metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C44⋊2Q8, C4.4D44, C4⋊2Dic22, C44.27D4, C42.4D11, C11⋊1(C4⋊Q8), (C4×C44).2C2, C22.1(C2×D4), C2.4(C2×D44), C22.2(C2×Q8), (C2×C4).73D22, C44⋊C4.4C2, C2.4(C2×Dic22), (C2×C44).85C22, (C2×C22).10C23, (C2×Dic22).2C2, (C2×Dic11).1C22, C22.34(C22×D11), SmallGroup(352,64)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C44⋊2Q8
G = < a,b,c | a44=b4=1, c2=b2, ab=ba, cac-1=a-1, cbc-1=b-1 >
Subgroups: 354 in 68 conjugacy classes, 41 normal (11 characteristic)
C1, C2, C2, C4, C4, C22, C2×C4, C2×C4, C2×C4, Q8, C11, C42, C4⋊C4, C2×Q8, C22, C22, C4⋊Q8, Dic11, C44, C2×C22, Dic22, C2×Dic11, C2×C44, C2×C44, C44⋊C4, C4×C44, C2×Dic22, C44⋊2Q8
Quotients: C1, C2, C22, D4, Q8, C23, C2×D4, C2×Q8, D11, C4⋊Q8, D22, Dic22, D44, C22×D11, C2×Dic22, C2×D44, C44⋊2Q8
►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)
(1 328 281 108)(2 329 282 109)(3 330 283 110)(4 331 284 111)(5 332 285 112)(6 333 286 113)(7 334 287 114)(8 335 288 115)(9 336 289 116)(10 337 290 117)(11 338 291 118)(12 339 292 119)(13 340 293 120)(14 341 294 121)(15 342 295 122)(16 343 296 123)(17 344 297 124)(18 345 298 125)(19 346 299 126)(20 347 300 127)(21 348 301 128)(22 349 302 129)(23 350 303 130)(24 351 304 131)(25 352 305 132)(26 309 306 89)(27 310 307 90)(28 311 308 91)(29 312 265 92)(30 313 266 93)(31 314 267 94)(32 315 268 95)(33 316 269 96)(34 317 270 97)(35 318 271 98)(36 319 272 99)(37 320 273 100)(38 321 274 101)(39 322 275 102)(40 323 276 103)(41 324 277 104)(42 325 278 105)(43 326 279 106)(44 327 280 107)(45 261 137 190)(46 262 138 191)(47 263 139 192)(48 264 140 193)(49 221 141 194)(50 222 142 195)(51 223 143 196)(52 224 144 197)(53 225 145 198)(54 226 146 199)(55 227 147 200)(56 228 148 201)(57 229 149 202)(58 230 150 203)(59 231 151 204)(60 232 152 205)(61 233 153 206)(62 234 154 207)(63 235 155 208)(64 236 156 209)(65 237 157 210)(66 238 158 211)(67 239 159 212)(68 240 160 213)(69 241 161 214)(70 242 162 215)(71 243 163 216)(72 244 164 217)(73 245 165 218)(74 246 166 219)(75 247 167 220)(76 248 168 177)(77 249 169 178)(78 250 170 179)(79 251 171 180)(80 252 172 181)(81 253 173 182)(82 254 174 183)(83 255 175 184)(84 256 176 185)(85 257 133 186)(86 258 134 187)(87 259 135 188)(88 260 136 189)
(1 62 281 154)(2 61 282 153)(3 60 283 152)(4 59 284 151)(5 58 285 150)(6 57 286 149)(7 56 287 148)(8 55 288 147)(9 54 289 146)(10 53 290 145)(11 52 291 144)(12 51 292 143)(13 50 293 142)(14 49 294 141)(15 48 295 140)(16 47 296 139)(17 46 297 138)(18 45 298 137)(19 88 299 136)(20 87 300 135)(21 86 301 134)(22 85 302 133)(23 84 303 176)(24 83 304 175)(25 82 305 174)(26 81 306 173)(27 80 307 172)(28 79 308 171)(29 78 265 170)(30 77 266 169)(31 76 267 168)(32 75 268 167)(33 74 269 166)(34 73 270 165)(35 72 271 164)(36 71 272 163)(37 70 273 162)(38 69 274 161)(39 68 275 160)(40 67 276 159)(41 66 277 158)(42 65 278 157)(43 64 279 156)(44 63 280 155)(89 253 309 182)(90 252 310 181)(91 251 311 180)(92 250 312 179)(93 249 313 178)(94 248 314 177)(95 247 315 220)(96 246 316 219)(97 245 317 218)(98 244 318 217)(99 243 319 216)(100 242 320 215)(101 241 321 214)(102 240 322 213)(103 239 323 212)(104 238 324 211)(105 237 325 210)(106 236 326 209)(107 235 327 208)(108 234 328 207)(109 233 329 206)(110 232 330 205)(111 231 331 204)(112 230 332 203)(113 229 333 202)(114 228 334 201)(115 227 335 200)(116 226 336 199)(117 225 337 198)(118 224 338 197)(119 223 339 196)(120 222 340 195)(121 221 341 194)(122 264 342 193)(123 263 343 192)(124 262 344 191)(125 261 345 190)(126 260 346 189)(127 259 347 188)(128 258 348 187)(129 257 349 186)(130 256 350 185)(131 255 351 184)(132 254 352 183)
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), (1,328,281,108)(2,329,282,109)(3,330,283,110)(4,331,284,111)(5,332,285,112)(6,333,286,113)(7,334,287,114)(8,335,288,115)(9,336,289,116)(10,337,290,117)(11,338,291,118)(12,339,292,119)(13,340,293,120)(14,341,294,121)(15,342,295,122)(16,343,296,123)(17,344,297,124)(18,345,298,125)(19,346,299,126)(20,347,300,127)(21,348,301,128)(22,349,302,129)(23,350,303,130)(24,351,304,131)(25,352,305,132)(26,309,306,89)(27,310,307,90)(28,311,308,91)(29,312,265,92)(30,313,266,93)(31,314,267,94)(32,315,268,95)(33,316,269,96)(34,317,270,97)(35,318,271,98)(36,319,272,99)(37,320,273,100)(38,321,274,101)(39,322,275,102)(40,323,276,103)(41,324,277,104)(42,325,278,105)(43,326,279,106)(44,327,280,107)(45,261,137,190)(46,262,138,191)(47,263,139,192)(48,264,140,193)(49,221,141,194)(50,222,142,195)(51,223,143,196)(52,224,144,197)(53,225,145,198)(54,226,146,199)(55,227,147,200)(56,228,148,201)(57,229,149,202)(58,230,150,203)(59,231,151,204)(60,232,152,205)(61,233,153,206)(62,234,154,207)(63,235,155,208)(64,236,156,209)(65,237,157,210)(66,238,158,211)(67,239,159,212)(68,240,160,213)(69,241,161,214)(70,242,162,215)(71,243,163,216)(72,244,164,217)(73,245,165,218)(74,246,166,219)(75,247,167,220)(76,248,168,177)(77,249,169,178)(78,250,170,179)(79,251,171,180)(80,252,172,181)(81,253,173,182)(82,254,174,183)(83,255,175,184)(84,256,176,185)(85,257,133,186)(86,258,134,187)(87,259,135,188)(88,260,136,189), (1,62,281,154)(2,61,282,153)(3,60,283,152)(4,59,284,151)(5,58,285,150)(6,57,286,149)(7,56,287,148)(8,55,288,147)(9,54,289,146)(10,53,290,145)(11,52,291,144)(12,51,292,143)(13,50,293,142)(14,49,294,141)(15,48,295,140)(16,47,296,139)(17,46,297,138)(18,45,298,137)(19,88,299,136)(20,87,300,135)(21,86,301,134)(22,85,302,133)(23,84,303,176)(24,83,304,175)(25,82,305,174)(26,81,306,173)(27,80,307,172)(28,79,308,171)(29,78,265,170)(30,77,266,169)(31,76,267,168)(32,75,268,167)(33,74,269,166)(34,73,270,165)(35,72,271,164)(36,71,272,163)(37,70,273,162)(38,69,274,161)(39,68,275,160)(40,67,276,159)(41,66,277,158)(42,65,278,157)(43,64,279,156)(44,63,280,155)(89,253,309,182)(90,252,310,181)(91,251,311,180)(92,250,312,179)(93,249,313,178)(94,248,314,177)(95,247,315,220)(96,246,316,219)(97,245,317,218)(98,244,318,217)(99,243,319,216)(100,242,320,215)(101,241,321,214)(102,240,322,213)(103,239,323,212)(104,238,324,211)(105,237,325,210)(106,236,326,209)(107,235,327,208)(108,234,328,207)(109,233,329,206)(110,232,330,205)(111,231,331,204)(112,230,332,203)(113,229,333,202)(114,228,334,201)(115,227,335,200)(116,226,336,199)(117,225,337,198)(118,224,338,197)(119,223,339,196)(120,222,340,195)(121,221,341,194)(122,264,342,193)(123,263,343,192)(124,262,344,191)(125,261,345,190)(126,260,346,189)(127,259,347,188)(128,258,348,187)(129,257,349,186)(130,256,350,185)(131,255,351,184)(132,254,352,183)>;
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), (1,328,281,108)(2,329,282,109)(3,330,283,110)(4,331,284,111)(5,332,285,112)(6,333,286,113)(7,334,287,114)(8,335,288,115)(9,336,289,116)(10,337,290,117)(11,338,291,118)(12,339,292,119)(13,340,293,120)(14,341,294,121)(15,342,295,122)(16,343,296,123)(17,344,297,124)(18,345,298,125)(19,346,299,126)(20,347,300,127)(21,348,301,128)(22,349,302,129)(23,350,303,130)(24,351,304,131)(25,352,305,132)(26,309,306,89)(27,310,307,90)(28,311,308,91)(29,312,265,92)(30,313,266,93)(31,314,267,94)(32,315,268,95)(33,316,269,96)(34,317,270,97)(35,318,271,98)(36,319,272,99)(37,320,273,100)(38,321,274,101)(39,322,275,102)(40,323,276,103)(41,324,277,104)(42,325,278,105)(43,326,279,106)(44,327,280,107)(45,261,137,190)(46,262,138,191)(47,263,139,192)(48,264,140,193)(49,221,141,194)(50,222,142,195)(51,223,143,196)(52,224,144,197)(53,225,145,198)(54,226,146,199)(55,227,147,200)(56,228,148,201)(57,229,149,202)(58,230,150,203)(59,231,151,204)(60,232,152,205)(61,233,153,206)(62,234,154,207)(63,235,155,208)(64,236,156,209)(65,237,157,210)(66,238,158,211)(67,239,159,212)(68,240,160,213)(69,241,161,214)(70,242,162,215)(71,243,163,216)(72,244,164,217)(73,245,165,218)(74,246,166,219)(75,247,167,220)(76,248,168,177)(77,249,169,178)(78,250,170,179)(79,251,171,180)(80,252,172,181)(81,253,173,182)(82,254,174,183)(83,255,175,184)(84,256,176,185)(85,257,133,186)(86,258,134,187)(87,259,135,188)(88,260,136,189), (1,62,281,154)(2,61,282,153)(3,60,283,152)(4,59,284,151)(5,58,285,150)(6,57,286,149)(7,56,287,148)(8,55,288,147)(9,54,289,146)(10,53,290,145)(11,52,291,144)(12,51,292,143)(13,50,293,142)(14,49,294,141)(15,48,295,140)(16,47,296,139)(17,46,297,138)(18,45,298,137)(19,88,299,136)(20,87,300,135)(21,86,301,134)(22,85,302,133)(23,84,303,176)(24,83,304,175)(25,82,305,174)(26,81,306,173)(27,80,307,172)(28,79,308,171)(29,78,265,170)(30,77,266,169)(31,76,267,168)(32,75,268,167)(33,74,269,166)(34,73,270,165)(35,72,271,164)(36,71,272,163)(37,70,273,162)(38,69,274,161)(39,68,275,160)(40,67,276,159)(41,66,277,158)(42,65,278,157)(43,64,279,156)(44,63,280,155)(89,253,309,182)(90,252,310,181)(91,251,311,180)(92,250,312,179)(93,249,313,178)(94,248,314,177)(95,247,315,220)(96,246,316,219)(97,245,317,218)(98,244,318,217)(99,243,319,216)(100,242,320,215)(101,241,321,214)(102,240,322,213)(103,239,323,212)(104,238,324,211)(105,237,325,210)(106,236,326,209)(107,235,327,208)(108,234,328,207)(109,233,329,206)(110,232,330,205)(111,231,331,204)(112,230,332,203)(113,229,333,202)(114,228,334,201)(115,227,335,200)(116,226,336,199)(117,225,337,198)(118,224,338,197)(119,223,339,196)(120,222,340,195)(121,221,341,194)(122,264,342,193)(123,263,343,192)(124,262,344,191)(125,261,345,190)(126,260,346,189)(127,259,347,188)(128,258,348,187)(129,257,349,186)(130,256,350,185)(131,255,351,184)(132,254,352,183) );
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)], [(1,328,281,108),(2,329,282,109),(3,330,283,110),(4,331,284,111),(5,332,285,112),(6,333,286,113),(7,334,287,114),(8,335,288,115),(9,336,289,116),(10,337,290,117),(11,338,291,118),(12,339,292,119),(13,340,293,120),(14,341,294,121),(15,342,295,122),(16,343,296,123),(17,344,297,124),(18,345,298,125),(19,346,299,126),(20,347,300,127),(21,348,301,128),(22,349,302,129),(23,350,303,130),(24,351,304,131),(25,352,305,132),(26,309,306,89),(27,310,307,90),(28,311,308,91),(29,312,265,92),(30,313,266,93),(31,314,267,94),(32,315,268,95),(33,316,269,96),(34,317,270,97),(35,318,271,98),(36,319,272,99),(37,320,273,100),(38,321,274,101),(39,322,275,102),(40,323,276,103),(41,324,277,104),(42,325,278,105),(43,326,279,106),(44,327,280,107),(45,261,137,190),(46,262,138,191),(47,263,139,192),(48,264,140,193),(49,221,141,194),(50,222,142,195),(51,223,143,196),(52,224,144,197),(53,225,145,198),(54,226,146,199),(55,227,147,200),(56,228,148,201),(57,229,149,202),(58,230,150,203),(59,231,151,204),(60,232,152,205),(61,233,153,206),(62,234,154,207),(63,235,155,208),(64,236,156,209),(65,237,157,210),(66,238,158,211),(67,239,159,212),(68,240,160,213),(69,241,161,214),(70,242,162,215),(71,243,163,216),(72,244,164,217),(73,245,165,218),(74,246,166,219),(75,247,167,220),(76,248,168,177),(77,249,169,178),(78,250,170,179),(79,251,171,180),(80,252,172,181),(81,253,173,182),(82,254,174,183),(83,255,175,184),(84,256,176,185),(85,257,133,186),(86,258,134,187),(87,259,135,188),(88,260,136,189)], [(1,62,281,154),(2,61,282,153),(3,60,283,152),(4,59,284,151),(5,58,285,150),(6,57,286,149),(7,56,287,148),(8,55,288,147),(9,54,289,146),(10,53,290,145),(11,52,291,144),(12,51,292,143),(13,50,293,142),(14,49,294,141),(15,48,295,140),(16,47,296,139),(17,46,297,138),(18,45,298,137),(19,88,299,136),(20,87,300,135),(21,86,301,134),(22,85,302,133),(23,84,303,176),(24,83,304,175),(25,82,305,174),(26,81,306,173),(27,80,307,172),(28,79,308,171),(29,78,265,170),(30,77,266,169),(31,76,267,168),(32,75,268,167),(33,74,269,166),(34,73,270,165),(35,72,271,164),(36,71,272,163),(37,70,273,162),(38,69,274,161),(39,68,275,160),(40,67,276,159),(41,66,277,158),(42,65,278,157),(43,64,279,156),(44,63,280,155),(89,253,309,182),(90,252,310,181),(91,251,311,180),(92,250,312,179),(93,249,313,178),(94,248,314,177),(95,247,315,220),(96,246,316,219),(97,245,317,218),(98,244,318,217),(99,243,319,216),(100,242,320,215),(101,241,321,214),(102,240,322,213),(103,239,323,212),(104,238,324,211),(105,237,325,210),(106,236,326,209),(107,235,327,208),(108,234,328,207),(109,233,329,206),(110,232,330,205),(111,231,331,204),(112,230,332,203),(113,229,333,202),(114,228,334,201),(115,227,335,200),(116,226,336,199),(117,225,337,198),(118,224,338,197),(119,223,339,196),(120,222,340,195),(121,221,341,194),(122,264,342,193),(123,263,343,192),(124,262,344,191),(125,261,345,190),(126,260,346,189),(127,259,347,188),(128,258,348,187),(129,257,349,186),(130,256,350,185),(131,255,351,184),(132,254,352,183)]])
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 | D4 | Q8 | D11 | D22 | Dic22 | D44 |
| kernel | C44⋊2Q8 | C44⋊C4 | C4×C44 | C2×Dic22 | C44 | C44 | C42 | C2×C4 | C4 | C4 |
| # reps | 1 | 4 | 1 | 2 | 2 | 4 | 5 | 15 | 40 | 20 |
Matrix representation of C44⋊2Q8 ►in GL4(𝔽89) generated by
| 50 | 65 | 0 | 0 |
| 24 | 33 | 0 | 0 |
| 0 | 0 | 8 | 56 |
| 0 | 0 | 65 | 88 |
| 88 | 0 | 0 | 0 |
| 0 | 88 | 0 | 0 |
| 0 | 0 | 4 | 30 |
| 0 | 0 | 38 | 85 |
| 3 | 1 | 0 | 0 |
| 81 | 86 | 0 | 0 |
| 0 | 0 | 42 | 48 |
| 0 | 0 | 17 | 47 |
G:=sub<GL(4,GF(89))| [50,24,0,0,65,33,0,0,0,0,8,65,0,0,56,88],[88,0,0,0,0,88,0,0,0,0,4,38,0,0,30,85],[3,81,0,0,1,86,0,0,0,0,42,17,0,0,48,47] >;
C44⋊2Q8 in GAP, Magma, Sage, TeX
C_{44}\rtimes_2Q_8 % in TeX
G:=Group("C44:2Q8"); // GroupNames label
G:=SmallGroup(352,64);
// by ID
G=gap.SmallGroup(352,64);
# by ID
G:=PCGroup([6,-2,-2,-2,-2,-2,-11,96,217,103,218,50,11525]);
// Polycyclic
G:=Group<a,b,c|a^44=b^4=1,c^2=b^2,a*b=b*a,c*a*c^-1=a^-1,c*b*c^-1=b^-1>;
// generators/relations