metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C44.2Q8, C4.2Dic22, C22.4SD16, C11⋊C8⋊2C4, C44.2(C2×C4), C4⋊C4.2D11, C11⋊1(C4.Q8), C22.3(C4⋊C4), (C2×C22).29D4, C4.12(C4×D11), (C2×C4).34D22, C44⋊C4.9C2, C2.1(Q8⋊D11), (C2×C44).9C22, C2.1(D4.D11), C2.4(Dic11⋊C4), C22.13(C11⋊D4), (C2×C11⋊C8).2C2, (C11×C4⋊C4).2C2, SmallGroup(352,14)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C4.Dic22
G = < a,b,c | a22=b8=1, c2=a11, bab-1=a-1, ac=ca, cbc-1=b3 >
Smallest permutation representation of C4.Dic22
►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)
(1 145 234 162 40 102 194 309)(2 144 235 161 41 101 195 330)(3 143 236 160 42 100 196 329)(4 142 237 159 43 99 197 328)(5 141 238 158 44 98 198 327)(6 140 239 157 23 97 177 326)(7 139 240 156 24 96 178 325)(8 138 241 155 25 95 179 324)(9 137 242 176 26 94 180 323)(10 136 221 175 27 93 181 322)(11 135 222 174 28 92 182 321)(12 134 223 173 29 91 183 320)(13 133 224 172 30 90 184 319)(14 154 225 171 31 89 185 318)(15 153 226 170 32 110 186 317)(16 152 227 169 33 109 187 316)(17 151 228 168 34 108 188 315)(18 150 229 167 35 107 189 314)(19 149 230 166 36 106 190 313)(20 148 231 165 37 105 191 312)(21 147 232 164 38 104 192 311)(22 146 233 163 39 103 193 310)(45 209 268 118 351 261 78 287)(46 208 269 117 352 260 79 308)(47 207 270 116 331 259 80 307)(48 206 271 115 332 258 81 306)(49 205 272 114 333 257 82 305)(50 204 273 113 334 256 83 304)(51 203 274 112 335 255 84 303)(52 202 275 111 336 254 85 302)(53 201 276 132 337 253 86 301)(54 200 277 131 338 252 87 300)(55 199 278 130 339 251 88 299)(56 220 279 129 340 250 67 298)(57 219 280 128 341 249 68 297)(58 218 281 127 342 248 69 296)(59 217 282 126 343 247 70 295)(60 216 283 125 344 246 71 294)(61 215 284 124 345 245 72 293)(62 214 285 123 346 244 73 292)(63 213 286 122 347 243 74 291)(64 212 265 121 348 264 75 290)(65 211 266 120 349 263 76 289)(66 210 267 119 350 262 77 288)
(1 86 12 75)(2 87 13 76)(3 88 14 77)(4 67 15 78)(5 68 16 79)(6 69 17 80)(7 70 18 81)(8 71 19 82)(9 72 20 83)(10 73 21 84)(11 74 22 85)(23 281 34 270)(24 282 35 271)(25 283 36 272)(26 284 37 273)(27 285 38 274)(28 286 39 275)(29 265 40 276)(30 266 41 277)(31 267 42 278)(32 268 43 279)(33 269 44 280)(45 197 56 186)(46 198 57 187)(47 177 58 188)(48 178 59 189)(49 179 60 190)(50 180 61 191)(51 181 62 192)(52 182 63 193)(53 183 64 194)(54 184 65 195)(55 185 66 196)(89 262 100 251)(90 263 101 252)(91 264 102 253)(92 243 103 254)(93 244 104 255)(94 245 105 256)(95 246 106 257)(96 247 107 258)(97 248 108 259)(98 249 109 260)(99 250 110 261)(111 321 122 310)(112 322 123 311)(113 323 124 312)(114 324 125 313)(115 325 126 314)(116 326 127 315)(117 327 128 316)(118 328 129 317)(119 329 130 318)(120 330 131 319)(121 309 132 320)(133 211 144 200)(134 212 145 201)(135 213 146 202)(136 214 147 203)(137 215 148 204)(138 216 149 205)(139 217 150 206)(140 218 151 207)(141 219 152 208)(142 220 153 209)(143 199 154 210)(155 294 166 305)(156 295 167 306)(157 296 168 307)(158 297 169 308)(159 298 170 287)(160 299 171 288)(161 300 172 289)(162 301 173 290)(163 302 174 291)(164 303 175 292)(165 304 176 293)(221 346 232 335)(222 347 233 336)(223 348 234 337)(224 349 235 338)(225 350 236 339)(226 351 237 340)(227 352 238 341)(228 331 239 342)(229 332 240 343)(230 333 241 344)(231 334 242 345)
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), (1,145,234,162,40,102,194,309)(2,144,235,161,41,101,195,330)(3,143,236,160,42,100,196,329)(4,142,237,159,43,99,197,328)(5,141,238,158,44,98,198,327)(6,140,239,157,23,97,177,326)(7,139,240,156,24,96,178,325)(8,138,241,155,25,95,179,324)(9,137,242,176,26,94,180,323)(10,136,221,175,27,93,181,322)(11,135,222,174,28,92,182,321)(12,134,223,173,29,91,183,320)(13,133,224,172,30,90,184,319)(14,154,225,171,31,89,185,318)(15,153,226,170,32,110,186,317)(16,152,227,169,33,109,187,316)(17,151,228,168,34,108,188,315)(18,150,229,167,35,107,189,314)(19,149,230,166,36,106,190,313)(20,148,231,165,37,105,191,312)(21,147,232,164,38,104,192,311)(22,146,233,163,39,103,193,310)(45,209,268,118,351,261,78,287)(46,208,269,117,352,260,79,308)(47,207,270,116,331,259,80,307)(48,206,271,115,332,258,81,306)(49,205,272,114,333,257,82,305)(50,204,273,113,334,256,83,304)(51,203,274,112,335,255,84,303)(52,202,275,111,336,254,85,302)(53,201,276,132,337,253,86,301)(54,200,277,131,338,252,87,300)(55,199,278,130,339,251,88,299)(56,220,279,129,340,250,67,298)(57,219,280,128,341,249,68,297)(58,218,281,127,342,248,69,296)(59,217,282,126,343,247,70,295)(60,216,283,125,344,246,71,294)(61,215,284,124,345,245,72,293)(62,214,285,123,346,244,73,292)(63,213,286,122,347,243,74,291)(64,212,265,121,348,264,75,290)(65,211,266,120,349,263,76,289)(66,210,267,119,350,262,77,288), (1,86,12,75)(2,87,13,76)(3,88,14,77)(4,67,15,78)(5,68,16,79)(6,69,17,80)(7,70,18,81)(8,71,19,82)(9,72,20,83)(10,73,21,84)(11,74,22,85)(23,281,34,270)(24,282,35,271)(25,283,36,272)(26,284,37,273)(27,285,38,274)(28,286,39,275)(29,265,40,276)(30,266,41,277)(31,267,42,278)(32,268,43,279)(33,269,44,280)(45,197,56,186)(46,198,57,187)(47,177,58,188)(48,178,59,189)(49,179,60,190)(50,180,61,191)(51,181,62,192)(52,182,63,193)(53,183,64,194)(54,184,65,195)(55,185,66,196)(89,262,100,251)(90,263,101,252)(91,264,102,253)(92,243,103,254)(93,244,104,255)(94,245,105,256)(95,246,106,257)(96,247,107,258)(97,248,108,259)(98,249,109,260)(99,250,110,261)(111,321,122,310)(112,322,123,311)(113,323,124,312)(114,324,125,313)(115,325,126,314)(116,326,127,315)(117,327,128,316)(118,328,129,317)(119,329,130,318)(120,330,131,319)(121,309,132,320)(133,211,144,200)(134,212,145,201)(135,213,146,202)(136,214,147,203)(137,215,148,204)(138,216,149,205)(139,217,150,206)(140,218,151,207)(141,219,152,208)(142,220,153,209)(143,199,154,210)(155,294,166,305)(156,295,167,306)(157,296,168,307)(158,297,169,308)(159,298,170,287)(160,299,171,288)(161,300,172,289)(162,301,173,290)(163,302,174,291)(164,303,175,292)(165,304,176,293)(221,346,232,335)(222,347,233,336)(223,348,234,337)(224,349,235,338)(225,350,236,339)(226,351,237,340)(227,352,238,341)(228,331,239,342)(229,332,240,343)(230,333,241,344)(231,334,242,345)>;
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), (1,145,234,162,40,102,194,309)(2,144,235,161,41,101,195,330)(3,143,236,160,42,100,196,329)(4,142,237,159,43,99,197,328)(5,141,238,158,44,98,198,327)(6,140,239,157,23,97,177,326)(7,139,240,156,24,96,178,325)(8,138,241,155,25,95,179,324)(9,137,242,176,26,94,180,323)(10,136,221,175,27,93,181,322)(11,135,222,174,28,92,182,321)(12,134,223,173,29,91,183,320)(13,133,224,172,30,90,184,319)(14,154,225,171,31,89,185,318)(15,153,226,170,32,110,186,317)(16,152,227,169,33,109,187,316)(17,151,228,168,34,108,188,315)(18,150,229,167,35,107,189,314)(19,149,230,166,36,106,190,313)(20,148,231,165,37,105,191,312)(21,147,232,164,38,104,192,311)(22,146,233,163,39,103,193,310)(45,209,268,118,351,261,78,287)(46,208,269,117,352,260,79,308)(47,207,270,116,331,259,80,307)(48,206,271,115,332,258,81,306)(49,205,272,114,333,257,82,305)(50,204,273,113,334,256,83,304)(51,203,274,112,335,255,84,303)(52,202,275,111,336,254,85,302)(53,201,276,132,337,253,86,301)(54,200,277,131,338,252,87,300)(55,199,278,130,339,251,88,299)(56,220,279,129,340,250,67,298)(57,219,280,128,341,249,68,297)(58,218,281,127,342,248,69,296)(59,217,282,126,343,247,70,295)(60,216,283,125,344,246,71,294)(61,215,284,124,345,245,72,293)(62,214,285,123,346,244,73,292)(63,213,286,122,347,243,74,291)(64,212,265,121,348,264,75,290)(65,211,266,120,349,263,76,289)(66,210,267,119,350,262,77,288), (1,86,12,75)(2,87,13,76)(3,88,14,77)(4,67,15,78)(5,68,16,79)(6,69,17,80)(7,70,18,81)(8,71,19,82)(9,72,20,83)(10,73,21,84)(11,74,22,85)(23,281,34,270)(24,282,35,271)(25,283,36,272)(26,284,37,273)(27,285,38,274)(28,286,39,275)(29,265,40,276)(30,266,41,277)(31,267,42,278)(32,268,43,279)(33,269,44,280)(45,197,56,186)(46,198,57,187)(47,177,58,188)(48,178,59,189)(49,179,60,190)(50,180,61,191)(51,181,62,192)(52,182,63,193)(53,183,64,194)(54,184,65,195)(55,185,66,196)(89,262,100,251)(90,263,101,252)(91,264,102,253)(92,243,103,254)(93,244,104,255)(94,245,105,256)(95,246,106,257)(96,247,107,258)(97,248,108,259)(98,249,109,260)(99,250,110,261)(111,321,122,310)(112,322,123,311)(113,323,124,312)(114,324,125,313)(115,325,126,314)(116,326,127,315)(117,327,128,316)(118,328,129,317)(119,329,130,318)(120,330,131,319)(121,309,132,320)(133,211,144,200)(134,212,145,201)(135,213,146,202)(136,214,147,203)(137,215,148,204)(138,216,149,205)(139,217,150,206)(140,218,151,207)(141,219,152,208)(142,220,153,209)(143,199,154,210)(155,294,166,305)(156,295,167,306)(157,296,168,307)(158,297,169,308)(159,298,170,287)(160,299,171,288)(161,300,172,289)(162,301,173,290)(163,302,174,291)(164,303,175,292)(165,304,176,293)(221,346,232,335)(222,347,233,336)(223,348,234,337)(224,349,235,338)(225,350,236,339)(226,351,237,340)(227,352,238,341)(228,331,239,342)(229,332,240,343)(230,333,241,344)(231,334,242,345) );
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)], [(1,145,234,162,40,102,194,309),(2,144,235,161,41,101,195,330),(3,143,236,160,42,100,196,329),(4,142,237,159,43,99,197,328),(5,141,238,158,44,98,198,327),(6,140,239,157,23,97,177,326),(7,139,240,156,24,96,178,325),(8,138,241,155,25,95,179,324),(9,137,242,176,26,94,180,323),(10,136,221,175,27,93,181,322),(11,135,222,174,28,92,182,321),(12,134,223,173,29,91,183,320),(13,133,224,172,30,90,184,319),(14,154,225,171,31,89,185,318),(15,153,226,170,32,110,186,317),(16,152,227,169,33,109,187,316),(17,151,228,168,34,108,188,315),(18,150,229,167,35,107,189,314),(19,149,230,166,36,106,190,313),(20,148,231,165,37,105,191,312),(21,147,232,164,38,104,192,311),(22,146,233,163,39,103,193,310),(45,209,268,118,351,261,78,287),(46,208,269,117,352,260,79,308),(47,207,270,116,331,259,80,307),(48,206,271,115,332,258,81,306),(49,205,272,114,333,257,82,305),(50,204,273,113,334,256,83,304),(51,203,274,112,335,255,84,303),(52,202,275,111,336,254,85,302),(53,201,276,132,337,253,86,301),(54,200,277,131,338,252,87,300),(55,199,278,130,339,251,88,299),(56,220,279,129,340,250,67,298),(57,219,280,128,341,249,68,297),(58,218,281,127,342,248,69,296),(59,217,282,126,343,247,70,295),(60,216,283,125,344,246,71,294),(61,215,284,124,345,245,72,293),(62,214,285,123,346,244,73,292),(63,213,286,122,347,243,74,291),(64,212,265,121,348,264,75,290),(65,211,266,120,349,263,76,289),(66,210,267,119,350,262,77,288)], [(1,86,12,75),(2,87,13,76),(3,88,14,77),(4,67,15,78),(5,68,16,79),(6,69,17,80),(7,70,18,81),(8,71,19,82),(9,72,20,83),(10,73,21,84),(11,74,22,85),(23,281,34,270),(24,282,35,271),(25,283,36,272),(26,284,37,273),(27,285,38,274),(28,286,39,275),(29,265,40,276),(30,266,41,277),(31,267,42,278),(32,268,43,279),(33,269,44,280),(45,197,56,186),(46,198,57,187),(47,177,58,188),(48,178,59,189),(49,179,60,190),(50,180,61,191),(51,181,62,192),(52,182,63,193),(53,183,64,194),(54,184,65,195),(55,185,66,196),(89,262,100,251),(90,263,101,252),(91,264,102,253),(92,243,103,254),(93,244,104,255),(94,245,105,256),(95,246,106,257),(96,247,107,258),(97,248,108,259),(98,249,109,260),(99,250,110,261),(111,321,122,310),(112,322,123,311),(113,323,124,312),(114,324,125,313),(115,325,126,314),(116,326,127,315),(117,327,128,316),(118,328,129,317),(119,329,130,318),(120,330,131,319),(121,309,132,320),(133,211,144,200),(134,212,145,201),(135,213,146,202),(136,214,147,203),(137,215,148,204),(138,216,149,205),(139,217,150,206),(140,218,151,207),(141,219,152,208),(142,220,153,209),(143,199,154,210),(155,294,166,305),(156,295,167,306),(157,296,168,307),(158,297,169,308),(159,298,170,287),(160,299,171,288),(161,300,172,289),(162,301,173,290),(163,302,174,291),(164,303,175,292),(165,304,176,293),(221,346,232,335),(222,347,233,336),(223,348,234,337),(224,349,235,338),(225,350,236,339),(226,351,237,340),(227,352,238,341),(228,331,239,342),(229,332,240,343),(230,333,241,344),(231,334,242,345)]])
64 conjugacy classes
| class | 1 | 2A | 2B | 2C | 4A | 4B | 4C | 4D | 4E | 4F | 8A | 8B | 8C | 8D | 11A | ··· | 11E | 22A | ··· | 22O | 44A | ··· | 44AD |
| order | 1 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 8 | 8 | 8 | 8 | 11 | ··· | 11 | 22 | ··· | 22 | 44 | ··· | 44 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 4 | 4 | 44 | 44 | 22 | 22 | 22 | 22 | 2 | ··· | 2 | 2 | ··· | 2 | 4 | ··· | 4 |
64 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | - | + | + | + | - | - | + | ||||
| image | C1 | C2 | C2 | C2 | C4 | Q8 | D4 | SD16 | D11 | D22 | Dic22 | C4×D11 | C11⋊D4 | D4.D11 | Q8⋊D11 |
| kernel | C4.Dic22 | C2×C11⋊C8 | C44⋊C4 | C11×C4⋊C4 | C11⋊C8 | C44 | C2×C22 | C22 | C4⋊C4 | C2×C4 | C4 | C4 | C22 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 4 | 1 | 1 | 4 | 5 | 5 | 10 | 10 | 10 | 5 | 5 |
Matrix representation of C4.Dic22 ►in GL6(𝔽89)
| 4 | 0 | 0 | 0 | 0 | 0 |
| 56 | 67 | 0 | 0 | 0 | 0 |
| 0 | 0 | 88 | 0 | 0 | 0 |
| 0 | 0 | 0 | 88 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 84 | 50 | 0 | 0 | 0 | 0 |
| 28 | 5 | 0 | 0 | 0 | 0 |
| 0 | 0 | 65 | 20 | 0 | 0 |
| 0 | 0 | 29 | 24 | 0 | 0 |
| 0 | 0 | 0 | 0 | 6 | 52 |
| 0 | 0 | 0 | 0 | 82 | 43 |
| 88 | 0 | 0 | 0 | 0 | 0 |
| 0 | 88 | 0 | 0 | 0 | 0 |
| 0 | 0 | 45 | 79 | 0 | 0 |
| 0 | 0 | 78 | 44 | 0 | 0 |
| 0 | 0 | 0 | 0 | 75 | 84 |
| 0 | 0 | 0 | 0 | 39 | 14 |
G:=sub<GL(6,GF(89))| [4,56,0,0,0,0,0,67,0,0,0,0,0,0,88,0,0,0,0,0,0,88,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[84,28,0,0,0,0,50,5,0,0,0,0,0,0,65,29,0,0,0,0,20,24,0,0,0,0,0,0,6,82,0,0,0,0,52,43],[88,0,0,0,0,0,0,88,0,0,0,0,0,0,45,78,0,0,0,0,79,44,0,0,0,0,0,0,75,39,0,0,0,0,84,14] >;
C4.Dic22 in GAP, Magma, Sage, TeX
C_4.{\rm Dic}_{22} % in TeX
G:=Group("C4.Dic22"); // GroupNames label
G:=SmallGroup(352,14);
// by ID
G=gap.SmallGroup(352,14);
# by ID
G:=PCGroup([6,-2,-2,-2,-2,-2,-11,48,313,31,297,69,11525]);
// Polycyclic
G:=Group<a,b,c|a^22=b^8=1,c^2=a^11,b*a*b^-1=a^-1,a*c=c*a,c*b*c^-1=b^3>;
// generators/relations
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