metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C44.6Q8, C4.6Dic22, C42.5D11, (C4×C44).3C2, C22.3(C2×Q8), (C2×C4).74D22, C44⋊C4.5C2, C22.2(C4○D4), C2.5(C2×Dic22), C11⋊1(C42.C2), Dic11⋊C4.1C2, (C2×C44).72C22, (C2×C22).11C23, C2.6(D44⋊5C2), (C2×Dic11).2C22, C22.35(C22×D11), SmallGroup(352,65)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C44.6Q8
G = < a,b,c | a44=b4=1, c2=a22b2, ab=ba, cac-1=a-1, cbc-1=a22b-1 >
Subgroups: 258 in 56 conjugacy classes, 33 normal (11 characteristic)
C1, C2, C2, C4, C4, C22, C2×C4, C2×C4, C2×C4, C11, C42, C4⋊C4, C22, C22, C42.C2, Dic11, C44, C44, C2×C22, C2×Dic11, C2×C44, C2×C44, Dic11⋊C4, C44⋊C4, C4×C44, C44.6Q8
Quotients: C1, C2, C22, Q8, C23, C2×Q8, C4○D4, D11, C42.C2, D22, Dic22, C22×D11, C2×Dic22, D44⋊5C2, C44.6Q8
►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)
(1 216 144 291)(2 217 145 292)(3 218 146 293)(4 219 147 294)(5 220 148 295)(6 177 149 296)(7 178 150 297)(8 179 151 298)(9 180 152 299)(10 181 153 300)(11 182 154 301)(12 183 155 302)(13 184 156 303)(14 185 157 304)(15 186 158 305)(16 187 159 306)(17 188 160 307)(18 189 161 308)(19 190 162 265)(20 191 163 266)(21 192 164 267)(22 193 165 268)(23 194 166 269)(24 195 167 270)(25 196 168 271)(26 197 169 272)(27 198 170 273)(28 199 171 274)(29 200 172 275)(30 201 173 276)(31 202 174 277)(32 203 175 278)(33 204 176 279)(34 205 133 280)(35 206 134 281)(36 207 135 282)(37 208 136 283)(38 209 137 284)(39 210 138 285)(40 211 139 286)(41 212 140 287)(42 213 141 288)(43 214 142 289)(44 215 143 290)(45 130 231 309)(46 131 232 310)(47 132 233 311)(48 89 234 312)(49 90 235 313)(50 91 236 314)(51 92 237 315)(52 93 238 316)(53 94 239 317)(54 95 240 318)(55 96 241 319)(56 97 242 320)(57 98 243 321)(58 99 244 322)(59 100 245 323)(60 101 246 324)(61 102 247 325)(62 103 248 326)(63 104 249 327)(64 105 250 328)(65 106 251 329)(66 107 252 330)(67 108 253 331)(68 109 254 332)(69 110 255 333)(70 111 256 334)(71 112 257 335)(72 113 258 336)(73 114 259 337)(74 115 260 338)(75 116 261 339)(76 117 262 340)(77 118 263 341)(78 119 264 342)(79 120 221 343)(80 121 222 344)(81 122 223 345)(82 123 224 346)(83 124 225 347)(84 125 226 348)(85 126 227 349)(86 127 228 350)(87 128 229 351)(88 129 230 352)
(1 328 166 127)(2 327 167 126)(3 326 168 125)(4 325 169 124)(5 324 170 123)(6 323 171 122)(7 322 172 121)(8 321 173 120)(9 320 174 119)(10 319 175 118)(11 318 176 117)(12 317 133 116)(13 316 134 115)(14 315 135 114)(15 314 136 113)(16 313 137 112)(17 312 138 111)(18 311 139 110)(19 310 140 109)(20 309 141 108)(21 352 142 107)(22 351 143 106)(23 350 144 105)(24 349 145 104)(25 348 146 103)(26 347 147 102)(27 346 148 101)(28 345 149 100)(29 344 150 99)(30 343 151 98)(31 342 152 97)(32 341 153 96)(33 340 154 95)(34 339 155 94)(35 338 156 93)(36 337 157 92)(37 336 158 91)(38 335 159 90)(39 334 160 89)(40 333 161 132)(41 332 162 131)(42 331 163 130)(43 330 164 129)(44 329 165 128)(45 191 253 288)(46 190 254 287)(47 189 255 286)(48 188 256 285)(49 187 257 284)(50 186 258 283)(51 185 259 282)(52 184 260 281)(53 183 261 280)(54 182 262 279)(55 181 263 278)(56 180 264 277)(57 179 221 276)(58 178 222 275)(59 177 223 274)(60 220 224 273)(61 219 225 272)(62 218 226 271)(63 217 227 270)(64 216 228 269)(65 215 229 268)(66 214 230 267)(67 213 231 266)(68 212 232 265)(69 211 233 308)(70 210 234 307)(71 209 235 306)(72 208 236 305)(73 207 237 304)(74 206 238 303)(75 205 239 302)(76 204 240 301)(77 203 241 300)(78 202 242 299)(79 201 243 298)(80 200 244 297)(81 199 245 296)(82 198 246 295)(83 197 247 294)(84 196 248 293)(85 195 249 292)(86 194 250 291)(87 193 251 290)(88 192 252 289)
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), (1,216,144,291)(2,217,145,292)(3,218,146,293)(4,219,147,294)(5,220,148,295)(6,177,149,296)(7,178,150,297)(8,179,151,298)(9,180,152,299)(10,181,153,300)(11,182,154,301)(12,183,155,302)(13,184,156,303)(14,185,157,304)(15,186,158,305)(16,187,159,306)(17,188,160,307)(18,189,161,308)(19,190,162,265)(20,191,163,266)(21,192,164,267)(22,193,165,268)(23,194,166,269)(24,195,167,270)(25,196,168,271)(26,197,169,272)(27,198,170,273)(28,199,171,274)(29,200,172,275)(30,201,173,276)(31,202,174,277)(32,203,175,278)(33,204,176,279)(34,205,133,280)(35,206,134,281)(36,207,135,282)(37,208,136,283)(38,209,137,284)(39,210,138,285)(40,211,139,286)(41,212,140,287)(42,213,141,288)(43,214,142,289)(44,215,143,290)(45,130,231,309)(46,131,232,310)(47,132,233,311)(48,89,234,312)(49,90,235,313)(50,91,236,314)(51,92,237,315)(52,93,238,316)(53,94,239,317)(54,95,240,318)(55,96,241,319)(56,97,242,320)(57,98,243,321)(58,99,244,322)(59,100,245,323)(60,101,246,324)(61,102,247,325)(62,103,248,326)(63,104,249,327)(64,105,250,328)(65,106,251,329)(66,107,252,330)(67,108,253,331)(68,109,254,332)(69,110,255,333)(70,111,256,334)(71,112,257,335)(72,113,258,336)(73,114,259,337)(74,115,260,338)(75,116,261,339)(76,117,262,340)(77,118,263,341)(78,119,264,342)(79,120,221,343)(80,121,222,344)(81,122,223,345)(82,123,224,346)(83,124,225,347)(84,125,226,348)(85,126,227,349)(86,127,228,350)(87,128,229,351)(88,129,230,352), (1,328,166,127)(2,327,167,126)(3,326,168,125)(4,325,169,124)(5,324,170,123)(6,323,171,122)(7,322,172,121)(8,321,173,120)(9,320,174,119)(10,319,175,118)(11,318,176,117)(12,317,133,116)(13,316,134,115)(14,315,135,114)(15,314,136,113)(16,313,137,112)(17,312,138,111)(18,311,139,110)(19,310,140,109)(20,309,141,108)(21,352,142,107)(22,351,143,106)(23,350,144,105)(24,349,145,104)(25,348,146,103)(26,347,147,102)(27,346,148,101)(28,345,149,100)(29,344,150,99)(30,343,151,98)(31,342,152,97)(32,341,153,96)(33,340,154,95)(34,339,155,94)(35,338,156,93)(36,337,157,92)(37,336,158,91)(38,335,159,90)(39,334,160,89)(40,333,161,132)(41,332,162,131)(42,331,163,130)(43,330,164,129)(44,329,165,128)(45,191,253,288)(46,190,254,287)(47,189,255,286)(48,188,256,285)(49,187,257,284)(50,186,258,283)(51,185,259,282)(52,184,260,281)(53,183,261,280)(54,182,262,279)(55,181,263,278)(56,180,264,277)(57,179,221,276)(58,178,222,275)(59,177,223,274)(60,220,224,273)(61,219,225,272)(62,218,226,271)(63,217,227,270)(64,216,228,269)(65,215,229,268)(66,214,230,267)(67,213,231,266)(68,212,232,265)(69,211,233,308)(70,210,234,307)(71,209,235,306)(72,208,236,305)(73,207,237,304)(74,206,238,303)(75,205,239,302)(76,204,240,301)(77,203,241,300)(78,202,242,299)(79,201,243,298)(80,200,244,297)(81,199,245,296)(82,198,246,295)(83,197,247,294)(84,196,248,293)(85,195,249,292)(86,194,250,291)(87,193,251,290)(88,192,252,289)>;
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), (1,216,144,291)(2,217,145,292)(3,218,146,293)(4,219,147,294)(5,220,148,295)(6,177,149,296)(7,178,150,297)(8,179,151,298)(9,180,152,299)(10,181,153,300)(11,182,154,301)(12,183,155,302)(13,184,156,303)(14,185,157,304)(15,186,158,305)(16,187,159,306)(17,188,160,307)(18,189,161,308)(19,190,162,265)(20,191,163,266)(21,192,164,267)(22,193,165,268)(23,194,166,269)(24,195,167,270)(25,196,168,271)(26,197,169,272)(27,198,170,273)(28,199,171,274)(29,200,172,275)(30,201,173,276)(31,202,174,277)(32,203,175,278)(33,204,176,279)(34,205,133,280)(35,206,134,281)(36,207,135,282)(37,208,136,283)(38,209,137,284)(39,210,138,285)(40,211,139,286)(41,212,140,287)(42,213,141,288)(43,214,142,289)(44,215,143,290)(45,130,231,309)(46,131,232,310)(47,132,233,311)(48,89,234,312)(49,90,235,313)(50,91,236,314)(51,92,237,315)(52,93,238,316)(53,94,239,317)(54,95,240,318)(55,96,241,319)(56,97,242,320)(57,98,243,321)(58,99,244,322)(59,100,245,323)(60,101,246,324)(61,102,247,325)(62,103,248,326)(63,104,249,327)(64,105,250,328)(65,106,251,329)(66,107,252,330)(67,108,253,331)(68,109,254,332)(69,110,255,333)(70,111,256,334)(71,112,257,335)(72,113,258,336)(73,114,259,337)(74,115,260,338)(75,116,261,339)(76,117,262,340)(77,118,263,341)(78,119,264,342)(79,120,221,343)(80,121,222,344)(81,122,223,345)(82,123,224,346)(83,124,225,347)(84,125,226,348)(85,126,227,349)(86,127,228,350)(87,128,229,351)(88,129,230,352), (1,328,166,127)(2,327,167,126)(3,326,168,125)(4,325,169,124)(5,324,170,123)(6,323,171,122)(7,322,172,121)(8,321,173,120)(9,320,174,119)(10,319,175,118)(11,318,176,117)(12,317,133,116)(13,316,134,115)(14,315,135,114)(15,314,136,113)(16,313,137,112)(17,312,138,111)(18,311,139,110)(19,310,140,109)(20,309,141,108)(21,352,142,107)(22,351,143,106)(23,350,144,105)(24,349,145,104)(25,348,146,103)(26,347,147,102)(27,346,148,101)(28,345,149,100)(29,344,150,99)(30,343,151,98)(31,342,152,97)(32,341,153,96)(33,340,154,95)(34,339,155,94)(35,338,156,93)(36,337,157,92)(37,336,158,91)(38,335,159,90)(39,334,160,89)(40,333,161,132)(41,332,162,131)(42,331,163,130)(43,330,164,129)(44,329,165,128)(45,191,253,288)(46,190,254,287)(47,189,255,286)(48,188,256,285)(49,187,257,284)(50,186,258,283)(51,185,259,282)(52,184,260,281)(53,183,261,280)(54,182,262,279)(55,181,263,278)(56,180,264,277)(57,179,221,276)(58,178,222,275)(59,177,223,274)(60,220,224,273)(61,219,225,272)(62,218,226,271)(63,217,227,270)(64,216,228,269)(65,215,229,268)(66,214,230,267)(67,213,231,266)(68,212,232,265)(69,211,233,308)(70,210,234,307)(71,209,235,306)(72,208,236,305)(73,207,237,304)(74,206,238,303)(75,205,239,302)(76,204,240,301)(77,203,241,300)(78,202,242,299)(79,201,243,298)(80,200,244,297)(81,199,245,296)(82,198,246,295)(83,197,247,294)(84,196,248,293)(85,195,249,292)(86,194,250,291)(87,193,251,290)(88,192,252,289) );
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)], [(1,216,144,291),(2,217,145,292),(3,218,146,293),(4,219,147,294),(5,220,148,295),(6,177,149,296),(7,178,150,297),(8,179,151,298),(9,180,152,299),(10,181,153,300),(11,182,154,301),(12,183,155,302),(13,184,156,303),(14,185,157,304),(15,186,158,305),(16,187,159,306),(17,188,160,307),(18,189,161,308),(19,190,162,265),(20,191,163,266),(21,192,164,267),(22,193,165,268),(23,194,166,269),(24,195,167,270),(25,196,168,271),(26,197,169,272),(27,198,170,273),(28,199,171,274),(29,200,172,275),(30,201,173,276),(31,202,174,277),(32,203,175,278),(33,204,176,279),(34,205,133,280),(35,206,134,281),(36,207,135,282),(37,208,136,283),(38,209,137,284),(39,210,138,285),(40,211,139,286),(41,212,140,287),(42,213,141,288),(43,214,142,289),(44,215,143,290),(45,130,231,309),(46,131,232,310),(47,132,233,311),(48,89,234,312),(49,90,235,313),(50,91,236,314),(51,92,237,315),(52,93,238,316),(53,94,239,317),(54,95,240,318),(55,96,241,319),(56,97,242,320),(57,98,243,321),(58,99,244,322),(59,100,245,323),(60,101,246,324),(61,102,247,325),(62,103,248,326),(63,104,249,327),(64,105,250,328),(65,106,251,329),(66,107,252,330),(67,108,253,331),(68,109,254,332),(69,110,255,333),(70,111,256,334),(71,112,257,335),(72,113,258,336),(73,114,259,337),(74,115,260,338),(75,116,261,339),(76,117,262,340),(77,118,263,341),(78,119,264,342),(79,120,221,343),(80,121,222,344),(81,122,223,345),(82,123,224,346),(83,124,225,347),(84,125,226,348),(85,126,227,349),(86,127,228,350),(87,128,229,351),(88,129,230,352)], [(1,328,166,127),(2,327,167,126),(3,326,168,125),(4,325,169,124),(5,324,170,123),(6,323,171,122),(7,322,172,121),(8,321,173,120),(9,320,174,119),(10,319,175,118),(11,318,176,117),(12,317,133,116),(13,316,134,115),(14,315,135,114),(15,314,136,113),(16,313,137,112),(17,312,138,111),(18,311,139,110),(19,310,140,109),(20,309,141,108),(21,352,142,107),(22,351,143,106),(23,350,144,105),(24,349,145,104),(25,348,146,103),(26,347,147,102),(27,346,148,101),(28,345,149,100),(29,344,150,99),(30,343,151,98),(31,342,152,97),(32,341,153,96),(33,340,154,95),(34,339,155,94),(35,338,156,93),(36,337,157,92),(37,336,158,91),(38,335,159,90),(39,334,160,89),(40,333,161,132),(41,332,162,131),(42,331,163,130),(43,330,164,129),(44,329,165,128),(45,191,253,288),(46,190,254,287),(47,189,255,286),(48,188,256,285),(49,187,257,284),(50,186,258,283),(51,185,259,282),(52,184,260,281),(53,183,261,280),(54,182,262,279),(55,181,263,278),(56,180,264,277),(57,179,221,276),(58,178,222,275),(59,177,223,274),(60,220,224,273),(61,219,225,272),(62,218,226,271),(63,217,227,270),(64,216,228,269),(65,215,229,268),(66,214,230,267),(67,213,231,266),(68,212,232,265),(69,211,233,308),(70,210,234,307),(71,209,235,306),(72,208,236,305),(73,207,237,304),(74,206,238,303),(75,205,239,302),(76,204,240,301),(77,203,241,300),(78,202,242,299),(79,201,243,298),(80,200,244,297),(81,199,245,296),(82,198,246,295),(83,197,247,294),(84,196,248,293),(85,195,249,292),(86,194,250,291),(87,193,251,290),(88,192,252,289)]])
94 conjugacy classes
| class | 1 | 2A | 2B | 2C | 4A | ··· | 4F | 4G | 4H | 4I | 4J | 11A | ··· | 11E | 22A | ··· | 22O | 44A | ··· | 44BH |
| order | 1 | 2 | 2 | 2 | 4 | ··· | 4 | 4 | 4 | 4 | 4 | 11 | ··· | 11 | 22 | ··· | 22 | 44 | ··· | 44 |
| size | 1 | 1 | 1 | 1 | 2 | ··· | 2 | 44 | 44 | 44 | 44 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
94 irreducible representations
| dim | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | - | + | + | - | ||
| image | C1 | C2 | C2 | C2 | Q8 | C4○D4 | D11 | D22 | Dic22 | D44⋊5C2 |
| kernel | C44.6Q8 | Dic11⋊C4 | C44⋊C4 | C4×C44 | C44 | C22 | C42 | C2×C4 | C4 | C2 |
| # reps | 1 | 4 | 2 | 1 | 2 | 4 | 5 | 15 | 20 | 40 |
Matrix representation of C44.6Q8 ►in GL4(𝔽89) generated by
| 35 | 68 | 0 | 0 |
| 84 | 31 | 0 | 0 |
| 0 | 0 | 42 | 72 |
| 0 | 0 | 17 | 44 |
| 55 | 0 | 0 | 0 |
| 0 | 55 | 0 | 0 |
| 0 | 0 | 27 | 14 |
| 0 | 0 | 75 | 62 |
| 11 | 22 | 0 | 0 |
| 35 | 78 | 0 | 0 |
| 0 | 0 | 87 | 82 |
| 0 | 0 | 77 | 2 |
G:=sub<GL(4,GF(89))| [35,84,0,0,68,31,0,0,0,0,42,17,0,0,72,44],[55,0,0,0,0,55,0,0,0,0,27,75,0,0,14,62],[11,35,0,0,22,78,0,0,0,0,87,77,0,0,82,2] >;
C44.6Q8 in GAP, Magma, Sage, TeX
C_{44}._6Q_8 % in TeX
G:=Group("C44.6Q8"); // GroupNames label
G:=SmallGroup(352,65);
// by ID
G=gap.SmallGroup(352,65);
# by ID
G:=PCGroup([6,-2,-2,-2,-2,-2,-11,96,217,55,218,86,11525]);
// Polycyclic
G:=Group<a,b,c|a^44=b^4=1,c^2=a^22*b^2,a*b=b*a,c*a*c^-1=a^-1,c*b*c^-1=a^22*b^-1>;
// generators/relations