direct product, metabelian, nilpotent (class 2), monomial, 2-elementary
Aliases: Q8×C44, C42.3C22, C4⋊C4.6C22, (C4×C44).9C2, C4.4(C2×C44), C2.2(Q8×C22), C44.31(C2×C4), (C2×Q8).5C22, C22.19(C2×Q8), C2.5(C22×C44), (Q8×C22).10C2, C22.40(C4○D4), (C2×C22).74C23, C22.33(C22×C4), (C2×C44).122C22, C22.8(C22×C22), C2.3(C11×C4○D4), (C11×C4⋊C4).13C2, (C2×C4).16(C2×C22), SmallGroup(352,154)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for Q8×C44
G = < a,b,c | a44=b4=1, c2=b2, ab=ba, ac=ca, cbc-1=b-1 >
Subgroups: 76 in 70 conjugacy classes, 64 normal (16 characteristic)
C1, C2, C4, C4, C22, C2×C4, C2×C4, Q8, C11, C42, C4⋊C4, C2×Q8, C22, C4×Q8, C44, C44, C2×C22, C2×C44, C2×C44, Q8×C11, C4×C44, C11×C4⋊C4, Q8×C22, Q8×C44
Quotients: C1, C2, C4, C22, C2×C4, Q8, C23, C11, C22×C4, C2×Q8, C4○D4, C22, C4×Q8, C44, C2×C22, C2×C44, Q8×C11, C22×C22, C22×C44, Q8×C22, C11×C4○D4, Q8×C44
►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)
(1 226 183 173)(2 227 184 174)(3 228 185 175)(4 229 186 176)(5 230 187 133)(6 231 188 134)(7 232 189 135)(8 233 190 136)(9 234 191 137)(10 235 192 138)(11 236 193 139)(12 237 194 140)(13 238 195 141)(14 239 196 142)(15 240 197 143)(16 241 198 144)(17 242 199 145)(18 243 200 146)(19 244 201 147)(20 245 202 148)(21 246 203 149)(22 247 204 150)(23 248 205 151)(24 249 206 152)(25 250 207 153)(26 251 208 154)(27 252 209 155)(28 253 210 156)(29 254 211 157)(30 255 212 158)(31 256 213 159)(32 257 214 160)(33 258 215 161)(34 259 216 162)(35 260 217 163)(36 261 218 164)(37 262 219 165)(38 263 220 166)(39 264 177 167)(40 221 178 168)(41 222 179 169)(42 223 180 170)(43 224 181 171)(44 225 182 172)(45 273 115 315)(46 274 116 316)(47 275 117 317)(48 276 118 318)(49 277 119 319)(50 278 120 320)(51 279 121 321)(52 280 122 322)(53 281 123 323)(54 282 124 324)(55 283 125 325)(56 284 126 326)(57 285 127 327)(58 286 128 328)(59 287 129 329)(60 288 130 330)(61 289 131 331)(62 290 132 332)(63 291 89 333)(64 292 90 334)(65 293 91 335)(66 294 92 336)(67 295 93 337)(68 296 94 338)(69 297 95 339)(70 298 96 340)(71 299 97 341)(72 300 98 342)(73 301 99 343)(74 302 100 344)(75 303 101 345)(76 304 102 346)(77 305 103 347)(78 306 104 348)(79 307 105 349)(80 308 106 350)(81 265 107 351)(82 266 108 352)(83 267 109 309)(84 268 110 310)(85 269 111 311)(86 270 112 312)(87 271 113 313)(88 272 114 314)
(1 271 183 313)(2 272 184 314)(3 273 185 315)(4 274 186 316)(5 275 187 317)(6 276 188 318)(7 277 189 319)(8 278 190 320)(9 279 191 321)(10 280 192 322)(11 281 193 323)(12 282 194 324)(13 283 195 325)(14 284 196 326)(15 285 197 327)(16 286 198 328)(17 287 199 329)(18 288 200 330)(19 289 201 331)(20 290 202 332)(21 291 203 333)(22 292 204 334)(23 293 205 335)(24 294 206 336)(25 295 207 337)(26 296 208 338)(27 297 209 339)(28 298 210 340)(29 299 211 341)(30 300 212 342)(31 301 213 343)(32 302 214 344)(33 303 215 345)(34 304 216 346)(35 305 217 347)(36 306 218 348)(37 307 219 349)(38 308 220 350)(39 265 177 351)(40 266 178 352)(41 267 179 309)(42 268 180 310)(43 269 181 311)(44 270 182 312)(45 175 115 228)(46 176 116 229)(47 133 117 230)(48 134 118 231)(49 135 119 232)(50 136 120 233)(51 137 121 234)(52 138 122 235)(53 139 123 236)(54 140 124 237)(55 141 125 238)(56 142 126 239)(57 143 127 240)(58 144 128 241)(59 145 129 242)(60 146 130 243)(61 147 131 244)(62 148 132 245)(63 149 89 246)(64 150 90 247)(65 151 91 248)(66 152 92 249)(67 153 93 250)(68 154 94 251)(69 155 95 252)(70 156 96 253)(71 157 97 254)(72 158 98 255)(73 159 99 256)(74 160 100 257)(75 161 101 258)(76 162 102 259)(77 163 103 260)(78 164 104 261)(79 165 105 262)(80 166 106 263)(81 167 107 264)(82 168 108 221)(83 169 109 222)(84 170 110 223)(85 171 111 224)(86 172 112 225)(87 173 113 226)(88 174 114 227)
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), (1,226,183,173)(2,227,184,174)(3,228,185,175)(4,229,186,176)(5,230,187,133)(6,231,188,134)(7,232,189,135)(8,233,190,136)(9,234,191,137)(10,235,192,138)(11,236,193,139)(12,237,194,140)(13,238,195,141)(14,239,196,142)(15,240,197,143)(16,241,198,144)(17,242,199,145)(18,243,200,146)(19,244,201,147)(20,245,202,148)(21,246,203,149)(22,247,204,150)(23,248,205,151)(24,249,206,152)(25,250,207,153)(26,251,208,154)(27,252,209,155)(28,253,210,156)(29,254,211,157)(30,255,212,158)(31,256,213,159)(32,257,214,160)(33,258,215,161)(34,259,216,162)(35,260,217,163)(36,261,218,164)(37,262,219,165)(38,263,220,166)(39,264,177,167)(40,221,178,168)(41,222,179,169)(42,223,180,170)(43,224,181,171)(44,225,182,172)(45,273,115,315)(46,274,116,316)(47,275,117,317)(48,276,118,318)(49,277,119,319)(50,278,120,320)(51,279,121,321)(52,280,122,322)(53,281,123,323)(54,282,124,324)(55,283,125,325)(56,284,126,326)(57,285,127,327)(58,286,128,328)(59,287,129,329)(60,288,130,330)(61,289,131,331)(62,290,132,332)(63,291,89,333)(64,292,90,334)(65,293,91,335)(66,294,92,336)(67,295,93,337)(68,296,94,338)(69,297,95,339)(70,298,96,340)(71,299,97,341)(72,300,98,342)(73,301,99,343)(74,302,100,344)(75,303,101,345)(76,304,102,346)(77,305,103,347)(78,306,104,348)(79,307,105,349)(80,308,106,350)(81,265,107,351)(82,266,108,352)(83,267,109,309)(84,268,110,310)(85,269,111,311)(86,270,112,312)(87,271,113,313)(88,272,114,314), (1,271,183,313)(2,272,184,314)(3,273,185,315)(4,274,186,316)(5,275,187,317)(6,276,188,318)(7,277,189,319)(8,278,190,320)(9,279,191,321)(10,280,192,322)(11,281,193,323)(12,282,194,324)(13,283,195,325)(14,284,196,326)(15,285,197,327)(16,286,198,328)(17,287,199,329)(18,288,200,330)(19,289,201,331)(20,290,202,332)(21,291,203,333)(22,292,204,334)(23,293,205,335)(24,294,206,336)(25,295,207,337)(26,296,208,338)(27,297,209,339)(28,298,210,340)(29,299,211,341)(30,300,212,342)(31,301,213,343)(32,302,214,344)(33,303,215,345)(34,304,216,346)(35,305,217,347)(36,306,218,348)(37,307,219,349)(38,308,220,350)(39,265,177,351)(40,266,178,352)(41,267,179,309)(42,268,180,310)(43,269,181,311)(44,270,182,312)(45,175,115,228)(46,176,116,229)(47,133,117,230)(48,134,118,231)(49,135,119,232)(50,136,120,233)(51,137,121,234)(52,138,122,235)(53,139,123,236)(54,140,124,237)(55,141,125,238)(56,142,126,239)(57,143,127,240)(58,144,128,241)(59,145,129,242)(60,146,130,243)(61,147,131,244)(62,148,132,245)(63,149,89,246)(64,150,90,247)(65,151,91,248)(66,152,92,249)(67,153,93,250)(68,154,94,251)(69,155,95,252)(70,156,96,253)(71,157,97,254)(72,158,98,255)(73,159,99,256)(74,160,100,257)(75,161,101,258)(76,162,102,259)(77,163,103,260)(78,164,104,261)(79,165,105,262)(80,166,106,263)(81,167,107,264)(82,168,108,221)(83,169,109,222)(84,170,110,223)(85,171,111,224)(86,172,112,225)(87,173,113,226)(88,174,114,227)>;
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), (1,226,183,173)(2,227,184,174)(3,228,185,175)(4,229,186,176)(5,230,187,133)(6,231,188,134)(7,232,189,135)(8,233,190,136)(9,234,191,137)(10,235,192,138)(11,236,193,139)(12,237,194,140)(13,238,195,141)(14,239,196,142)(15,240,197,143)(16,241,198,144)(17,242,199,145)(18,243,200,146)(19,244,201,147)(20,245,202,148)(21,246,203,149)(22,247,204,150)(23,248,205,151)(24,249,206,152)(25,250,207,153)(26,251,208,154)(27,252,209,155)(28,253,210,156)(29,254,211,157)(30,255,212,158)(31,256,213,159)(32,257,214,160)(33,258,215,161)(34,259,216,162)(35,260,217,163)(36,261,218,164)(37,262,219,165)(38,263,220,166)(39,264,177,167)(40,221,178,168)(41,222,179,169)(42,223,180,170)(43,224,181,171)(44,225,182,172)(45,273,115,315)(46,274,116,316)(47,275,117,317)(48,276,118,318)(49,277,119,319)(50,278,120,320)(51,279,121,321)(52,280,122,322)(53,281,123,323)(54,282,124,324)(55,283,125,325)(56,284,126,326)(57,285,127,327)(58,286,128,328)(59,287,129,329)(60,288,130,330)(61,289,131,331)(62,290,132,332)(63,291,89,333)(64,292,90,334)(65,293,91,335)(66,294,92,336)(67,295,93,337)(68,296,94,338)(69,297,95,339)(70,298,96,340)(71,299,97,341)(72,300,98,342)(73,301,99,343)(74,302,100,344)(75,303,101,345)(76,304,102,346)(77,305,103,347)(78,306,104,348)(79,307,105,349)(80,308,106,350)(81,265,107,351)(82,266,108,352)(83,267,109,309)(84,268,110,310)(85,269,111,311)(86,270,112,312)(87,271,113,313)(88,272,114,314), (1,271,183,313)(2,272,184,314)(3,273,185,315)(4,274,186,316)(5,275,187,317)(6,276,188,318)(7,277,189,319)(8,278,190,320)(9,279,191,321)(10,280,192,322)(11,281,193,323)(12,282,194,324)(13,283,195,325)(14,284,196,326)(15,285,197,327)(16,286,198,328)(17,287,199,329)(18,288,200,330)(19,289,201,331)(20,290,202,332)(21,291,203,333)(22,292,204,334)(23,293,205,335)(24,294,206,336)(25,295,207,337)(26,296,208,338)(27,297,209,339)(28,298,210,340)(29,299,211,341)(30,300,212,342)(31,301,213,343)(32,302,214,344)(33,303,215,345)(34,304,216,346)(35,305,217,347)(36,306,218,348)(37,307,219,349)(38,308,220,350)(39,265,177,351)(40,266,178,352)(41,267,179,309)(42,268,180,310)(43,269,181,311)(44,270,182,312)(45,175,115,228)(46,176,116,229)(47,133,117,230)(48,134,118,231)(49,135,119,232)(50,136,120,233)(51,137,121,234)(52,138,122,235)(53,139,123,236)(54,140,124,237)(55,141,125,238)(56,142,126,239)(57,143,127,240)(58,144,128,241)(59,145,129,242)(60,146,130,243)(61,147,131,244)(62,148,132,245)(63,149,89,246)(64,150,90,247)(65,151,91,248)(66,152,92,249)(67,153,93,250)(68,154,94,251)(69,155,95,252)(70,156,96,253)(71,157,97,254)(72,158,98,255)(73,159,99,256)(74,160,100,257)(75,161,101,258)(76,162,102,259)(77,163,103,260)(78,164,104,261)(79,165,105,262)(80,166,106,263)(81,167,107,264)(82,168,108,221)(83,169,109,222)(84,170,110,223)(85,171,111,224)(86,172,112,225)(87,173,113,226)(88,174,114,227) );
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)], [(1,226,183,173),(2,227,184,174),(3,228,185,175),(4,229,186,176),(5,230,187,133),(6,231,188,134),(7,232,189,135),(8,233,190,136),(9,234,191,137),(10,235,192,138),(11,236,193,139),(12,237,194,140),(13,238,195,141),(14,239,196,142),(15,240,197,143),(16,241,198,144),(17,242,199,145),(18,243,200,146),(19,244,201,147),(20,245,202,148),(21,246,203,149),(22,247,204,150),(23,248,205,151),(24,249,206,152),(25,250,207,153),(26,251,208,154),(27,252,209,155),(28,253,210,156),(29,254,211,157),(30,255,212,158),(31,256,213,159),(32,257,214,160),(33,258,215,161),(34,259,216,162),(35,260,217,163),(36,261,218,164),(37,262,219,165),(38,263,220,166),(39,264,177,167),(40,221,178,168),(41,222,179,169),(42,223,180,170),(43,224,181,171),(44,225,182,172),(45,273,115,315),(46,274,116,316),(47,275,117,317),(48,276,118,318),(49,277,119,319),(50,278,120,320),(51,279,121,321),(52,280,122,322),(53,281,123,323),(54,282,124,324),(55,283,125,325),(56,284,126,326),(57,285,127,327),(58,286,128,328),(59,287,129,329),(60,288,130,330),(61,289,131,331),(62,290,132,332),(63,291,89,333),(64,292,90,334),(65,293,91,335),(66,294,92,336),(67,295,93,337),(68,296,94,338),(69,297,95,339),(70,298,96,340),(71,299,97,341),(72,300,98,342),(73,301,99,343),(74,302,100,344),(75,303,101,345),(76,304,102,346),(77,305,103,347),(78,306,104,348),(79,307,105,349),(80,308,106,350),(81,265,107,351),(82,266,108,352),(83,267,109,309),(84,268,110,310),(85,269,111,311),(86,270,112,312),(87,271,113,313),(88,272,114,314)], [(1,271,183,313),(2,272,184,314),(3,273,185,315),(4,274,186,316),(5,275,187,317),(6,276,188,318),(7,277,189,319),(8,278,190,320),(9,279,191,321),(10,280,192,322),(11,281,193,323),(12,282,194,324),(13,283,195,325),(14,284,196,326),(15,285,197,327),(16,286,198,328),(17,287,199,329),(18,288,200,330),(19,289,201,331),(20,290,202,332),(21,291,203,333),(22,292,204,334),(23,293,205,335),(24,294,206,336),(25,295,207,337),(26,296,208,338),(27,297,209,339),(28,298,210,340),(29,299,211,341),(30,300,212,342),(31,301,213,343),(32,302,214,344),(33,303,215,345),(34,304,216,346),(35,305,217,347),(36,306,218,348),(37,307,219,349),(38,308,220,350),(39,265,177,351),(40,266,178,352),(41,267,179,309),(42,268,180,310),(43,269,181,311),(44,270,182,312),(45,175,115,228),(46,176,116,229),(47,133,117,230),(48,134,118,231),(49,135,119,232),(50,136,120,233),(51,137,121,234),(52,138,122,235),(53,139,123,236),(54,140,124,237),(55,141,125,238),(56,142,126,239),(57,143,127,240),(58,144,128,241),(59,145,129,242),(60,146,130,243),(61,147,131,244),(62,148,132,245),(63,149,89,246),(64,150,90,247),(65,151,91,248),(66,152,92,249),(67,153,93,250),(68,154,94,251),(69,155,95,252),(70,156,96,253),(71,157,97,254),(72,158,98,255),(73,159,99,256),(74,160,100,257),(75,161,101,258),(76,162,102,259),(77,163,103,260),(78,164,104,261),(79,165,105,262),(80,166,106,263),(81,167,107,264),(82,168,108,221),(83,169,109,222),(84,170,110,223),(85,171,111,224),(86,172,112,225),(87,173,113,226),(88,174,114,227)]])
220 conjugacy classes
| class | 1 | 2A | 2B | 2C | 4A | 4B | 4C | 4D | 4E | ··· | 4P | 11A | ··· | 11J | 22A | ··· | 22AD | 44A | ··· | 44AN | 44AO | ··· | 44FD |
| order | 1 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 11 | ··· | 11 | 22 | ··· | 22 | 44 | ··· | 44 | 44 | ··· | 44 |
| size | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | ··· | 2 | 1 | ··· | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 2 | ··· | 2 |
220 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | - | |||||||||
| image | C1 | C2 | C2 | C2 | C4 | C11 | C22 | C22 | C22 | C44 | Q8 | C4○D4 | Q8×C11 | C11×C4○D4 |
| kernel | Q8×C44 | C4×C44 | C11×C4⋊C4 | Q8×C22 | Q8×C11 | C4×Q8 | C42 | C4⋊C4 | C2×Q8 | Q8 | C44 | C22 | C4 | C2 |
| # reps | 1 | 3 | 3 | 1 | 8 | 10 | 30 | 30 | 10 | 80 | 2 | 2 | 20 | 20 |
Matrix representation of Q8×C44 ►in GL3(𝔽89) generated by
| 55 | 0 | 0 |
| 0 | 79 | 0 |
| 0 | 0 | 79 |
| 88 | 0 | 0 |
| 0 | 88 | 2 |
| 0 | 88 | 1 |
| 1 | 0 | 0 |
| 0 | 11 | 1 |
| 0 | 56 | 78 |
G:=sub<GL(3,GF(89))| [55,0,0,0,79,0,0,0,79],[88,0,0,0,88,88,0,2,1],[1,0,0,0,11,56,0,1,78] >;
Q8×C44 in GAP, Magma, Sage, TeX
Q_8\times C_{44} % in TeX
G:=Group("Q8xC44"); // GroupNames label
G:=SmallGroup(352,154);
// by ID
G=gap.SmallGroup(352,154);
# by ID
G:=PCGroup([6,-2,-2,-2,-11,-2,-2,1056,1081,535,1202]);
// Polycyclic
G:=Group<a,b,c|a^44=b^4=1,c^2=b^2,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations