metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C44.44D4, C22.1Q16, Dic22⋊2C4, C2.1Dic44, C22.1SD16, C22.7D44, (C2×C88).2C2, C4.7(C4×D11), (C2×C8).2D11, C44.17(C2×C4), (C2×C4).67D22, (C2×C22).12D4, C44⋊C4.1C2, C2.7(D22⋊C4), C11⋊2(Q8⋊C4), C2.1(C8⋊D11), C4.19(C11⋊D4), C22.5(C22⋊C4), (C2×C44).80C22, (C2×Dic22).1C2, SmallGroup(352,22)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C44.44D4
G = < a,b,c | a44=b4=1, c2=a22, bab-1=cac-1=a-1, cbc-1=a33b-1 >
Smallest permutation representation of C44.44D4
►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)
(1 248 208 65)(2 247 209 64)(3 246 210 63)(4 245 211 62)(5 244 212 61)(6 243 213 60)(7 242 214 59)(8 241 215 58)(9 240 216 57)(10 239 217 56)(11 238 218 55)(12 237 219 54)(13 236 220 53)(14 235 177 52)(15 234 178 51)(16 233 179 50)(17 232 180 49)(18 231 181 48)(19 230 182 47)(20 229 183 46)(21 228 184 45)(22 227 185 88)(23 226 186 87)(24 225 187 86)(25 224 188 85)(26 223 189 84)(27 222 190 83)(28 221 191 82)(29 264 192 81)(30 263 193 80)(31 262 194 79)(32 261 195 78)(33 260 196 77)(34 259 197 76)(35 258 198 75)(36 257 199 74)(37 256 200 73)(38 255 201 72)(39 254 202 71)(40 253 203 70)(41 252 204 69)(42 251 205 68)(43 250 206 67)(44 249 207 66)(89 164 313 305)(90 163 314 304)(91 162 315 303)(92 161 316 302)(93 160 317 301)(94 159 318 300)(95 158 319 299)(96 157 320 298)(97 156 321 297)(98 155 322 296)(99 154 323 295)(100 153 324 294)(101 152 325 293)(102 151 326 292)(103 150 327 291)(104 149 328 290)(105 148 329 289)(106 147 330 288)(107 146 331 287)(108 145 332 286)(109 144 333 285)(110 143 334 284)(111 142 335 283)(112 141 336 282)(113 140 337 281)(114 139 338 280)(115 138 339 279)(116 137 340 278)(117 136 341 277)(118 135 342 276)(119 134 343 275)(120 133 344 274)(121 176 345 273)(122 175 346 272)(123 174 347 271)(124 173 348 270)(125 172 349 269)(126 171 350 268)(127 170 351 267)(128 169 352 266)(129 168 309 265)(130 167 310 308)(131 166 311 307)(132 165 312 306)
(1 319 23 341)(2 318 24 340)(3 317 25 339)(4 316 26 338)(5 315 27 337)(6 314 28 336)(7 313 29 335)(8 312 30 334)(9 311 31 333)(10 310 32 332)(11 309 33 331)(12 352 34 330)(13 351 35 329)(14 350 36 328)(15 349 37 327)(16 348 38 326)(17 347 39 325)(18 346 40 324)(19 345 41 323)(20 344 42 322)(21 343 43 321)(22 342 44 320)(45 286 67 308)(46 285 68 307)(47 284 69 306)(48 283 70 305)(49 282 71 304)(50 281 72 303)(51 280 73 302)(52 279 74 301)(53 278 75 300)(54 277 76 299)(55 276 77 298)(56 275 78 297)(57 274 79 296)(58 273 80 295)(59 272 81 294)(60 271 82 293)(61 270 83 292)(62 269 84 291)(63 268 85 290)(64 267 86 289)(65 266 87 288)(66 265 88 287)(89 192 111 214)(90 191 112 213)(91 190 113 212)(92 189 114 211)(93 188 115 210)(94 187 116 209)(95 186 117 208)(96 185 118 207)(97 184 119 206)(98 183 120 205)(99 182 121 204)(100 181 122 203)(101 180 123 202)(102 179 124 201)(103 178 125 200)(104 177 126 199)(105 220 127 198)(106 219 128 197)(107 218 129 196)(108 217 130 195)(109 216 131 194)(110 215 132 193)(133 262 155 240)(134 261 156 239)(135 260 157 238)(136 259 158 237)(137 258 159 236)(138 257 160 235)(139 256 161 234)(140 255 162 233)(141 254 163 232)(142 253 164 231)(143 252 165 230)(144 251 166 229)(145 250 167 228)(146 249 168 227)(147 248 169 226)(148 247 170 225)(149 246 171 224)(150 245 172 223)(151 244 173 222)(152 243 174 221)(153 242 175 264)(154 241 176 263)
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), (1,248,208,65)(2,247,209,64)(3,246,210,63)(4,245,211,62)(5,244,212,61)(6,243,213,60)(7,242,214,59)(8,241,215,58)(9,240,216,57)(10,239,217,56)(11,238,218,55)(12,237,219,54)(13,236,220,53)(14,235,177,52)(15,234,178,51)(16,233,179,50)(17,232,180,49)(18,231,181,48)(19,230,182,47)(20,229,183,46)(21,228,184,45)(22,227,185,88)(23,226,186,87)(24,225,187,86)(25,224,188,85)(26,223,189,84)(27,222,190,83)(28,221,191,82)(29,264,192,81)(30,263,193,80)(31,262,194,79)(32,261,195,78)(33,260,196,77)(34,259,197,76)(35,258,198,75)(36,257,199,74)(37,256,200,73)(38,255,201,72)(39,254,202,71)(40,253,203,70)(41,252,204,69)(42,251,205,68)(43,250,206,67)(44,249,207,66)(89,164,313,305)(90,163,314,304)(91,162,315,303)(92,161,316,302)(93,160,317,301)(94,159,318,300)(95,158,319,299)(96,157,320,298)(97,156,321,297)(98,155,322,296)(99,154,323,295)(100,153,324,294)(101,152,325,293)(102,151,326,292)(103,150,327,291)(104,149,328,290)(105,148,329,289)(106,147,330,288)(107,146,331,287)(108,145,332,286)(109,144,333,285)(110,143,334,284)(111,142,335,283)(112,141,336,282)(113,140,337,281)(114,139,338,280)(115,138,339,279)(116,137,340,278)(117,136,341,277)(118,135,342,276)(119,134,343,275)(120,133,344,274)(121,176,345,273)(122,175,346,272)(123,174,347,271)(124,173,348,270)(125,172,349,269)(126,171,350,268)(127,170,351,267)(128,169,352,266)(129,168,309,265)(130,167,310,308)(131,166,311,307)(132,165,312,306), (1,319,23,341)(2,318,24,340)(3,317,25,339)(4,316,26,338)(5,315,27,337)(6,314,28,336)(7,313,29,335)(8,312,30,334)(9,311,31,333)(10,310,32,332)(11,309,33,331)(12,352,34,330)(13,351,35,329)(14,350,36,328)(15,349,37,327)(16,348,38,326)(17,347,39,325)(18,346,40,324)(19,345,41,323)(20,344,42,322)(21,343,43,321)(22,342,44,320)(45,286,67,308)(46,285,68,307)(47,284,69,306)(48,283,70,305)(49,282,71,304)(50,281,72,303)(51,280,73,302)(52,279,74,301)(53,278,75,300)(54,277,76,299)(55,276,77,298)(56,275,78,297)(57,274,79,296)(58,273,80,295)(59,272,81,294)(60,271,82,293)(61,270,83,292)(62,269,84,291)(63,268,85,290)(64,267,86,289)(65,266,87,288)(66,265,88,287)(89,192,111,214)(90,191,112,213)(91,190,113,212)(92,189,114,211)(93,188,115,210)(94,187,116,209)(95,186,117,208)(96,185,118,207)(97,184,119,206)(98,183,120,205)(99,182,121,204)(100,181,122,203)(101,180,123,202)(102,179,124,201)(103,178,125,200)(104,177,126,199)(105,220,127,198)(106,219,128,197)(107,218,129,196)(108,217,130,195)(109,216,131,194)(110,215,132,193)(133,262,155,240)(134,261,156,239)(135,260,157,238)(136,259,158,237)(137,258,159,236)(138,257,160,235)(139,256,161,234)(140,255,162,233)(141,254,163,232)(142,253,164,231)(143,252,165,230)(144,251,166,229)(145,250,167,228)(146,249,168,227)(147,248,169,226)(148,247,170,225)(149,246,171,224)(150,245,172,223)(151,244,173,222)(152,243,174,221)(153,242,175,264)(154,241,176,263)>;
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), (1,248,208,65)(2,247,209,64)(3,246,210,63)(4,245,211,62)(5,244,212,61)(6,243,213,60)(7,242,214,59)(8,241,215,58)(9,240,216,57)(10,239,217,56)(11,238,218,55)(12,237,219,54)(13,236,220,53)(14,235,177,52)(15,234,178,51)(16,233,179,50)(17,232,180,49)(18,231,181,48)(19,230,182,47)(20,229,183,46)(21,228,184,45)(22,227,185,88)(23,226,186,87)(24,225,187,86)(25,224,188,85)(26,223,189,84)(27,222,190,83)(28,221,191,82)(29,264,192,81)(30,263,193,80)(31,262,194,79)(32,261,195,78)(33,260,196,77)(34,259,197,76)(35,258,198,75)(36,257,199,74)(37,256,200,73)(38,255,201,72)(39,254,202,71)(40,253,203,70)(41,252,204,69)(42,251,205,68)(43,250,206,67)(44,249,207,66)(89,164,313,305)(90,163,314,304)(91,162,315,303)(92,161,316,302)(93,160,317,301)(94,159,318,300)(95,158,319,299)(96,157,320,298)(97,156,321,297)(98,155,322,296)(99,154,323,295)(100,153,324,294)(101,152,325,293)(102,151,326,292)(103,150,327,291)(104,149,328,290)(105,148,329,289)(106,147,330,288)(107,146,331,287)(108,145,332,286)(109,144,333,285)(110,143,334,284)(111,142,335,283)(112,141,336,282)(113,140,337,281)(114,139,338,280)(115,138,339,279)(116,137,340,278)(117,136,341,277)(118,135,342,276)(119,134,343,275)(120,133,344,274)(121,176,345,273)(122,175,346,272)(123,174,347,271)(124,173,348,270)(125,172,349,269)(126,171,350,268)(127,170,351,267)(128,169,352,266)(129,168,309,265)(130,167,310,308)(131,166,311,307)(132,165,312,306), (1,319,23,341)(2,318,24,340)(3,317,25,339)(4,316,26,338)(5,315,27,337)(6,314,28,336)(7,313,29,335)(8,312,30,334)(9,311,31,333)(10,310,32,332)(11,309,33,331)(12,352,34,330)(13,351,35,329)(14,350,36,328)(15,349,37,327)(16,348,38,326)(17,347,39,325)(18,346,40,324)(19,345,41,323)(20,344,42,322)(21,343,43,321)(22,342,44,320)(45,286,67,308)(46,285,68,307)(47,284,69,306)(48,283,70,305)(49,282,71,304)(50,281,72,303)(51,280,73,302)(52,279,74,301)(53,278,75,300)(54,277,76,299)(55,276,77,298)(56,275,78,297)(57,274,79,296)(58,273,80,295)(59,272,81,294)(60,271,82,293)(61,270,83,292)(62,269,84,291)(63,268,85,290)(64,267,86,289)(65,266,87,288)(66,265,88,287)(89,192,111,214)(90,191,112,213)(91,190,113,212)(92,189,114,211)(93,188,115,210)(94,187,116,209)(95,186,117,208)(96,185,118,207)(97,184,119,206)(98,183,120,205)(99,182,121,204)(100,181,122,203)(101,180,123,202)(102,179,124,201)(103,178,125,200)(104,177,126,199)(105,220,127,198)(106,219,128,197)(107,218,129,196)(108,217,130,195)(109,216,131,194)(110,215,132,193)(133,262,155,240)(134,261,156,239)(135,260,157,238)(136,259,158,237)(137,258,159,236)(138,257,160,235)(139,256,161,234)(140,255,162,233)(141,254,163,232)(142,253,164,231)(143,252,165,230)(144,251,166,229)(145,250,167,228)(146,249,168,227)(147,248,169,226)(148,247,170,225)(149,246,171,224)(150,245,172,223)(151,244,173,222)(152,243,174,221)(153,242,175,264)(154,241,176,263) );
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)], [(1,248,208,65),(2,247,209,64),(3,246,210,63),(4,245,211,62),(5,244,212,61),(6,243,213,60),(7,242,214,59),(8,241,215,58),(9,240,216,57),(10,239,217,56),(11,238,218,55),(12,237,219,54),(13,236,220,53),(14,235,177,52),(15,234,178,51),(16,233,179,50),(17,232,180,49),(18,231,181,48),(19,230,182,47),(20,229,183,46),(21,228,184,45),(22,227,185,88),(23,226,186,87),(24,225,187,86),(25,224,188,85),(26,223,189,84),(27,222,190,83),(28,221,191,82),(29,264,192,81),(30,263,193,80),(31,262,194,79),(32,261,195,78),(33,260,196,77),(34,259,197,76),(35,258,198,75),(36,257,199,74),(37,256,200,73),(38,255,201,72),(39,254,202,71),(40,253,203,70),(41,252,204,69),(42,251,205,68),(43,250,206,67),(44,249,207,66),(89,164,313,305),(90,163,314,304),(91,162,315,303),(92,161,316,302),(93,160,317,301),(94,159,318,300),(95,158,319,299),(96,157,320,298),(97,156,321,297),(98,155,322,296),(99,154,323,295),(100,153,324,294),(101,152,325,293),(102,151,326,292),(103,150,327,291),(104,149,328,290),(105,148,329,289),(106,147,330,288),(107,146,331,287),(108,145,332,286),(109,144,333,285),(110,143,334,284),(111,142,335,283),(112,141,336,282),(113,140,337,281),(114,139,338,280),(115,138,339,279),(116,137,340,278),(117,136,341,277),(118,135,342,276),(119,134,343,275),(120,133,344,274),(121,176,345,273),(122,175,346,272),(123,174,347,271),(124,173,348,270),(125,172,349,269),(126,171,350,268),(127,170,351,267),(128,169,352,266),(129,168,309,265),(130,167,310,308),(131,166,311,307),(132,165,312,306)], [(1,319,23,341),(2,318,24,340),(3,317,25,339),(4,316,26,338),(5,315,27,337),(6,314,28,336),(7,313,29,335),(8,312,30,334),(9,311,31,333),(10,310,32,332),(11,309,33,331),(12,352,34,330),(13,351,35,329),(14,350,36,328),(15,349,37,327),(16,348,38,326),(17,347,39,325),(18,346,40,324),(19,345,41,323),(20,344,42,322),(21,343,43,321),(22,342,44,320),(45,286,67,308),(46,285,68,307),(47,284,69,306),(48,283,70,305),(49,282,71,304),(50,281,72,303),(51,280,73,302),(52,279,74,301),(53,278,75,300),(54,277,76,299),(55,276,77,298),(56,275,78,297),(57,274,79,296),(58,273,80,295),(59,272,81,294),(60,271,82,293),(61,270,83,292),(62,269,84,291),(63,268,85,290),(64,267,86,289),(65,266,87,288),(66,265,88,287),(89,192,111,214),(90,191,112,213),(91,190,113,212),(92,189,114,211),(93,188,115,210),(94,187,116,209),(95,186,117,208),(96,185,118,207),(97,184,119,206),(98,183,120,205),(99,182,121,204),(100,181,122,203),(101,180,123,202),(102,179,124,201),(103,178,125,200),(104,177,126,199),(105,220,127,198),(106,219,128,197),(107,218,129,196),(108,217,130,195),(109,216,131,194),(110,215,132,193),(133,262,155,240),(134,261,156,239),(135,260,157,238),(136,259,158,237),(137,258,159,236),(138,257,160,235),(139,256,161,234),(140,255,162,233),(141,254,163,232),(142,253,164,231),(143,252,165,230),(144,251,166,229),(145,250,167,228),(146,249,168,227),(147,248,169,226),(148,247,170,225),(149,246,171,224),(150,245,172,223),(151,244,173,222),(152,243,174,221),(153,242,175,264),(154,241,176,263)]])
94 conjugacy classes
| class | 1 | 2A | 2B | 2C | 4A | 4B | 4C | 4D | 4E | 4F | 8A | 8B | 8C | 8D | 11A | ··· | 11E | 22A | ··· | 22O | 44A | ··· | 44T | 88A | ··· | 88AN |
| order | 1 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 8 | 8 | 8 | 8 | 11 | ··· | 11 | 22 | ··· | 22 | 44 | ··· | 44 | 88 | ··· | 88 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 44 | 44 | 44 | 44 | 2 | 2 | 2 | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
94 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | + | - | + | + | + | - | |||||
| image | C1 | C2 | C2 | C2 | C4 | D4 | D4 | SD16 | Q16 | D11 | D22 | C4×D11 | C11⋊D4 | D44 | C8⋊D11 | Dic44 |
| kernel | C44.44D4 | C44⋊C4 | C2×C88 | C2×Dic22 | Dic22 | C44 | C2×C22 | C22 | C22 | C2×C8 | C2×C4 | C4 | C4 | C22 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 4 | 1 | 1 | 2 | 2 | 5 | 5 | 10 | 10 | 10 | 20 | 20 |
Matrix representation of C44.44D4 ►in GL4(𝔽89) generated by
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 40 | 73 |
| 0 | 0 | 11 | 29 |
| 0 | 1 | 0 | 0 |
| 88 | 0 | 0 | 0 |
| 0 | 0 | 61 | 41 |
| 0 | 0 | 59 | 28 |
| 88 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 26 | 23 |
| 0 | 0 | 17 | 63 |
G:=sub<GL(4,GF(89))| [1,0,0,0,0,1,0,0,0,0,40,11,0,0,73,29],[0,88,0,0,1,0,0,0,0,0,61,59,0,0,41,28],[88,0,0,0,0,1,0,0,0,0,26,17,0,0,23,63] >;
C44.44D4 in GAP, Magma, Sage, TeX
C_{44}._{44}D_4 % in TeX
G:=Group("C44.44D4"); // GroupNames label
G:=SmallGroup(352,22);
// by ID
G=gap.SmallGroup(352,22);
# by ID
G:=PCGroup([6,-2,-2,-2,-2,-2,-11,48,73,79,362,86,11525]);
// Polycyclic
G:=Group<a,b,c|a^44=b^4=1,c^2=a^22,b*a*b^-1=c*a*c^-1=a^-1,c*b*c^-1=a^33*b^-1>;
// generators/relations
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