metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C22.6D8, C44.1Q8, C22.3Q16, C4.1Dic22, C11⋊C8⋊1C4, C44.1(C2×C4), C4⋊C4.1D11, C11⋊1(C2.D8), C22.2(C4⋊C4), C4.11(C4×D11), (C2×C22).28D4, (C2×C4).33D22, C44⋊C4.8C2, C2.1(D4⋊D11), (C2×C44).8C22, C2.1(C11⋊Q16), C2.3(Dic11⋊C4), C22.12(C11⋊D4), (C2×C11⋊C8).1C2, (C11×C4⋊C4).1C2, SmallGroup(352,13)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C44.Q8
G = < a,b,c | a44=b4=1, c2=a33b2, bab-1=a23, cac-1=a21, cbc-1=a33b-1 >
Smallest permutation representation of C44.Q8
►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)
(1 289 317 119)(2 268 318 98)(3 291 319 121)(4 270 320 100)(5 293 321 123)(6 272 322 102)(7 295 323 125)(8 274 324 104)(9 297 325 127)(10 276 326 106)(11 299 327 129)(12 278 328 108)(13 301 329 131)(14 280 330 110)(15 303 331 89)(16 282 332 112)(17 305 333 91)(18 284 334 114)(19 307 335 93)(20 286 336 116)(21 265 337 95)(22 288 338 118)(23 267 339 97)(24 290 340 120)(25 269 341 99)(26 292 342 122)(27 271 343 101)(28 294 344 124)(29 273 345 103)(30 296 346 126)(31 275 347 105)(32 298 348 128)(33 277 349 107)(34 300 350 130)(35 279 351 109)(36 302 352 132)(37 281 309 111)(38 304 310 90)(39 283 311 113)(40 306 312 92)(41 285 313 115)(42 308 314 94)(43 287 315 117)(44 266 316 96)(45 239 188 159)(46 262 189 138)(47 241 190 161)(48 264 191 140)(49 243 192 163)(50 222 193 142)(51 245 194 165)(52 224 195 144)(53 247 196 167)(54 226 197 146)(55 249 198 169)(56 228 199 148)(57 251 200 171)(58 230 201 150)(59 253 202 173)(60 232 203 152)(61 255 204 175)(62 234 205 154)(63 257 206 133)(64 236 207 156)(65 259 208 135)(66 238 209 158)(67 261 210 137)(68 240 211 160)(69 263 212 139)(70 242 213 162)(71 221 214 141)(72 244 215 164)(73 223 216 143)(74 246 217 166)(75 225 218 145)(76 248 219 168)(77 227 220 147)(78 250 177 170)(79 229 178 149)(80 252 179 172)(81 231 180 151)(82 254 181 174)(83 233 182 153)(84 256 183 176)(85 235 184 155)(86 258 185 134)(87 237 186 157)(88 260 187 136)
(1 263 350 172 23 241 328 150)(2 240 351 149 24 262 329 171)(3 261 352 170 25 239 330 148)(4 238 309 147 26 260 331 169)(5 259 310 168 27 237 332 146)(6 236 311 145 28 258 333 167)(7 257 312 166 29 235 334 144)(8 234 313 143 30 256 335 165)(9 255 314 164 31 233 336 142)(10 232 315 141 32 254 337 163)(11 253 316 162 33 231 338 140)(12 230 317 139 34 252 339 161)(13 251 318 160 35 229 340 138)(14 228 319 137 36 250 341 159)(15 249 320 158 37 227 342 136)(16 226 321 135 38 248 343 157)(17 247 322 156 39 225 344 134)(18 224 323 133 40 246 345 155)(19 245 324 154 41 223 346 176)(20 222 325 175 42 244 347 153)(21 243 326 152 43 221 348 174)(22 264 327 173 44 242 349 151)(45 99 177 302 67 121 199 280)(46 120 178 279 68 98 200 301)(47 97 179 300 69 119 201 278)(48 118 180 277 70 96 202 299)(49 95 181 298 71 117 203 276)(50 116 182 275 72 94 204 297)(51 93 183 296 73 115 205 274)(52 114 184 273 74 92 206 295)(53 91 185 294 75 113 207 272)(54 112 186 271 76 90 208 293)(55 89 187 292 77 111 209 270)(56 110 188 269 78 132 210 291)(57 131 189 290 79 109 211 268)(58 108 190 267 80 130 212 289)(59 129 191 288 81 107 213 266)(60 106 192 265 82 128 214 287)(61 127 193 286 83 105 215 308)(62 104 194 307 84 126 216 285)(63 125 195 284 85 103 217 306)(64 102 196 305 86 124 218 283)(65 123 197 282 87 101 219 304)(66 100 198 303 88 122 220 281)
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), (1,289,317,119)(2,268,318,98)(3,291,319,121)(4,270,320,100)(5,293,321,123)(6,272,322,102)(7,295,323,125)(8,274,324,104)(9,297,325,127)(10,276,326,106)(11,299,327,129)(12,278,328,108)(13,301,329,131)(14,280,330,110)(15,303,331,89)(16,282,332,112)(17,305,333,91)(18,284,334,114)(19,307,335,93)(20,286,336,116)(21,265,337,95)(22,288,338,118)(23,267,339,97)(24,290,340,120)(25,269,341,99)(26,292,342,122)(27,271,343,101)(28,294,344,124)(29,273,345,103)(30,296,346,126)(31,275,347,105)(32,298,348,128)(33,277,349,107)(34,300,350,130)(35,279,351,109)(36,302,352,132)(37,281,309,111)(38,304,310,90)(39,283,311,113)(40,306,312,92)(41,285,313,115)(42,308,314,94)(43,287,315,117)(44,266,316,96)(45,239,188,159)(46,262,189,138)(47,241,190,161)(48,264,191,140)(49,243,192,163)(50,222,193,142)(51,245,194,165)(52,224,195,144)(53,247,196,167)(54,226,197,146)(55,249,198,169)(56,228,199,148)(57,251,200,171)(58,230,201,150)(59,253,202,173)(60,232,203,152)(61,255,204,175)(62,234,205,154)(63,257,206,133)(64,236,207,156)(65,259,208,135)(66,238,209,158)(67,261,210,137)(68,240,211,160)(69,263,212,139)(70,242,213,162)(71,221,214,141)(72,244,215,164)(73,223,216,143)(74,246,217,166)(75,225,218,145)(76,248,219,168)(77,227,220,147)(78,250,177,170)(79,229,178,149)(80,252,179,172)(81,231,180,151)(82,254,181,174)(83,233,182,153)(84,256,183,176)(85,235,184,155)(86,258,185,134)(87,237,186,157)(88,260,187,136), (1,263,350,172,23,241,328,150)(2,240,351,149,24,262,329,171)(3,261,352,170,25,239,330,148)(4,238,309,147,26,260,331,169)(5,259,310,168,27,237,332,146)(6,236,311,145,28,258,333,167)(7,257,312,166,29,235,334,144)(8,234,313,143,30,256,335,165)(9,255,314,164,31,233,336,142)(10,232,315,141,32,254,337,163)(11,253,316,162,33,231,338,140)(12,230,317,139,34,252,339,161)(13,251,318,160,35,229,340,138)(14,228,319,137,36,250,341,159)(15,249,320,158,37,227,342,136)(16,226,321,135,38,248,343,157)(17,247,322,156,39,225,344,134)(18,224,323,133,40,246,345,155)(19,245,324,154,41,223,346,176)(20,222,325,175,42,244,347,153)(21,243,326,152,43,221,348,174)(22,264,327,173,44,242,349,151)(45,99,177,302,67,121,199,280)(46,120,178,279,68,98,200,301)(47,97,179,300,69,119,201,278)(48,118,180,277,70,96,202,299)(49,95,181,298,71,117,203,276)(50,116,182,275,72,94,204,297)(51,93,183,296,73,115,205,274)(52,114,184,273,74,92,206,295)(53,91,185,294,75,113,207,272)(54,112,186,271,76,90,208,293)(55,89,187,292,77,111,209,270)(56,110,188,269,78,132,210,291)(57,131,189,290,79,109,211,268)(58,108,190,267,80,130,212,289)(59,129,191,288,81,107,213,266)(60,106,192,265,82,128,214,287)(61,127,193,286,83,105,215,308)(62,104,194,307,84,126,216,285)(63,125,195,284,85,103,217,306)(64,102,196,305,86,124,218,283)(65,123,197,282,87,101,219,304)(66,100,198,303,88,122,220,281)>;
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), (1,289,317,119)(2,268,318,98)(3,291,319,121)(4,270,320,100)(5,293,321,123)(6,272,322,102)(7,295,323,125)(8,274,324,104)(9,297,325,127)(10,276,326,106)(11,299,327,129)(12,278,328,108)(13,301,329,131)(14,280,330,110)(15,303,331,89)(16,282,332,112)(17,305,333,91)(18,284,334,114)(19,307,335,93)(20,286,336,116)(21,265,337,95)(22,288,338,118)(23,267,339,97)(24,290,340,120)(25,269,341,99)(26,292,342,122)(27,271,343,101)(28,294,344,124)(29,273,345,103)(30,296,346,126)(31,275,347,105)(32,298,348,128)(33,277,349,107)(34,300,350,130)(35,279,351,109)(36,302,352,132)(37,281,309,111)(38,304,310,90)(39,283,311,113)(40,306,312,92)(41,285,313,115)(42,308,314,94)(43,287,315,117)(44,266,316,96)(45,239,188,159)(46,262,189,138)(47,241,190,161)(48,264,191,140)(49,243,192,163)(50,222,193,142)(51,245,194,165)(52,224,195,144)(53,247,196,167)(54,226,197,146)(55,249,198,169)(56,228,199,148)(57,251,200,171)(58,230,201,150)(59,253,202,173)(60,232,203,152)(61,255,204,175)(62,234,205,154)(63,257,206,133)(64,236,207,156)(65,259,208,135)(66,238,209,158)(67,261,210,137)(68,240,211,160)(69,263,212,139)(70,242,213,162)(71,221,214,141)(72,244,215,164)(73,223,216,143)(74,246,217,166)(75,225,218,145)(76,248,219,168)(77,227,220,147)(78,250,177,170)(79,229,178,149)(80,252,179,172)(81,231,180,151)(82,254,181,174)(83,233,182,153)(84,256,183,176)(85,235,184,155)(86,258,185,134)(87,237,186,157)(88,260,187,136), (1,263,350,172,23,241,328,150)(2,240,351,149,24,262,329,171)(3,261,352,170,25,239,330,148)(4,238,309,147,26,260,331,169)(5,259,310,168,27,237,332,146)(6,236,311,145,28,258,333,167)(7,257,312,166,29,235,334,144)(8,234,313,143,30,256,335,165)(9,255,314,164,31,233,336,142)(10,232,315,141,32,254,337,163)(11,253,316,162,33,231,338,140)(12,230,317,139,34,252,339,161)(13,251,318,160,35,229,340,138)(14,228,319,137,36,250,341,159)(15,249,320,158,37,227,342,136)(16,226,321,135,38,248,343,157)(17,247,322,156,39,225,344,134)(18,224,323,133,40,246,345,155)(19,245,324,154,41,223,346,176)(20,222,325,175,42,244,347,153)(21,243,326,152,43,221,348,174)(22,264,327,173,44,242,349,151)(45,99,177,302,67,121,199,280)(46,120,178,279,68,98,200,301)(47,97,179,300,69,119,201,278)(48,118,180,277,70,96,202,299)(49,95,181,298,71,117,203,276)(50,116,182,275,72,94,204,297)(51,93,183,296,73,115,205,274)(52,114,184,273,74,92,206,295)(53,91,185,294,75,113,207,272)(54,112,186,271,76,90,208,293)(55,89,187,292,77,111,209,270)(56,110,188,269,78,132,210,291)(57,131,189,290,79,109,211,268)(58,108,190,267,80,130,212,289)(59,129,191,288,81,107,213,266)(60,106,192,265,82,128,214,287)(61,127,193,286,83,105,215,308)(62,104,194,307,84,126,216,285)(63,125,195,284,85,103,217,306)(64,102,196,305,86,124,218,283)(65,123,197,282,87,101,219,304)(66,100,198,303,88,122,220,281) );
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)], [(1,289,317,119),(2,268,318,98),(3,291,319,121),(4,270,320,100),(5,293,321,123),(6,272,322,102),(7,295,323,125),(8,274,324,104),(9,297,325,127),(10,276,326,106),(11,299,327,129),(12,278,328,108),(13,301,329,131),(14,280,330,110),(15,303,331,89),(16,282,332,112),(17,305,333,91),(18,284,334,114),(19,307,335,93),(20,286,336,116),(21,265,337,95),(22,288,338,118),(23,267,339,97),(24,290,340,120),(25,269,341,99),(26,292,342,122),(27,271,343,101),(28,294,344,124),(29,273,345,103),(30,296,346,126),(31,275,347,105),(32,298,348,128),(33,277,349,107),(34,300,350,130),(35,279,351,109),(36,302,352,132),(37,281,309,111),(38,304,310,90),(39,283,311,113),(40,306,312,92),(41,285,313,115),(42,308,314,94),(43,287,315,117),(44,266,316,96),(45,239,188,159),(46,262,189,138),(47,241,190,161),(48,264,191,140),(49,243,192,163),(50,222,193,142),(51,245,194,165),(52,224,195,144),(53,247,196,167),(54,226,197,146),(55,249,198,169),(56,228,199,148),(57,251,200,171),(58,230,201,150),(59,253,202,173),(60,232,203,152),(61,255,204,175),(62,234,205,154),(63,257,206,133),(64,236,207,156),(65,259,208,135),(66,238,209,158),(67,261,210,137),(68,240,211,160),(69,263,212,139),(70,242,213,162),(71,221,214,141),(72,244,215,164),(73,223,216,143),(74,246,217,166),(75,225,218,145),(76,248,219,168),(77,227,220,147),(78,250,177,170),(79,229,178,149),(80,252,179,172),(81,231,180,151),(82,254,181,174),(83,233,182,153),(84,256,183,176),(85,235,184,155),(86,258,185,134),(87,237,186,157),(88,260,187,136)], [(1,263,350,172,23,241,328,150),(2,240,351,149,24,262,329,171),(3,261,352,170,25,239,330,148),(4,238,309,147,26,260,331,169),(5,259,310,168,27,237,332,146),(6,236,311,145,28,258,333,167),(7,257,312,166,29,235,334,144),(8,234,313,143,30,256,335,165),(9,255,314,164,31,233,336,142),(10,232,315,141,32,254,337,163),(11,253,316,162,33,231,338,140),(12,230,317,139,34,252,339,161),(13,251,318,160,35,229,340,138),(14,228,319,137,36,250,341,159),(15,249,320,158,37,227,342,136),(16,226,321,135,38,248,343,157),(17,247,322,156,39,225,344,134),(18,224,323,133,40,246,345,155),(19,245,324,154,41,223,346,176),(20,222,325,175,42,244,347,153),(21,243,326,152,43,221,348,174),(22,264,327,173,44,242,349,151),(45,99,177,302,67,121,199,280),(46,120,178,279,68,98,200,301),(47,97,179,300,69,119,201,278),(48,118,180,277,70,96,202,299),(49,95,181,298,71,117,203,276),(50,116,182,275,72,94,204,297),(51,93,183,296,73,115,205,274),(52,114,184,273,74,92,206,295),(53,91,185,294,75,113,207,272),(54,112,186,271,76,90,208,293),(55,89,187,292,77,111,209,270),(56,110,188,269,78,132,210,291),(57,131,189,290,79,109,211,268),(58,108,190,267,80,130,212,289),(59,129,191,288,81,107,213,266),(60,106,192,265,82,128,214,287),(61,127,193,286,83,105,215,308),(62,104,194,307,84,126,216,285),(63,125,195,284,85,103,217,306),(64,102,196,305,86,124,218,283),(65,123,197,282,87,101,219,304),(66,100,198,303,88,122,220,281)]])
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 | 2 | 4 | 4 |
| type | + | + | + | + | - | + | + | - | + | + | - | + | - | |||
| image | C1 | C2 | C2 | C2 | C4 | Q8 | D4 | D8 | Q16 | D11 | D22 | Dic22 | C4×D11 | C11⋊D4 | D4⋊D11 | C11⋊Q16 |
| kernel | C44.Q8 | C2×C11⋊C8 | C44⋊C4 | C11×C4⋊C4 | C11⋊C8 | C44 | C2×C22 | C22 | C22 | C4⋊C4 | C2×C4 | C4 | C4 | C22 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 4 | 1 | 1 | 2 | 2 | 5 | 5 | 10 | 10 | 10 | 5 | 5 |
Matrix representation of C44.Q8 ►in GL4(𝔽89) generated by
| 35 | 8 | 0 | 0 |
| 35 | 36 | 0 | 0 |
| 0 | 0 | 88 | 9 |
| 0 | 0 | 69 | 1 |
| 74 | 62 | 0 | 0 |
| 71 | 15 | 0 | 0 |
| 0 | 0 | 44 | 76 |
| 0 | 0 | 60 | 45 |
| 83 | 11 | 0 | 0 |
| 29 | 6 | 0 | 0 |
| 0 | 0 | 25 | 21 |
| 0 | 0 | 72 | 0 |
G:=sub<GL(4,GF(89))| [35,35,0,0,8,36,0,0,0,0,88,69,0,0,9,1],[74,71,0,0,62,15,0,0,0,0,44,60,0,0,76,45],[83,29,0,0,11,6,0,0,0,0,25,72,0,0,21,0] >;
C44.Q8 in GAP, Magma, Sage, TeX
C_{44}.Q_8 % in TeX
G:=Group("C44.Q8"); // GroupNames label
G:=SmallGroup(352,13);
// by ID
G=gap.SmallGroup(352,13);
# by ID
G:=PCGroup([6,-2,-2,-2,-2,-2,-11,48,121,31,297,69,11525]);
// Polycyclic
G:=Group<a,b,c|a^44=b^4=1,c^2=a^33*b^2,b*a*b^-1=a^23,c*a*c^-1=a^21,c*b*c^-1=a^33*b^-1>;
// generators/relations
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