M4(2), C11⋊2(C4⋊C8), C22.4(C2×C8), (C2×C88).1C2, C2.4(C8×D11), (C2×C8).1D11, C22.4(C4⋊C4), (C2×C4).91D22, C2.1(C88⋊C2), C22.9(C4×D11), C4.26(C11⋊D4), (C2×Dic11).2C4, (C4×Dic11).5C2, C2.1(Dic11⋊C4), (C2×C44).105C22, (C2×C11⋊C8).9C2, (C2×C22).10(C2×C4), SmallGroup(352,20)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for Dic11⋊C8
G = < a,b,c | a22=c8=1, b2=a11, bab-1=a-1, ac=ca, cbc-1=a11b >
Smallest permutation representation of Dic11⋊C8
►Regular action on 352 points
Generators in S352
(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)
(1 333 12 344)(2 332 13 343)(3 331 14 342)(4 352 15 341)(5 351 16 340)(6 350 17 339)(7 349 18 338)(8 348 19 337)(9 347 20 336)(10 346 21 335)(11 345 22 334)(23 83 34 72)(24 82 35 71)(25 81 36 70)(26 80 37 69)(27 79 38 68)(28 78 39 67)(29 77 40 88)(30 76 41 87)(31 75 42 86)(32 74 43 85)(33 73 44 84)(45 313 56 324)(46 312 57 323)(47 311 58 322)(48 310 59 321)(49 309 60 320)(50 330 61 319)(51 329 62 318)(52 328 63 317)(53 327 64 316)(54 326 65 315)(55 325 66 314)(89 294 100 305)(90 293 101 304)(91 292 102 303)(92 291 103 302)(93 290 104 301)(94 289 105 300)(95 288 106 299)(96 287 107 298)(97 308 108 297)(98 307 109 296)(99 306 110 295)(111 194 122 183)(112 193 123 182)(113 192 124 181)(114 191 125 180)(115 190 126 179)(116 189 127 178)(117 188 128 177)(118 187 129 198)(119 186 130 197)(120 185 131 196)(121 184 132 195)(133 213 144 202)(134 212 145 201)(135 211 146 200)(136 210 147 199)(137 209 148 220)(138 208 149 219)(139 207 150 218)(140 206 151 217)(141 205 152 216)(142 204 153 215)(143 203 154 214)(155 265 166 276)(156 286 167 275)(157 285 168 274)(158 284 169 273)(159 283 170 272)(160 282 171 271)(161 281 172 270)(162 280 173 269)(163 279 174 268)(164 278 175 267)(165 277 176 266)(221 250 232 261)(222 249 233 260)(223 248 234 259)(224 247 235 258)(225 246 236 257)(226 245 237 256)(227 244 238 255)(228 243 239 254)(229 264 240 253)(230 263 241 252)(231 262 242 251)
(1 179 299 328 234 272 204 25)(2 180 300 329 235 273 205 26)(3 181 301 330 236 274 206 27)(4 182 302 309 237 275 207 28)(5 183 303 310 238 276 208 29)(6 184 304 311 239 277 209 30)(7 185 305 312 240 278 210 31)(8 186 306 313 241 279 211 32)(9 187 307 314 242 280 212 33)(10 188 308 315 221 281 213 34)(11 189 287 316 222 282 214 35)(12 190 288 317 223 283 215 36)(13 191 289 318 224 284 216 37)(14 192 290 319 225 285 217 38)(15 193 291 320 226 286 218 39)(16 194 292 321 227 265 219 40)(17 195 293 322 228 266 220 41)(18 196 294 323 229 267 199 42)(19 197 295 324 230 268 200 43)(20 198 296 325 231 269 201 44)(21 177 297 326 232 270 202 23)(22 178 298 327 233 271 203 24)(45 252 163 146 85 348 119 110)(46 253 164 147 86 349 120 89)(47 254 165 148 87 350 121 90)(48 255 166 149 88 351 122 91)(49 256 167 150 67 352 123 92)(50 257 168 151 68 331 124 93)(51 258 169 152 69 332 125 94)(52 259 170 153 70 333 126 95)(53 260 171 154 71 334 127 96)(54 261 172 133 72 335 128 97)(55 262 173 134 73 336 129 98)(56 263 174 135 74 337 130 99)(57 264 175 136 75 338 131 100)(58 243 176 137 76 339 132 101)(59 244 155 138 77 340 111 102)(60 245 156 139 78 341 112 103)(61 246 157 140 79 342 113 104)(62 247 158 141 80 343 114 105)(63 248 159 142 81 344 115 106)(64 249 160 143 82 345 116 107)(65 250 161 144 83 346 117 108)(66 251 162 145 84 347 118 109)
G:=sub<Sym(352)| (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), (1,333,12,344)(2,332,13,343)(3,331,14,342)(4,352,15,341)(5,351,16,340)(6,350,17,339)(7,349,18,338)(8,348,19,337)(9,347,20,336)(10,346,21,335)(11,345,22,334)(23,83,34,72)(24,82,35,71)(25,81,36,70)(26,80,37,69)(27,79,38,68)(28,78,39,67)(29,77,40,88)(30,76,41,87)(31,75,42,86)(32,74,43,85)(33,73,44,84)(45,313,56,324)(46,312,57,323)(47,311,58,322)(48,310,59,321)(49,309,60,320)(50,330,61,319)(51,329,62,318)(52,328,63,317)(53,327,64,316)(54,326,65,315)(55,325,66,314)(89,294,100,305)(90,293,101,304)(91,292,102,303)(92,291,103,302)(93,290,104,301)(94,289,105,300)(95,288,106,299)(96,287,107,298)(97,308,108,297)(98,307,109,296)(99,306,110,295)(111,194,122,183)(112,193,123,182)(113,192,124,181)(114,191,125,180)(115,190,126,179)(116,189,127,178)(117,188,128,177)(118,187,129,198)(119,186,130,197)(120,185,131,196)(121,184,132,195)(133,213,144,202)(134,212,145,201)(135,211,146,200)(136,210,147,199)(137,209,148,220)(138,208,149,219)(139,207,150,218)(140,206,151,217)(141,205,152,216)(142,204,153,215)(143,203,154,214)(155,265,166,276)(156,286,167,275)(157,285,168,274)(158,284,169,273)(159,283,170,272)(160,282,171,271)(161,281,172,270)(162,280,173,269)(163,279,174,268)(164,278,175,267)(165,277,176,266)(221,250,232,261)(222,249,233,260)(223,248,234,259)(224,247,235,258)(225,246,236,257)(226,245,237,256)(227,244,238,255)(228,243,239,254)(229,264,240,253)(230,263,241,252)(231,262,242,251), (1,179,299,328,234,272,204,25)(2,180,300,329,235,273,205,26)(3,181,301,330,236,274,206,27)(4,182,302,309,237,275,207,28)(5,183,303,310,238,276,208,29)(6,184,304,311,239,277,209,30)(7,185,305,312,240,278,210,31)(8,186,306,313,241,279,211,32)(9,187,307,314,242,280,212,33)(10,188,308,315,221,281,213,34)(11,189,287,316,222,282,214,35)(12,190,288,317,223,283,215,36)(13,191,289,318,224,284,216,37)(14,192,290,319,225,285,217,38)(15,193,291,320,226,286,218,39)(16,194,292,321,227,265,219,40)(17,195,293,322,228,266,220,41)(18,196,294,323,229,267,199,42)(19,197,295,324,230,268,200,43)(20,198,296,325,231,269,201,44)(21,177,297,326,232,270,202,23)(22,178,298,327,233,271,203,24)(45,252,163,146,85,348,119,110)(46,253,164,147,86,349,120,89)(47,254,165,148,87,350,121,90)(48,255,166,149,88,351,122,91)(49,256,167,150,67,352,123,92)(50,257,168,151,68,331,124,93)(51,258,169,152,69,332,125,94)(52,259,170,153,70,333,126,95)(53,260,171,154,71,334,127,96)(54,261,172,133,72,335,128,97)(55,262,173,134,73,336,129,98)(56,263,174,135,74,337,130,99)(57,264,175,136,75,338,131,100)(58,243,176,137,76,339,132,101)(59,244,155,138,77,340,111,102)(60,245,156,139,78,341,112,103)(61,246,157,140,79,342,113,104)(62,247,158,141,80,343,114,105)(63,248,159,142,81,344,115,106)(64,249,160,143,82,345,116,107)(65,250,161,144,83,346,117,108)(66,251,162,145,84,347,118,109)>;
G:=Group( (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), (1,333,12,344)(2,332,13,343)(3,331,14,342)(4,352,15,341)(5,351,16,340)(6,350,17,339)(7,349,18,338)(8,348,19,337)(9,347,20,336)(10,346,21,335)(11,345,22,334)(23,83,34,72)(24,82,35,71)(25,81,36,70)(26,80,37,69)(27,79,38,68)(28,78,39,67)(29,77,40,88)(30,76,41,87)(31,75,42,86)(32,74,43,85)(33,73,44,84)(45,313,56,324)(46,312,57,323)(47,311,58,322)(48,310,59,321)(49,309,60,320)(50,330,61,319)(51,329,62,318)(52,328,63,317)(53,327,64,316)(54,326,65,315)(55,325,66,314)(89,294,100,305)(90,293,101,304)(91,292,102,303)(92,291,103,302)(93,290,104,301)(94,289,105,300)(95,288,106,299)(96,287,107,298)(97,308,108,297)(98,307,109,296)(99,306,110,295)(111,194,122,183)(112,193,123,182)(113,192,124,181)(114,191,125,180)(115,190,126,179)(116,189,127,178)(117,188,128,177)(118,187,129,198)(119,186,130,197)(120,185,131,196)(121,184,132,195)(133,213,144,202)(134,212,145,201)(135,211,146,200)(136,210,147,199)(137,209,148,220)(138,208,149,219)(139,207,150,218)(140,206,151,217)(141,205,152,216)(142,204,153,215)(143,203,154,214)(155,265,166,276)(156,286,167,275)(157,285,168,274)(158,284,169,273)(159,283,170,272)(160,282,171,271)(161,281,172,270)(162,280,173,269)(163,279,174,268)(164,278,175,267)(165,277,176,266)(221,250,232,261)(222,249,233,260)(223,248,234,259)(224,247,235,258)(225,246,236,257)(226,245,237,256)(227,244,238,255)(228,243,239,254)(229,264,240,253)(230,263,241,252)(231,262,242,251), (1,179,299,328,234,272,204,25)(2,180,300,329,235,273,205,26)(3,181,301,330,236,274,206,27)(4,182,302,309,237,275,207,28)(5,183,303,310,238,276,208,29)(6,184,304,311,239,277,209,30)(7,185,305,312,240,278,210,31)(8,186,306,313,241,279,211,32)(9,187,307,314,242,280,212,33)(10,188,308,315,221,281,213,34)(11,189,287,316,222,282,214,35)(12,190,288,317,223,283,215,36)(13,191,289,318,224,284,216,37)(14,192,290,319,225,285,217,38)(15,193,291,320,226,286,218,39)(16,194,292,321,227,265,219,40)(17,195,293,322,228,266,220,41)(18,196,294,323,229,267,199,42)(19,197,295,324,230,268,200,43)(20,198,296,325,231,269,201,44)(21,177,297,326,232,270,202,23)(22,178,298,327,233,271,203,24)(45,252,163,146,85,348,119,110)(46,253,164,147,86,349,120,89)(47,254,165,148,87,350,121,90)(48,255,166,149,88,351,122,91)(49,256,167,150,67,352,123,92)(50,257,168,151,68,331,124,93)(51,258,169,152,69,332,125,94)(52,259,170,153,70,333,126,95)(53,260,171,154,71,334,127,96)(54,261,172,133,72,335,128,97)(55,262,173,134,73,336,129,98)(56,263,174,135,74,337,130,99)(57,264,175,136,75,338,131,100)(58,243,176,137,76,339,132,101)(59,244,155,138,77,340,111,102)(60,245,156,139,78,341,112,103)(61,246,157,140,79,342,113,104)(62,247,158,141,80,343,114,105)(63,248,159,142,81,344,115,106)(64,249,160,143,82,345,116,107)(65,250,161,144,83,346,117,108)(66,251,162,145,84,347,118,109) );
G=PermutationGroup([[(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)], [(1,333,12,344),(2,332,13,343),(3,331,14,342),(4,352,15,341),(5,351,16,340),(6,350,17,339),(7,349,18,338),(8,348,19,337),(9,347,20,336),(10,346,21,335),(11,345,22,334),(23,83,34,72),(24,82,35,71),(25,81,36,70),(26,80,37,69),(27,79,38,68),(28,78,39,67),(29,77,40,88),(30,76,41,87),(31,75,42,86),(32,74,43,85),(33,73,44,84),(45,313,56,324),(46,312,57,323),(47,311,58,322),(48,310,59,321),(49,309,60,320),(50,330,61,319),(51,329,62,318),(52,328,63,317),(53,327,64,316),(54,326,65,315),(55,325,66,314),(89,294,100,305),(90,293,101,304),(91,292,102,303),(92,291,103,302),(93,290,104,301),(94,289,105,300),(95,288,106,299),(96,287,107,298),(97,308,108,297),(98,307,109,296),(99,306,110,295),(111,194,122,183),(112,193,123,182),(113,192,124,181),(114,191,125,180),(115,190,126,179),(116,189,127,178),(117,188,128,177),(118,187,129,198),(119,186,130,197),(120,185,131,196),(121,184,132,195),(133,213,144,202),(134,212,145,201),(135,211,146,200),(136,210,147,199),(137,209,148,220),(138,208,149,219),(139,207,150,218),(140,206,151,217),(141,205,152,216),(142,204,153,215),(143,203,154,214),(155,265,166,276),(156,286,167,275),(157,285,168,274),(158,284,169,273),(159,283,170,272),(160,282,171,271),(161,281,172,270),(162,280,173,269),(163,279,174,268),(164,278,175,267),(165,277,176,266),(221,250,232,261),(222,249,233,260),(223,248,234,259),(224,247,235,258),(225,246,236,257),(226,245,237,256),(227,244,238,255),(228,243,239,254),(229,264,240,253),(230,263,241,252),(231,262,242,251)], [(1,179,299,328,234,272,204,25),(2,180,300,329,235,273,205,26),(3,181,301,330,236,274,206,27),(4,182,302,309,237,275,207,28),(5,183,303,310,238,276,208,29),(6,184,304,311,239,277,209,30),(7,185,305,312,240,278,210,31),(8,186,306,313,241,279,211,32),(9,187,307,314,242,280,212,33),(10,188,308,315,221,281,213,34),(11,189,287,316,222,282,214,35),(12,190,288,317,223,283,215,36),(13,191,289,318,224,284,216,37),(14,192,290,319,225,285,217,38),(15,193,291,320,226,286,218,39),(16,194,292,321,227,265,219,40),(17,195,293,322,228,266,220,41),(18,196,294,323,229,267,199,42),(19,197,295,324,230,268,200,43),(20,198,296,325,231,269,201,44),(21,177,297,326,232,270,202,23),(22,178,298,327,233,271,203,24),(45,252,163,146,85,348,119,110),(46,253,164,147,86,349,120,89),(47,254,165,148,87,350,121,90),(48,255,166,149,88,351,122,91),(49,256,167,150,67,352,123,92),(50,257,168,151,68,331,124,93),(51,258,169,152,69,332,125,94),(52,259,170,153,70,333,126,95),(53,260,171,154,71,334,127,96),(54,261,172,133,72,335,128,97),(55,262,173,134,73,336,129,98),(56,263,174,135,74,337,130,99),(57,264,175,136,75,338,131,100),(58,243,176,137,76,339,132,101),(59,244,155,138,77,340,111,102),(60,245,156,139,78,341,112,103),(61,246,157,140,79,342,113,104),(62,247,158,141,80,343,114,105),(63,248,159,142,81,344,115,106),(64,249,160,143,82,345,116,107),(65,250,161,144,83,346,117,108),(66,251,162,145,84,347,118,109)]])
100 conjugacy classes
| class | 1 | 2A | 2B | 2C | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 8A | 8B | 8C | 8D | 8E | 8F | 8G | 8H | 11A | ··· | 11E | 22A | ··· | 22O | 44A | ··· | 44T | 88A | ··· | 88AN |
| order | 1 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 11 | ··· | 11 | 22 | ··· | 22 | 44 | ··· | 44 | 88 | ··· | 88 |
| size | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 22 | 22 | 22 | 22 | 2 | 2 | 2 | 2 | 22 | 22 | 22 | 22 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
100 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | - | + | + | - | |||||||
| image | C1 | C2 | C2 | C2 | C4 | C8 | D4 | Q8 | M4(2) | D11 | D22 | Dic22 | C11⋊D4 | C4×D11 | C8×D11 | C88⋊C2 |
| kernel | Dic11⋊C8 | C2×C11⋊C8 | C4×Dic11 | C2×C88 | C2×Dic11 | Dic11 | C44 | C44 | C22 | C2×C8 | C2×C4 | C4 | C4 | C22 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 4 | 8 | 1 | 1 | 2 | 5 | 5 | 10 | 10 | 10 | 20 | 20 |
Matrix representation of Dic11⋊C8 ►in GL4(𝔽89) generated by
| 0 | 1 | 0 | 0 |
| 88 | 71 | 0 | 0 |
| 0 | 0 | 71 | 88 |
| 0 | 0 | 13 | 60 |
| 64 | 14 | 0 | 0 |
| 19 | 25 | 0 | 0 |
| 0 | 0 | 13 | 45 |
| 0 | 0 | 16 | 76 |
| 12 | 0 | 0 | 0 |
| 0 | 12 | 0 | 0 |
| 0 | 0 | 77 | 75 |
| 0 | 0 | 4 | 12 |
G:=sub<GL(4,GF(89))| [0,88,0,0,1,71,0,0,0,0,71,13,0,0,88,60],[64,19,0,0,14,25,0,0,0,0,13,16,0,0,45,76],[12,0,0,0,0,12,0,0,0,0,77,4,0,0,75,12] >;
Dic11⋊C8 in GAP, Magma, Sage, TeX
{\rm Dic}_{11}\rtimes C_8 % in TeX
G:=Group("Dic11:C8"); // GroupNames label
G:=SmallGroup(352,20);
// by ID
G=gap.SmallGroup(352,20);
# by ID
G:=PCGroup([6,-2,-2,-2,-2,-2,-11,48,121,31,86,11525]);
// Polycyclic
G:=Group<a,b,c|a^22=c^8=1,b^2=a^11,b*a*b^-1=a^-1,a*c=c*a,c*b*c^-1=a^11*b>;
// generators/relations
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