metacyclic, supersoluble, monomial, 2-hyperelementary
Aliases: C88⋊2C4, C44.4Q8, C8⋊2Dic11, C22.2SD16, C4.4Dic22, C22.8D44, (C2×C88).8C2, (C2×C8).6D11, C11⋊2(C4.Q8), C22.5(C4⋊C4), C44.33(C2×C4), (C2×C4).68D22, (C2×C22).13D4, C44⋊C4.2C2, C4.6(C2×Dic11), C2.3(C44⋊C4), C2.2(C8⋊D11), (C2×C44).81C22, SmallGroup(352,23)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C44.4Q8
G = < a,b,c | a44=1, b4=a22, c2=a11b2, ab=ba, cac-1=a-1, cbc-1=b3 >
Smallest permutation representation of C44.4Q8
►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)
(1 306 171 327 23 284 149 349)(2 307 172 328 24 285 150 350)(3 308 173 329 25 286 151 351)(4 265 174 330 26 287 152 352)(5 266 175 331 27 288 153 309)(6 267 176 332 28 289 154 310)(7 268 133 333 29 290 155 311)(8 269 134 334 30 291 156 312)(9 270 135 335 31 292 157 313)(10 271 136 336 32 293 158 314)(11 272 137 337 33 294 159 315)(12 273 138 338 34 295 160 316)(13 274 139 339 35 296 161 317)(14 275 140 340 36 297 162 318)(15 276 141 341 37 298 163 319)(16 277 142 342 38 299 164 320)(17 278 143 343 39 300 165 321)(18 279 144 344 40 301 166 322)(19 280 145 345 41 302 167 323)(20 281 146 346 42 303 168 324)(21 282 147 347 43 304 169 325)(22 283 148 348 44 305 170 326)(45 216 259 108 67 194 237 130)(46 217 260 109 68 195 238 131)(47 218 261 110 69 196 239 132)(48 219 262 111 70 197 240 89)(49 220 263 112 71 198 241 90)(50 177 264 113 72 199 242 91)(51 178 221 114 73 200 243 92)(52 179 222 115 74 201 244 93)(53 180 223 116 75 202 245 94)(54 181 224 117 76 203 246 95)(55 182 225 118 77 204 247 96)(56 183 226 119 78 205 248 97)(57 184 227 120 79 206 249 98)(58 185 228 121 80 207 250 99)(59 186 229 122 81 208 251 100)(60 187 230 123 82 209 252 101)(61 188 231 124 83 210 253 102)(62 189 232 125 84 211 254 103)(63 190 233 126 85 212 255 104)(64 191 234 127 86 213 256 105)(65 192 235 128 87 214 257 106)(66 193 236 129 88 215 258 107)
(1 194 138 97)(2 193 139 96)(3 192 140 95)(4 191 141 94)(5 190 142 93)(6 189 143 92)(7 188 144 91)(8 187 145 90)(9 186 146 89)(10 185 147 132)(11 184 148 131)(12 183 149 130)(13 182 150 129)(14 181 151 128)(15 180 152 127)(16 179 153 126)(17 178 154 125)(18 177 155 124)(19 220 156 123)(20 219 157 122)(21 218 158 121)(22 217 159 120)(23 216 160 119)(24 215 161 118)(25 214 162 117)(26 213 163 116)(27 212 164 115)(28 211 165 114)(29 210 166 113)(30 209 167 112)(31 208 168 111)(32 207 169 110)(33 206 170 109)(34 205 171 108)(35 204 172 107)(36 203 173 106)(37 202 174 105)(38 201 175 104)(39 200 176 103)(40 199 133 102)(41 198 134 101)(42 197 135 100)(43 196 136 99)(44 195 137 98)(45 338 226 306)(46 337 227 305)(47 336 228 304)(48 335 229 303)(49 334 230 302)(50 333 231 301)(51 332 232 300)(52 331 233 299)(53 330 234 298)(54 329 235 297)(55 328 236 296)(56 327 237 295)(57 326 238 294)(58 325 239 293)(59 324 240 292)(60 323 241 291)(61 322 242 290)(62 321 243 289)(63 320 244 288)(64 319 245 287)(65 318 246 286)(66 317 247 285)(67 316 248 284)(68 315 249 283)(69 314 250 282)(70 313 251 281)(71 312 252 280)(72 311 253 279)(73 310 254 278)(74 309 255 277)(75 352 256 276)(76 351 257 275)(77 350 258 274)(78 349 259 273)(79 348 260 272)(80 347 261 271)(81 346 262 270)(82 345 263 269)(83 344 264 268)(84 343 221 267)(85 342 222 266)(86 341 223 265)(87 340 224 308)(88 339 225 307)
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), (1,306,171,327,23,284,149,349)(2,307,172,328,24,285,150,350)(3,308,173,329,25,286,151,351)(4,265,174,330,26,287,152,352)(5,266,175,331,27,288,153,309)(6,267,176,332,28,289,154,310)(7,268,133,333,29,290,155,311)(8,269,134,334,30,291,156,312)(9,270,135,335,31,292,157,313)(10,271,136,336,32,293,158,314)(11,272,137,337,33,294,159,315)(12,273,138,338,34,295,160,316)(13,274,139,339,35,296,161,317)(14,275,140,340,36,297,162,318)(15,276,141,341,37,298,163,319)(16,277,142,342,38,299,164,320)(17,278,143,343,39,300,165,321)(18,279,144,344,40,301,166,322)(19,280,145,345,41,302,167,323)(20,281,146,346,42,303,168,324)(21,282,147,347,43,304,169,325)(22,283,148,348,44,305,170,326)(45,216,259,108,67,194,237,130)(46,217,260,109,68,195,238,131)(47,218,261,110,69,196,239,132)(48,219,262,111,70,197,240,89)(49,220,263,112,71,198,241,90)(50,177,264,113,72,199,242,91)(51,178,221,114,73,200,243,92)(52,179,222,115,74,201,244,93)(53,180,223,116,75,202,245,94)(54,181,224,117,76,203,246,95)(55,182,225,118,77,204,247,96)(56,183,226,119,78,205,248,97)(57,184,227,120,79,206,249,98)(58,185,228,121,80,207,250,99)(59,186,229,122,81,208,251,100)(60,187,230,123,82,209,252,101)(61,188,231,124,83,210,253,102)(62,189,232,125,84,211,254,103)(63,190,233,126,85,212,255,104)(64,191,234,127,86,213,256,105)(65,192,235,128,87,214,257,106)(66,193,236,129,88,215,258,107), (1,194,138,97)(2,193,139,96)(3,192,140,95)(4,191,141,94)(5,190,142,93)(6,189,143,92)(7,188,144,91)(8,187,145,90)(9,186,146,89)(10,185,147,132)(11,184,148,131)(12,183,149,130)(13,182,150,129)(14,181,151,128)(15,180,152,127)(16,179,153,126)(17,178,154,125)(18,177,155,124)(19,220,156,123)(20,219,157,122)(21,218,158,121)(22,217,159,120)(23,216,160,119)(24,215,161,118)(25,214,162,117)(26,213,163,116)(27,212,164,115)(28,211,165,114)(29,210,166,113)(30,209,167,112)(31,208,168,111)(32,207,169,110)(33,206,170,109)(34,205,171,108)(35,204,172,107)(36,203,173,106)(37,202,174,105)(38,201,175,104)(39,200,176,103)(40,199,133,102)(41,198,134,101)(42,197,135,100)(43,196,136,99)(44,195,137,98)(45,338,226,306)(46,337,227,305)(47,336,228,304)(48,335,229,303)(49,334,230,302)(50,333,231,301)(51,332,232,300)(52,331,233,299)(53,330,234,298)(54,329,235,297)(55,328,236,296)(56,327,237,295)(57,326,238,294)(58,325,239,293)(59,324,240,292)(60,323,241,291)(61,322,242,290)(62,321,243,289)(63,320,244,288)(64,319,245,287)(65,318,246,286)(66,317,247,285)(67,316,248,284)(68,315,249,283)(69,314,250,282)(70,313,251,281)(71,312,252,280)(72,311,253,279)(73,310,254,278)(74,309,255,277)(75,352,256,276)(76,351,257,275)(77,350,258,274)(78,349,259,273)(79,348,260,272)(80,347,261,271)(81,346,262,270)(82,345,263,269)(83,344,264,268)(84,343,221,267)(85,342,222,266)(86,341,223,265)(87,340,224,308)(88,339,225,307)>;
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), (1,306,171,327,23,284,149,349)(2,307,172,328,24,285,150,350)(3,308,173,329,25,286,151,351)(4,265,174,330,26,287,152,352)(5,266,175,331,27,288,153,309)(6,267,176,332,28,289,154,310)(7,268,133,333,29,290,155,311)(8,269,134,334,30,291,156,312)(9,270,135,335,31,292,157,313)(10,271,136,336,32,293,158,314)(11,272,137,337,33,294,159,315)(12,273,138,338,34,295,160,316)(13,274,139,339,35,296,161,317)(14,275,140,340,36,297,162,318)(15,276,141,341,37,298,163,319)(16,277,142,342,38,299,164,320)(17,278,143,343,39,300,165,321)(18,279,144,344,40,301,166,322)(19,280,145,345,41,302,167,323)(20,281,146,346,42,303,168,324)(21,282,147,347,43,304,169,325)(22,283,148,348,44,305,170,326)(45,216,259,108,67,194,237,130)(46,217,260,109,68,195,238,131)(47,218,261,110,69,196,239,132)(48,219,262,111,70,197,240,89)(49,220,263,112,71,198,241,90)(50,177,264,113,72,199,242,91)(51,178,221,114,73,200,243,92)(52,179,222,115,74,201,244,93)(53,180,223,116,75,202,245,94)(54,181,224,117,76,203,246,95)(55,182,225,118,77,204,247,96)(56,183,226,119,78,205,248,97)(57,184,227,120,79,206,249,98)(58,185,228,121,80,207,250,99)(59,186,229,122,81,208,251,100)(60,187,230,123,82,209,252,101)(61,188,231,124,83,210,253,102)(62,189,232,125,84,211,254,103)(63,190,233,126,85,212,255,104)(64,191,234,127,86,213,256,105)(65,192,235,128,87,214,257,106)(66,193,236,129,88,215,258,107), (1,194,138,97)(2,193,139,96)(3,192,140,95)(4,191,141,94)(5,190,142,93)(6,189,143,92)(7,188,144,91)(8,187,145,90)(9,186,146,89)(10,185,147,132)(11,184,148,131)(12,183,149,130)(13,182,150,129)(14,181,151,128)(15,180,152,127)(16,179,153,126)(17,178,154,125)(18,177,155,124)(19,220,156,123)(20,219,157,122)(21,218,158,121)(22,217,159,120)(23,216,160,119)(24,215,161,118)(25,214,162,117)(26,213,163,116)(27,212,164,115)(28,211,165,114)(29,210,166,113)(30,209,167,112)(31,208,168,111)(32,207,169,110)(33,206,170,109)(34,205,171,108)(35,204,172,107)(36,203,173,106)(37,202,174,105)(38,201,175,104)(39,200,176,103)(40,199,133,102)(41,198,134,101)(42,197,135,100)(43,196,136,99)(44,195,137,98)(45,338,226,306)(46,337,227,305)(47,336,228,304)(48,335,229,303)(49,334,230,302)(50,333,231,301)(51,332,232,300)(52,331,233,299)(53,330,234,298)(54,329,235,297)(55,328,236,296)(56,327,237,295)(57,326,238,294)(58,325,239,293)(59,324,240,292)(60,323,241,291)(61,322,242,290)(62,321,243,289)(63,320,244,288)(64,319,245,287)(65,318,246,286)(66,317,247,285)(67,316,248,284)(68,315,249,283)(69,314,250,282)(70,313,251,281)(71,312,252,280)(72,311,253,279)(73,310,254,278)(74,309,255,277)(75,352,256,276)(76,351,257,275)(77,350,258,274)(78,349,259,273)(79,348,260,272)(80,347,261,271)(81,346,262,270)(82,345,263,269)(83,344,264,268)(84,343,221,267)(85,342,222,266)(86,341,223,265)(87,340,224,308)(88,339,225,307) );
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)], [(1,306,171,327,23,284,149,349),(2,307,172,328,24,285,150,350),(3,308,173,329,25,286,151,351),(4,265,174,330,26,287,152,352),(5,266,175,331,27,288,153,309),(6,267,176,332,28,289,154,310),(7,268,133,333,29,290,155,311),(8,269,134,334,30,291,156,312),(9,270,135,335,31,292,157,313),(10,271,136,336,32,293,158,314),(11,272,137,337,33,294,159,315),(12,273,138,338,34,295,160,316),(13,274,139,339,35,296,161,317),(14,275,140,340,36,297,162,318),(15,276,141,341,37,298,163,319),(16,277,142,342,38,299,164,320),(17,278,143,343,39,300,165,321),(18,279,144,344,40,301,166,322),(19,280,145,345,41,302,167,323),(20,281,146,346,42,303,168,324),(21,282,147,347,43,304,169,325),(22,283,148,348,44,305,170,326),(45,216,259,108,67,194,237,130),(46,217,260,109,68,195,238,131),(47,218,261,110,69,196,239,132),(48,219,262,111,70,197,240,89),(49,220,263,112,71,198,241,90),(50,177,264,113,72,199,242,91),(51,178,221,114,73,200,243,92),(52,179,222,115,74,201,244,93),(53,180,223,116,75,202,245,94),(54,181,224,117,76,203,246,95),(55,182,225,118,77,204,247,96),(56,183,226,119,78,205,248,97),(57,184,227,120,79,206,249,98),(58,185,228,121,80,207,250,99),(59,186,229,122,81,208,251,100),(60,187,230,123,82,209,252,101),(61,188,231,124,83,210,253,102),(62,189,232,125,84,211,254,103),(63,190,233,126,85,212,255,104),(64,191,234,127,86,213,256,105),(65,192,235,128,87,214,257,106),(66,193,236,129,88,215,258,107)], [(1,194,138,97),(2,193,139,96),(3,192,140,95),(4,191,141,94),(5,190,142,93),(6,189,143,92),(7,188,144,91),(8,187,145,90),(9,186,146,89),(10,185,147,132),(11,184,148,131),(12,183,149,130),(13,182,150,129),(14,181,151,128),(15,180,152,127),(16,179,153,126),(17,178,154,125),(18,177,155,124),(19,220,156,123),(20,219,157,122),(21,218,158,121),(22,217,159,120),(23,216,160,119),(24,215,161,118),(25,214,162,117),(26,213,163,116),(27,212,164,115),(28,211,165,114),(29,210,166,113),(30,209,167,112),(31,208,168,111),(32,207,169,110),(33,206,170,109),(34,205,171,108),(35,204,172,107),(36,203,173,106),(37,202,174,105),(38,201,175,104),(39,200,176,103),(40,199,133,102),(41,198,134,101),(42,197,135,100),(43,196,136,99),(44,195,137,98),(45,338,226,306),(46,337,227,305),(47,336,228,304),(48,335,229,303),(49,334,230,302),(50,333,231,301),(51,332,232,300),(52,331,233,299),(53,330,234,298),(54,329,235,297),(55,328,236,296),(56,327,237,295),(57,326,238,294),(58,325,239,293),(59,324,240,292),(60,323,241,291),(61,322,242,290),(62,321,243,289),(63,320,244,288),(64,319,245,287),(65,318,246,286),(66,317,247,285),(67,316,248,284),(68,315,249,283),(69,314,250,282),(70,313,251,281),(71,312,252,280),(72,311,253,279),(73,310,254,278),(74,309,255,277),(75,352,256,276),(76,351,257,275),(77,350,258,274),(78,349,259,273),(79,348,260,272),(80,347,261,271),(81,346,262,270),(82,345,263,269),(83,344,264,268),(84,343,221,267),(85,342,222,266),(86,341,223,265),(87,340,224,308),(88,339,225,307)]])
94 conjugacy classes
| class | 1 | 2A | 2B | 2C | 4A | 4B | 4C | 4D | 4E | 4F | 8A | 8B | 8C | 8D | 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 | 2 | 2 | 44 | 44 | 44 | 44 | 2 | 2 | 2 | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
94 irreducible representations
| dim | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | - | + | + | - | + | - | + | |||
| image | C1 | C2 | C2 | C4 | Q8 | D4 | SD16 | D11 | Dic11 | D22 | Dic22 | D44 | C8⋊D11 |
| kernel | C44.4Q8 | C44⋊C4 | C2×C88 | C88 | C44 | C2×C22 | C22 | C2×C8 | C8 | C2×C4 | C4 | C22 | C2 |
| # reps | 1 | 2 | 1 | 4 | 1 | 1 | 4 | 5 | 10 | 5 | 10 | 10 | 40 |
Matrix representation of C44.4Q8 ►in GL4(𝔽89) generated by
| 56 | 56 | 0 | 0 |
| 67 | 40 | 0 | 0 |
| 0 | 0 | 65 | 16 |
| 0 | 0 | 73 | 44 |
| 17 | 30 | 0 | 0 |
| 20 | 72 | 0 | 0 |
| 0 | 0 | 49 | 23 |
| 0 | 0 | 66 | 80 |
| 33 | 46 | 0 | 0 |
| 15 | 56 | 0 | 0 |
| 0 | 0 | 11 | 56 |
| 0 | 0 | 36 | 78 |
G:=sub<GL(4,GF(89))| [56,67,0,0,56,40,0,0,0,0,65,73,0,0,16,44],[17,20,0,0,30,72,0,0,0,0,49,66,0,0,23,80],[33,15,0,0,46,56,0,0,0,0,11,36,0,0,56,78] >;
C44.4Q8 in GAP, Magma, Sage, TeX
C_{44}._4Q_8 % in TeX
G:=Group("C44.4Q8"); // GroupNames label
G:=SmallGroup(352,23);
// by ID
G=gap.SmallGroup(352,23);
# by ID
G:=PCGroup([6,-2,-2,-2,-2,-2,-11,24,121,55,579,69,11525]);
// Polycyclic
G:=Group<a,b,c|a^44=1,b^4=a^22,c^2=a^11*b^2,a*b=b*a,c*a*c^-1=a^-1,c*b*c^-1=b^3>;
// generators/relations
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