metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C44⋊Q8, C4⋊1Dic22, Dic11⋊1Q8, Dic11.2D4, C11⋊2(C4⋊Q8), C4⋊C4.4D11, C2.4(Q8×D11), C22.5(C2×Q8), C2.11(D4×D11), C22.22(C2×D4), (C2×C4).42D22, (C2×C44).4C22, C44⋊C4.11C2, C2.7(C2×Dic22), Dic11⋊C4.2C2, (C2×C22).29C23, (C2×Dic22).3C2, (C4×Dic11).1C2, (C2×Dic11).8C22, C22.46(C22×D11), (C11×C4⋊C4).5C2, SmallGroup(352,83)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C44⋊Q8
G = < a,b,c | a44=b4=1, c2=b2, bab-1=a23, cac-1=a21, cbc-1=b-1 >
Subgroups: 354 in 68 conjugacy classes, 37 normal (19 characteristic)
C1, C2, C4, C4, C22, C2×C4, C2×C4, C2×C4, Q8, C11, C42, C4⋊C4, C4⋊C4, C2×Q8, C22, C4⋊Q8, Dic11, Dic11, C44, C44, C2×C22, Dic22, C2×Dic11, C2×Dic11, C2×C44, C2×C44, C4×Dic11, Dic11⋊C4, C44⋊C4, C11×C4⋊C4, C2×Dic22, C44⋊Q8
Quotients: C1, C2, C22, D4, Q8, C23, C2×D4, C2×Q8, D11, C4⋊Q8, D22, Dic22, C22×D11, C2×Dic22, D4×D11, Q8×D11, 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)
(1 309 210 260)(2 332 211 239)(3 311 212 262)(4 334 213 241)(5 313 214 264)(6 336 215 243)(7 315 216 222)(8 338 217 245)(9 317 218 224)(10 340 219 247)(11 319 220 226)(12 342 177 249)(13 321 178 228)(14 344 179 251)(15 323 180 230)(16 346 181 253)(17 325 182 232)(18 348 183 255)(19 327 184 234)(20 350 185 257)(21 329 186 236)(22 352 187 259)(23 331 188 238)(24 310 189 261)(25 333 190 240)(26 312 191 263)(27 335 192 242)(28 314 193 221)(29 337 194 244)(30 316 195 223)(31 339 196 246)(32 318 197 225)(33 341 198 248)(34 320 199 227)(35 343 200 250)(36 322 201 229)(37 345 202 252)(38 324 203 231)(39 347 204 254)(40 326 205 233)(41 349 206 256)(42 328 207 235)(43 351 208 258)(44 330 209 237)(45 174 115 288)(46 153 116 267)(47 176 117 290)(48 155 118 269)(49 134 119 292)(50 157 120 271)(51 136 121 294)(52 159 122 273)(53 138 123 296)(54 161 124 275)(55 140 125 298)(56 163 126 277)(57 142 127 300)(58 165 128 279)(59 144 129 302)(60 167 130 281)(61 146 131 304)(62 169 132 283)(63 148 89 306)(64 171 90 285)(65 150 91 308)(66 173 92 287)(67 152 93 266)(68 175 94 289)(69 154 95 268)(70 133 96 291)(71 156 97 270)(72 135 98 293)(73 158 99 272)(74 137 100 295)(75 160 101 274)(76 139 102 297)(77 162 103 276)(78 141 104 299)(79 164 105 278)(80 143 106 301)(81 166 107 280)(82 145 108 303)(83 168 109 282)(84 147 110 305)(85 170 111 284)(86 149 112 307)(87 172 113 286)(88 151 114 265)
(1 59 210 129)(2 80 211 106)(3 57 212 127)(4 78 213 104)(5 55 214 125)(6 76 215 102)(7 53 216 123)(8 74 217 100)(9 51 218 121)(10 72 219 98)(11 49 220 119)(12 70 177 96)(13 47 178 117)(14 68 179 94)(15 45 180 115)(16 66 181 92)(17 87 182 113)(18 64 183 90)(19 85 184 111)(20 62 185 132)(21 83 186 109)(22 60 187 130)(23 81 188 107)(24 58 189 128)(25 79 190 105)(26 56 191 126)(27 77 192 103)(28 54 193 124)(29 75 194 101)(30 52 195 122)(31 73 196 99)(32 50 197 120)(33 71 198 97)(34 48 199 118)(35 69 200 95)(36 46 201 116)(37 67 202 93)(38 88 203 114)(39 65 204 91)(40 86 205 112)(41 63 206 89)(42 84 207 110)(43 61 208 131)(44 82 209 108)(133 342 291 249)(134 319 292 226)(135 340 293 247)(136 317 294 224)(137 338 295 245)(138 315 296 222)(139 336 297 243)(140 313 298 264)(141 334 299 241)(142 311 300 262)(143 332 301 239)(144 309 302 260)(145 330 303 237)(146 351 304 258)(147 328 305 235)(148 349 306 256)(149 326 307 233)(150 347 308 254)(151 324 265 231)(152 345 266 252)(153 322 267 229)(154 343 268 250)(155 320 269 227)(156 341 270 248)(157 318 271 225)(158 339 272 246)(159 316 273 223)(160 337 274 244)(161 314 275 221)(162 335 276 242)(163 312 277 263)(164 333 278 240)(165 310 279 261)(166 331 280 238)(167 352 281 259)(168 329 282 236)(169 350 283 257)(170 327 284 234)(171 348 285 255)(172 325 286 232)(173 346 287 253)(174 323 288 230)(175 344 289 251)(176 321 290 228)
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), (1,309,210,260)(2,332,211,239)(3,311,212,262)(4,334,213,241)(5,313,214,264)(6,336,215,243)(7,315,216,222)(8,338,217,245)(9,317,218,224)(10,340,219,247)(11,319,220,226)(12,342,177,249)(13,321,178,228)(14,344,179,251)(15,323,180,230)(16,346,181,253)(17,325,182,232)(18,348,183,255)(19,327,184,234)(20,350,185,257)(21,329,186,236)(22,352,187,259)(23,331,188,238)(24,310,189,261)(25,333,190,240)(26,312,191,263)(27,335,192,242)(28,314,193,221)(29,337,194,244)(30,316,195,223)(31,339,196,246)(32,318,197,225)(33,341,198,248)(34,320,199,227)(35,343,200,250)(36,322,201,229)(37,345,202,252)(38,324,203,231)(39,347,204,254)(40,326,205,233)(41,349,206,256)(42,328,207,235)(43,351,208,258)(44,330,209,237)(45,174,115,288)(46,153,116,267)(47,176,117,290)(48,155,118,269)(49,134,119,292)(50,157,120,271)(51,136,121,294)(52,159,122,273)(53,138,123,296)(54,161,124,275)(55,140,125,298)(56,163,126,277)(57,142,127,300)(58,165,128,279)(59,144,129,302)(60,167,130,281)(61,146,131,304)(62,169,132,283)(63,148,89,306)(64,171,90,285)(65,150,91,308)(66,173,92,287)(67,152,93,266)(68,175,94,289)(69,154,95,268)(70,133,96,291)(71,156,97,270)(72,135,98,293)(73,158,99,272)(74,137,100,295)(75,160,101,274)(76,139,102,297)(77,162,103,276)(78,141,104,299)(79,164,105,278)(80,143,106,301)(81,166,107,280)(82,145,108,303)(83,168,109,282)(84,147,110,305)(85,170,111,284)(86,149,112,307)(87,172,113,286)(88,151,114,265), (1,59,210,129)(2,80,211,106)(3,57,212,127)(4,78,213,104)(5,55,214,125)(6,76,215,102)(7,53,216,123)(8,74,217,100)(9,51,218,121)(10,72,219,98)(11,49,220,119)(12,70,177,96)(13,47,178,117)(14,68,179,94)(15,45,180,115)(16,66,181,92)(17,87,182,113)(18,64,183,90)(19,85,184,111)(20,62,185,132)(21,83,186,109)(22,60,187,130)(23,81,188,107)(24,58,189,128)(25,79,190,105)(26,56,191,126)(27,77,192,103)(28,54,193,124)(29,75,194,101)(30,52,195,122)(31,73,196,99)(32,50,197,120)(33,71,198,97)(34,48,199,118)(35,69,200,95)(36,46,201,116)(37,67,202,93)(38,88,203,114)(39,65,204,91)(40,86,205,112)(41,63,206,89)(42,84,207,110)(43,61,208,131)(44,82,209,108)(133,342,291,249)(134,319,292,226)(135,340,293,247)(136,317,294,224)(137,338,295,245)(138,315,296,222)(139,336,297,243)(140,313,298,264)(141,334,299,241)(142,311,300,262)(143,332,301,239)(144,309,302,260)(145,330,303,237)(146,351,304,258)(147,328,305,235)(148,349,306,256)(149,326,307,233)(150,347,308,254)(151,324,265,231)(152,345,266,252)(153,322,267,229)(154,343,268,250)(155,320,269,227)(156,341,270,248)(157,318,271,225)(158,339,272,246)(159,316,273,223)(160,337,274,244)(161,314,275,221)(162,335,276,242)(163,312,277,263)(164,333,278,240)(165,310,279,261)(166,331,280,238)(167,352,281,259)(168,329,282,236)(169,350,283,257)(170,327,284,234)(171,348,285,255)(172,325,286,232)(173,346,287,253)(174,323,288,230)(175,344,289,251)(176,321,290,228)>;
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), (1,309,210,260)(2,332,211,239)(3,311,212,262)(4,334,213,241)(5,313,214,264)(6,336,215,243)(7,315,216,222)(8,338,217,245)(9,317,218,224)(10,340,219,247)(11,319,220,226)(12,342,177,249)(13,321,178,228)(14,344,179,251)(15,323,180,230)(16,346,181,253)(17,325,182,232)(18,348,183,255)(19,327,184,234)(20,350,185,257)(21,329,186,236)(22,352,187,259)(23,331,188,238)(24,310,189,261)(25,333,190,240)(26,312,191,263)(27,335,192,242)(28,314,193,221)(29,337,194,244)(30,316,195,223)(31,339,196,246)(32,318,197,225)(33,341,198,248)(34,320,199,227)(35,343,200,250)(36,322,201,229)(37,345,202,252)(38,324,203,231)(39,347,204,254)(40,326,205,233)(41,349,206,256)(42,328,207,235)(43,351,208,258)(44,330,209,237)(45,174,115,288)(46,153,116,267)(47,176,117,290)(48,155,118,269)(49,134,119,292)(50,157,120,271)(51,136,121,294)(52,159,122,273)(53,138,123,296)(54,161,124,275)(55,140,125,298)(56,163,126,277)(57,142,127,300)(58,165,128,279)(59,144,129,302)(60,167,130,281)(61,146,131,304)(62,169,132,283)(63,148,89,306)(64,171,90,285)(65,150,91,308)(66,173,92,287)(67,152,93,266)(68,175,94,289)(69,154,95,268)(70,133,96,291)(71,156,97,270)(72,135,98,293)(73,158,99,272)(74,137,100,295)(75,160,101,274)(76,139,102,297)(77,162,103,276)(78,141,104,299)(79,164,105,278)(80,143,106,301)(81,166,107,280)(82,145,108,303)(83,168,109,282)(84,147,110,305)(85,170,111,284)(86,149,112,307)(87,172,113,286)(88,151,114,265), (1,59,210,129)(2,80,211,106)(3,57,212,127)(4,78,213,104)(5,55,214,125)(6,76,215,102)(7,53,216,123)(8,74,217,100)(9,51,218,121)(10,72,219,98)(11,49,220,119)(12,70,177,96)(13,47,178,117)(14,68,179,94)(15,45,180,115)(16,66,181,92)(17,87,182,113)(18,64,183,90)(19,85,184,111)(20,62,185,132)(21,83,186,109)(22,60,187,130)(23,81,188,107)(24,58,189,128)(25,79,190,105)(26,56,191,126)(27,77,192,103)(28,54,193,124)(29,75,194,101)(30,52,195,122)(31,73,196,99)(32,50,197,120)(33,71,198,97)(34,48,199,118)(35,69,200,95)(36,46,201,116)(37,67,202,93)(38,88,203,114)(39,65,204,91)(40,86,205,112)(41,63,206,89)(42,84,207,110)(43,61,208,131)(44,82,209,108)(133,342,291,249)(134,319,292,226)(135,340,293,247)(136,317,294,224)(137,338,295,245)(138,315,296,222)(139,336,297,243)(140,313,298,264)(141,334,299,241)(142,311,300,262)(143,332,301,239)(144,309,302,260)(145,330,303,237)(146,351,304,258)(147,328,305,235)(148,349,306,256)(149,326,307,233)(150,347,308,254)(151,324,265,231)(152,345,266,252)(153,322,267,229)(154,343,268,250)(155,320,269,227)(156,341,270,248)(157,318,271,225)(158,339,272,246)(159,316,273,223)(160,337,274,244)(161,314,275,221)(162,335,276,242)(163,312,277,263)(164,333,278,240)(165,310,279,261)(166,331,280,238)(167,352,281,259)(168,329,282,236)(169,350,283,257)(170,327,284,234)(171,348,285,255)(172,325,286,232)(173,346,287,253)(174,323,288,230)(175,344,289,251)(176,321,290,228) );
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)], [(1,309,210,260),(2,332,211,239),(3,311,212,262),(4,334,213,241),(5,313,214,264),(6,336,215,243),(7,315,216,222),(8,338,217,245),(9,317,218,224),(10,340,219,247),(11,319,220,226),(12,342,177,249),(13,321,178,228),(14,344,179,251),(15,323,180,230),(16,346,181,253),(17,325,182,232),(18,348,183,255),(19,327,184,234),(20,350,185,257),(21,329,186,236),(22,352,187,259),(23,331,188,238),(24,310,189,261),(25,333,190,240),(26,312,191,263),(27,335,192,242),(28,314,193,221),(29,337,194,244),(30,316,195,223),(31,339,196,246),(32,318,197,225),(33,341,198,248),(34,320,199,227),(35,343,200,250),(36,322,201,229),(37,345,202,252),(38,324,203,231),(39,347,204,254),(40,326,205,233),(41,349,206,256),(42,328,207,235),(43,351,208,258),(44,330,209,237),(45,174,115,288),(46,153,116,267),(47,176,117,290),(48,155,118,269),(49,134,119,292),(50,157,120,271),(51,136,121,294),(52,159,122,273),(53,138,123,296),(54,161,124,275),(55,140,125,298),(56,163,126,277),(57,142,127,300),(58,165,128,279),(59,144,129,302),(60,167,130,281),(61,146,131,304),(62,169,132,283),(63,148,89,306),(64,171,90,285),(65,150,91,308),(66,173,92,287),(67,152,93,266),(68,175,94,289),(69,154,95,268),(70,133,96,291),(71,156,97,270),(72,135,98,293),(73,158,99,272),(74,137,100,295),(75,160,101,274),(76,139,102,297),(77,162,103,276),(78,141,104,299),(79,164,105,278),(80,143,106,301),(81,166,107,280),(82,145,108,303),(83,168,109,282),(84,147,110,305),(85,170,111,284),(86,149,112,307),(87,172,113,286),(88,151,114,265)], [(1,59,210,129),(2,80,211,106),(3,57,212,127),(4,78,213,104),(5,55,214,125),(6,76,215,102),(7,53,216,123),(8,74,217,100),(9,51,218,121),(10,72,219,98),(11,49,220,119),(12,70,177,96),(13,47,178,117),(14,68,179,94),(15,45,180,115),(16,66,181,92),(17,87,182,113),(18,64,183,90),(19,85,184,111),(20,62,185,132),(21,83,186,109),(22,60,187,130),(23,81,188,107),(24,58,189,128),(25,79,190,105),(26,56,191,126),(27,77,192,103),(28,54,193,124),(29,75,194,101),(30,52,195,122),(31,73,196,99),(32,50,197,120),(33,71,198,97),(34,48,199,118),(35,69,200,95),(36,46,201,116),(37,67,202,93),(38,88,203,114),(39,65,204,91),(40,86,205,112),(41,63,206,89),(42,84,207,110),(43,61,208,131),(44,82,209,108),(133,342,291,249),(134,319,292,226),(135,340,293,247),(136,317,294,224),(137,338,295,245),(138,315,296,222),(139,336,297,243),(140,313,298,264),(141,334,299,241),(142,311,300,262),(143,332,301,239),(144,309,302,260),(145,330,303,237),(146,351,304,258),(147,328,305,235),(148,349,306,256),(149,326,307,233),(150,347,308,254),(151,324,265,231),(152,345,266,252),(153,322,267,229),(154,343,268,250),(155,320,269,227),(156,341,270,248),(157,318,271,225),(158,339,272,246),(159,316,273,223),(160,337,274,244),(161,314,275,221),(162,335,276,242),(163,312,277,263),(164,333,278,240),(165,310,279,261),(166,331,280,238),(167,352,281,259),(168,329,282,236),(169,350,283,257),(170,327,284,234),(171,348,285,255),(172,325,286,232),(173,346,287,253),(174,323,288,230),(175,344,289,251),(176,321,290,228)]])
64 conjugacy classes
| class | 1 | 2A | 2B | 2C | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 11A | ··· | 11E | 22A | ··· | 22O | 44A | ··· | 44AD |
| order | 1 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 11 | ··· | 11 | 22 | ··· | 22 | 44 | ··· | 44 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 4 | 4 | 22 | 22 | 22 | 22 | 44 | 44 | 2 | ··· | 2 | 2 | ··· | 2 | 4 | ··· | 4 |
64 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | - | - | + | + | - | + | - |
| image | C1 | C2 | C2 | C2 | C2 | C2 | D4 | Q8 | Q8 | D11 | D22 | Dic22 | D4×D11 | Q8×D11 |
| kernel | C44⋊Q8 | C4×Dic11 | Dic11⋊C4 | C44⋊C4 | C11×C4⋊C4 | C2×Dic22 | Dic11 | Dic11 | C44 | C4⋊C4 | C2×C4 | C4 | C2 | C2 |
| # reps | 1 | 1 | 2 | 1 | 1 | 2 | 2 | 2 | 2 | 5 | 15 | 20 | 5 | 5 |
Matrix representation of C44⋊Q8 ►in GL6(𝔽89)
| 88 | 0 | 0 | 0 | 0 | 0 |
| 0 | 88 | 0 | 0 | 0 | 0 |
| 0 | 0 | 74 | 17 | 0 | 0 |
| 0 | 0 | 5 | 18 | 0 | 0 |
| 0 | 0 | 0 | 0 | 83 | 73 |
| 0 | 0 | 0 | 0 | 19 | 6 |
| 1 | 22 | 0 | 0 | 0 | 0 |
| 8 | 88 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 22 | 84 |
| 0 | 0 | 0 | 0 | 61 | 67 |
| 29 | 39 | 0 | 0 | 0 | 0 |
| 56 | 60 | 0 | 0 | 0 | 0 |
| 0 | 0 | 43 | 51 | 0 | 0 |
| 0 | 0 | 58 | 46 | 0 | 0 |
| 0 | 0 | 0 | 0 | 88 | 0 |
| 0 | 0 | 0 | 0 | 0 | 88 |
G:=sub<GL(6,GF(89))| [88,0,0,0,0,0,0,88,0,0,0,0,0,0,74,5,0,0,0,0,17,18,0,0,0,0,0,0,83,19,0,0,0,0,73,6],[1,8,0,0,0,0,22,88,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,22,61,0,0,0,0,84,67],[29,56,0,0,0,0,39,60,0,0,0,0,0,0,43,58,0,0,0,0,51,46,0,0,0,0,0,0,88,0,0,0,0,0,0,88] >;
C44⋊Q8 in GAP, Magma, Sage, TeX
C_{44}\rtimes Q_8 % in TeX
G:=Group("C44:Q8"); // GroupNames label
G:=SmallGroup(352,83);
// by ID
G=gap.SmallGroup(352,83);
# by ID
G:=PCGroup([6,-2,-2,-2,-2,-2,-11,48,103,218,188,50,11525]);
// Polycyclic
G:=Group<a,b,c|a^44=b^4=1,c^2=b^2,b*a*b^-1=a^23,c*a*c^-1=a^21,c*b*c^-1=b^-1>;
// generators/relations