direct product, metacyclic, supersoluble, monomial, A-group, 2-hyperelementary
Aliases: C8×Dic11, C88⋊3C4, C22.3C42, C11⋊C8⋊5C4, C11⋊2(C4×C8), C22.3(C2×C8), C2.2(C8×D11), (C2×C88).11C2, C44.40(C2×C4), (C2×C4).90D22, (C2×C8).10D11, C4.20(C4×D11), C2.2(C4×Dic11), C22.8(C4×D11), (C2×Dic11).7C4, C4.12(C2×Dic11), (C2×C44).104C22, (C4×Dic11).10C2, (C2×C11⋊C8).12C2, (C2×C22).9(C2×C4), SmallGroup(352,19)
Series: Derived ►Chief ►Lower central ►Upper central
| C11 — C8×Dic11 |
Generators and relations for C8×Dic11
G = < a,b,c | a8=b22=1, c2=b11, ab=ba, ac=ca, cbc-1=b-1 >
Smallest permutation representation of C8×Dic11
►Regular action on 352 points
Generators in S352
(1 65 313 33 201 85 307 334)(2 66 314 34 202 86 308 335)(3 45 315 35 203 87 287 336)(4 46 316 36 204 88 288 337)(5 47 317 37 205 67 289 338)(6 48 318 38 206 68 290 339)(7 49 319 39 207 69 291 340)(8 50 320 40 208 70 292 341)(9 51 321 41 209 71 293 342)(10 52 322 42 210 72 294 343)(11 53 323 43 211 73 295 344)(12 54 324 44 212 74 296 345)(13 55 325 23 213 75 297 346)(14 56 326 24 214 76 298 347)(15 57 327 25 215 77 299 348)(16 58 328 26 216 78 300 349)(17 59 329 27 217 79 301 350)(18 60 330 28 218 80 302 351)(19 61 309 29 219 81 303 352)(20 62 310 30 220 82 304 331)(21 63 311 31 199 83 305 332)(22 64 312 32 200 84 306 333)(89 258 242 277 125 147 180 170)(90 259 221 278 126 148 181 171)(91 260 222 279 127 149 182 172)(92 261 223 280 128 150 183 173)(93 262 224 281 129 151 184 174)(94 263 225 282 130 152 185 175)(95 264 226 283 131 153 186 176)(96 243 227 284 132 154 187 155)(97 244 228 285 111 133 188 156)(98 245 229 286 112 134 189 157)(99 246 230 265 113 135 190 158)(100 247 231 266 114 136 191 159)(101 248 232 267 115 137 192 160)(102 249 233 268 116 138 193 161)(103 250 234 269 117 139 194 162)(104 251 235 270 118 140 195 163)(105 252 236 271 119 141 196 164)(106 253 237 272 120 142 197 165)(107 254 238 273 121 143 198 166)(108 255 239 274 122 144 177 167)(109 256 240 275 123 145 178 168)(110 257 241 276 124 146 179 169)
(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)
(1 136 12 147)(2 135 13 146)(3 134 14 145)(4 133 15 144)(5 154 16 143)(6 153 17 142)(7 152 18 141)(8 151 19 140)(9 150 20 139)(10 149 21 138)(11 148 22 137)(23 110 34 99)(24 109 35 98)(25 108 36 97)(26 107 37 96)(27 106 38 95)(28 105 39 94)(29 104 40 93)(30 103 41 92)(31 102 42 91)(32 101 43 90)(33 100 44 89)(45 189 56 178)(46 188 57 177)(47 187 58 198)(48 186 59 197)(49 185 60 196)(50 184 61 195)(51 183 62 194)(52 182 63 193)(53 181 64 192)(54 180 65 191)(55 179 66 190)(67 227 78 238)(68 226 79 237)(69 225 80 236)(70 224 81 235)(71 223 82 234)(72 222 83 233)(73 221 84 232)(74 242 85 231)(75 241 86 230)(76 240 87 229)(77 239 88 228)(111 348 122 337)(112 347 123 336)(113 346 124 335)(114 345 125 334)(115 344 126 333)(116 343 127 332)(117 342 128 331)(118 341 129 352)(119 340 130 351)(120 339 131 350)(121 338 132 349)(155 328 166 317)(156 327 167 316)(157 326 168 315)(158 325 169 314)(159 324 170 313)(160 323 171 312)(161 322 172 311)(162 321 173 310)(163 320 174 309)(164 319 175 330)(165 318 176 329)(199 249 210 260)(200 248 211 259)(201 247 212 258)(202 246 213 257)(203 245 214 256)(204 244 215 255)(205 243 216 254)(206 264 217 253)(207 263 218 252)(208 262 219 251)(209 261 220 250)(265 297 276 308)(266 296 277 307)(267 295 278 306)(268 294 279 305)(269 293 280 304)(270 292 281 303)(271 291 282 302)(272 290 283 301)(273 289 284 300)(274 288 285 299)(275 287 286 298)
G:=sub<Sym(352)| (1,65,313,33,201,85,307,334)(2,66,314,34,202,86,308,335)(3,45,315,35,203,87,287,336)(4,46,316,36,204,88,288,337)(5,47,317,37,205,67,289,338)(6,48,318,38,206,68,290,339)(7,49,319,39,207,69,291,340)(8,50,320,40,208,70,292,341)(9,51,321,41,209,71,293,342)(10,52,322,42,210,72,294,343)(11,53,323,43,211,73,295,344)(12,54,324,44,212,74,296,345)(13,55,325,23,213,75,297,346)(14,56,326,24,214,76,298,347)(15,57,327,25,215,77,299,348)(16,58,328,26,216,78,300,349)(17,59,329,27,217,79,301,350)(18,60,330,28,218,80,302,351)(19,61,309,29,219,81,303,352)(20,62,310,30,220,82,304,331)(21,63,311,31,199,83,305,332)(22,64,312,32,200,84,306,333)(89,258,242,277,125,147,180,170)(90,259,221,278,126,148,181,171)(91,260,222,279,127,149,182,172)(92,261,223,280,128,150,183,173)(93,262,224,281,129,151,184,174)(94,263,225,282,130,152,185,175)(95,264,226,283,131,153,186,176)(96,243,227,284,132,154,187,155)(97,244,228,285,111,133,188,156)(98,245,229,286,112,134,189,157)(99,246,230,265,113,135,190,158)(100,247,231,266,114,136,191,159)(101,248,232,267,115,137,192,160)(102,249,233,268,116,138,193,161)(103,250,234,269,117,139,194,162)(104,251,235,270,118,140,195,163)(105,252,236,271,119,141,196,164)(106,253,237,272,120,142,197,165)(107,254,238,273,121,143,198,166)(108,255,239,274,122,144,177,167)(109,256,240,275,123,145,178,168)(110,257,241,276,124,146,179,169), (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), (1,136,12,147)(2,135,13,146)(3,134,14,145)(4,133,15,144)(5,154,16,143)(6,153,17,142)(7,152,18,141)(8,151,19,140)(9,150,20,139)(10,149,21,138)(11,148,22,137)(23,110,34,99)(24,109,35,98)(25,108,36,97)(26,107,37,96)(27,106,38,95)(28,105,39,94)(29,104,40,93)(30,103,41,92)(31,102,42,91)(32,101,43,90)(33,100,44,89)(45,189,56,178)(46,188,57,177)(47,187,58,198)(48,186,59,197)(49,185,60,196)(50,184,61,195)(51,183,62,194)(52,182,63,193)(53,181,64,192)(54,180,65,191)(55,179,66,190)(67,227,78,238)(68,226,79,237)(69,225,80,236)(70,224,81,235)(71,223,82,234)(72,222,83,233)(73,221,84,232)(74,242,85,231)(75,241,86,230)(76,240,87,229)(77,239,88,228)(111,348,122,337)(112,347,123,336)(113,346,124,335)(114,345,125,334)(115,344,126,333)(116,343,127,332)(117,342,128,331)(118,341,129,352)(119,340,130,351)(120,339,131,350)(121,338,132,349)(155,328,166,317)(156,327,167,316)(157,326,168,315)(158,325,169,314)(159,324,170,313)(160,323,171,312)(161,322,172,311)(162,321,173,310)(163,320,174,309)(164,319,175,330)(165,318,176,329)(199,249,210,260)(200,248,211,259)(201,247,212,258)(202,246,213,257)(203,245,214,256)(204,244,215,255)(205,243,216,254)(206,264,217,253)(207,263,218,252)(208,262,219,251)(209,261,220,250)(265,297,276,308)(266,296,277,307)(267,295,278,306)(268,294,279,305)(269,293,280,304)(270,292,281,303)(271,291,282,302)(272,290,283,301)(273,289,284,300)(274,288,285,299)(275,287,286,298)>;
G:=Group( (1,65,313,33,201,85,307,334)(2,66,314,34,202,86,308,335)(3,45,315,35,203,87,287,336)(4,46,316,36,204,88,288,337)(5,47,317,37,205,67,289,338)(6,48,318,38,206,68,290,339)(7,49,319,39,207,69,291,340)(8,50,320,40,208,70,292,341)(9,51,321,41,209,71,293,342)(10,52,322,42,210,72,294,343)(11,53,323,43,211,73,295,344)(12,54,324,44,212,74,296,345)(13,55,325,23,213,75,297,346)(14,56,326,24,214,76,298,347)(15,57,327,25,215,77,299,348)(16,58,328,26,216,78,300,349)(17,59,329,27,217,79,301,350)(18,60,330,28,218,80,302,351)(19,61,309,29,219,81,303,352)(20,62,310,30,220,82,304,331)(21,63,311,31,199,83,305,332)(22,64,312,32,200,84,306,333)(89,258,242,277,125,147,180,170)(90,259,221,278,126,148,181,171)(91,260,222,279,127,149,182,172)(92,261,223,280,128,150,183,173)(93,262,224,281,129,151,184,174)(94,263,225,282,130,152,185,175)(95,264,226,283,131,153,186,176)(96,243,227,284,132,154,187,155)(97,244,228,285,111,133,188,156)(98,245,229,286,112,134,189,157)(99,246,230,265,113,135,190,158)(100,247,231,266,114,136,191,159)(101,248,232,267,115,137,192,160)(102,249,233,268,116,138,193,161)(103,250,234,269,117,139,194,162)(104,251,235,270,118,140,195,163)(105,252,236,271,119,141,196,164)(106,253,237,272,120,142,197,165)(107,254,238,273,121,143,198,166)(108,255,239,274,122,144,177,167)(109,256,240,275,123,145,178,168)(110,257,241,276,124,146,179,169), (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), (1,136,12,147)(2,135,13,146)(3,134,14,145)(4,133,15,144)(5,154,16,143)(6,153,17,142)(7,152,18,141)(8,151,19,140)(9,150,20,139)(10,149,21,138)(11,148,22,137)(23,110,34,99)(24,109,35,98)(25,108,36,97)(26,107,37,96)(27,106,38,95)(28,105,39,94)(29,104,40,93)(30,103,41,92)(31,102,42,91)(32,101,43,90)(33,100,44,89)(45,189,56,178)(46,188,57,177)(47,187,58,198)(48,186,59,197)(49,185,60,196)(50,184,61,195)(51,183,62,194)(52,182,63,193)(53,181,64,192)(54,180,65,191)(55,179,66,190)(67,227,78,238)(68,226,79,237)(69,225,80,236)(70,224,81,235)(71,223,82,234)(72,222,83,233)(73,221,84,232)(74,242,85,231)(75,241,86,230)(76,240,87,229)(77,239,88,228)(111,348,122,337)(112,347,123,336)(113,346,124,335)(114,345,125,334)(115,344,126,333)(116,343,127,332)(117,342,128,331)(118,341,129,352)(119,340,130,351)(120,339,131,350)(121,338,132,349)(155,328,166,317)(156,327,167,316)(157,326,168,315)(158,325,169,314)(159,324,170,313)(160,323,171,312)(161,322,172,311)(162,321,173,310)(163,320,174,309)(164,319,175,330)(165,318,176,329)(199,249,210,260)(200,248,211,259)(201,247,212,258)(202,246,213,257)(203,245,214,256)(204,244,215,255)(205,243,216,254)(206,264,217,253)(207,263,218,252)(208,262,219,251)(209,261,220,250)(265,297,276,308)(266,296,277,307)(267,295,278,306)(268,294,279,305)(269,293,280,304)(270,292,281,303)(271,291,282,302)(272,290,283,301)(273,289,284,300)(274,288,285,299)(275,287,286,298) );
G=PermutationGroup([[(1,65,313,33,201,85,307,334),(2,66,314,34,202,86,308,335),(3,45,315,35,203,87,287,336),(4,46,316,36,204,88,288,337),(5,47,317,37,205,67,289,338),(6,48,318,38,206,68,290,339),(7,49,319,39,207,69,291,340),(8,50,320,40,208,70,292,341),(9,51,321,41,209,71,293,342),(10,52,322,42,210,72,294,343),(11,53,323,43,211,73,295,344),(12,54,324,44,212,74,296,345),(13,55,325,23,213,75,297,346),(14,56,326,24,214,76,298,347),(15,57,327,25,215,77,299,348),(16,58,328,26,216,78,300,349),(17,59,329,27,217,79,301,350),(18,60,330,28,218,80,302,351),(19,61,309,29,219,81,303,352),(20,62,310,30,220,82,304,331),(21,63,311,31,199,83,305,332),(22,64,312,32,200,84,306,333),(89,258,242,277,125,147,180,170),(90,259,221,278,126,148,181,171),(91,260,222,279,127,149,182,172),(92,261,223,280,128,150,183,173),(93,262,224,281,129,151,184,174),(94,263,225,282,130,152,185,175),(95,264,226,283,131,153,186,176),(96,243,227,284,132,154,187,155),(97,244,228,285,111,133,188,156),(98,245,229,286,112,134,189,157),(99,246,230,265,113,135,190,158),(100,247,231,266,114,136,191,159),(101,248,232,267,115,137,192,160),(102,249,233,268,116,138,193,161),(103,250,234,269,117,139,194,162),(104,251,235,270,118,140,195,163),(105,252,236,271,119,141,196,164),(106,253,237,272,120,142,197,165),(107,254,238,273,121,143,198,166),(108,255,239,274,122,144,177,167),(109,256,240,275,123,145,178,168),(110,257,241,276,124,146,179,169)], [(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)], [(1,136,12,147),(2,135,13,146),(3,134,14,145),(4,133,15,144),(5,154,16,143),(6,153,17,142),(7,152,18,141),(8,151,19,140),(9,150,20,139),(10,149,21,138),(11,148,22,137),(23,110,34,99),(24,109,35,98),(25,108,36,97),(26,107,37,96),(27,106,38,95),(28,105,39,94),(29,104,40,93),(30,103,41,92),(31,102,42,91),(32,101,43,90),(33,100,44,89),(45,189,56,178),(46,188,57,177),(47,187,58,198),(48,186,59,197),(49,185,60,196),(50,184,61,195),(51,183,62,194),(52,182,63,193),(53,181,64,192),(54,180,65,191),(55,179,66,190),(67,227,78,238),(68,226,79,237),(69,225,80,236),(70,224,81,235),(71,223,82,234),(72,222,83,233),(73,221,84,232),(74,242,85,231),(75,241,86,230),(76,240,87,229),(77,239,88,228),(111,348,122,337),(112,347,123,336),(113,346,124,335),(114,345,125,334),(115,344,126,333),(116,343,127,332),(117,342,128,331),(118,341,129,352),(119,340,130,351),(120,339,131,350),(121,338,132,349),(155,328,166,317),(156,327,167,316),(157,326,168,315),(158,325,169,314),(159,324,170,313),(160,323,171,312),(161,322,172,311),(162,321,173,310),(163,320,174,309),(164,319,175,330),(165,318,176,329),(199,249,210,260),(200,248,211,259),(201,247,212,258),(202,246,213,257),(203,245,214,256),(204,244,215,255),(205,243,216,254),(206,264,217,253),(207,263,218,252),(208,262,219,251),(209,261,220,250),(265,297,276,308),(266,296,277,307),(267,295,278,306),(268,294,279,305),(269,293,280,304),(270,292,281,303),(271,291,282,302),(272,290,283,301),(273,289,284,300),(274,288,285,299),(275,287,286,298)]])
112 conjugacy classes
| class | 1 | 2A | 2B | 2C | 4A | 4B | 4C | 4D | 4E | ··· | 4L | 8A | ··· | 8H | 8I | ··· | 8P | 11A | ··· | 11E | 22A | ··· | 22O | 44A | ··· | 44T | 88A | ··· | 88AN |
| order | 1 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 8 | ··· | 8 | 8 | ··· | 8 | 11 | ··· | 11 | 22 | ··· | 22 | 44 | ··· | 44 | 88 | ··· | 88 |
| size | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 11 | ··· | 11 | 1 | ··· | 1 | 11 | ··· | 11 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
112 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | - | + | |||||||
| image | C1 | C2 | C2 | C2 | C4 | C4 | C4 | C8 | D11 | Dic11 | D22 | C4×D11 | C4×D11 | C8×D11 |
| kernel | C8×Dic11 | C2×C11⋊C8 | C4×Dic11 | C2×C88 | C11⋊C8 | C88 | C2×Dic11 | Dic11 | C2×C8 | C8 | C2×C4 | C4 | C22 | C2 |
| # reps | 1 | 1 | 1 | 1 | 4 | 4 | 4 | 16 | 5 | 10 | 5 | 10 | 10 | 40 |
Matrix representation of C8×Dic11 ►in GL4(𝔽89) generated by
| 77 | 0 | 0 | 0 |
| 0 | 34 | 0 | 0 |
| 0 | 0 | 88 | 0 |
| 0 | 0 | 0 | 88 |
| 88 | 0 | 0 | 0 |
| 0 | 88 | 0 | 0 |
| 0 | 0 | 0 | 1 |
| 0 | 0 | 88 | 47 |
| 34 | 0 | 0 | 0 |
| 0 | 34 | 0 | 0 |
| 0 | 0 | 37 | 68 |
| 0 | 0 | 27 | 52 |
G:=sub<GL(4,GF(89))| [77,0,0,0,0,34,0,0,0,0,88,0,0,0,0,88],[88,0,0,0,0,88,0,0,0,0,0,88,0,0,1,47],[34,0,0,0,0,34,0,0,0,0,37,27,0,0,68,52] >;
C8×Dic11 in GAP, Magma, Sage, TeX
C_8\times {\rm Dic}_{11} % in TeX
G:=Group("C8xDic11"); // GroupNames label
G:=SmallGroup(352,19);
// by ID
G=gap.SmallGroup(352,19);
# by ID
G:=PCGroup([6,-2,-2,-2,-2,-2,-11,24,55,69,11525]);
// Polycyclic
G:=Group<a,b,c|a^8=b^22=1,c^2=b^11,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations
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