direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C2×Dic44, C22⋊1Q16, C4.8D44, C8.16D22, C44.31D4, C88.18C22, C44.31C23, C22.14D44, Dic22.7C22, C11⋊1(C2×Q16), (C2×C88).6C2, (C2×C8).4D11, C22.12(C2×D4), C2.14(C2×D44), (C2×C4).82D22, (C2×C22).19D4, (C2×C44).90C22, (C2×Dic22).4C2, C4.29(C22×D11), SmallGroup(352,100)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C2×Dic44
G = < a,b,c | a2=b88=1, c2=b44, ab=ba, ac=ca, cbc-1=b-1 >
Subgroups: 346 in 60 conjugacy classes, 33 normal (15 characteristic)
C1, C2, C2, C4, C4, C22, C8, C2×C4, C2×C4, Q8, C11, C2×C8, Q16, C2×Q8, C22, C22, C2×Q16, Dic11, C44, C2×C22, C88, Dic22, Dic22, C2×Dic11, C2×C44, Dic44, C2×C88, C2×Dic22, C2×Dic44
Quotients: C1, C2, C22, D4, C23, Q16, C2×D4, D11, C2×Q16, D22, D44, C22×D11, Dic44, C2×D44, C2×Dic44
►Regular action on 352 points
Generators in S352
(1 251)(2 252)(3 253)(4 254)(5 255)(6 256)(7 257)(8 258)(9 259)(10 260)(11 261)(12 262)(13 263)(14 264)(15 177)(16 178)(17 179)(18 180)(19 181)(20 182)(21 183)(22 184)(23 185)(24 186)(25 187)(26 188)(27 189)(28 190)(29 191)(30 192)(31 193)(32 194)(33 195)(34 196)(35 197)(36 198)(37 199)(38 200)(39 201)(40 202)(41 203)(42 204)(43 205)(44 206)(45 207)(46 208)(47 209)(48 210)(49 211)(50 212)(51 213)(52 214)(53 215)(54 216)(55 217)(56 218)(57 219)(58 220)(59 221)(60 222)(61 223)(62 224)(63 225)(64 226)(65 227)(66 228)(67 229)(68 230)(69 231)(70 232)(71 233)(72 234)(73 235)(74 236)(75 237)(76 238)(77 239)(78 240)(79 241)(80 242)(81 243)(82 244)(83 245)(84 246)(85 247)(86 248)(87 249)(88 250)(89 272)(90 273)(91 274)(92 275)(93 276)(94 277)(95 278)(96 279)(97 280)(98 281)(99 282)(100 283)(101 284)(102 285)(103 286)(104 287)(105 288)(106 289)(107 290)(108 291)(109 292)(110 293)(111 294)(112 295)(113 296)(114 297)(115 298)(116 299)(117 300)(118 301)(119 302)(120 303)(121 304)(122 305)(123 306)(124 307)(125 308)(126 309)(127 310)(128 311)(129 312)(130 313)(131 314)(132 315)(133 316)(134 317)(135 318)(136 319)(137 320)(138 321)(139 322)(140 323)(141 324)(142 325)(143 326)(144 327)(145 328)(146 329)(147 330)(148 331)(149 332)(150 333)(151 334)(152 335)(153 336)(154 337)(155 338)(156 339)(157 340)(158 341)(159 342)(160 343)(161 344)(162 345)(163 346)(164 347)(165 348)(166 349)(167 350)(168 351)(169 352)(170 265)(171 266)(172 267)(173 268)(174 269)(175 270)(176 271)
(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)
(1 323 45 279)(2 322 46 278)(3 321 47 277)(4 320 48 276)(5 319 49 275)(6 318 50 274)(7 317 51 273)(8 316 52 272)(9 315 53 271)(10 314 54 270)(11 313 55 269)(12 312 56 268)(13 311 57 267)(14 310 58 266)(15 309 59 265)(16 308 60 352)(17 307 61 351)(18 306 62 350)(19 305 63 349)(20 304 64 348)(21 303 65 347)(22 302 66 346)(23 301 67 345)(24 300 68 344)(25 299 69 343)(26 298 70 342)(27 297 71 341)(28 296 72 340)(29 295 73 339)(30 294 74 338)(31 293 75 337)(32 292 76 336)(33 291 77 335)(34 290 78 334)(35 289 79 333)(36 288 80 332)(37 287 81 331)(38 286 82 330)(39 285 83 329)(40 284 84 328)(41 283 85 327)(42 282 86 326)(43 281 87 325)(44 280 88 324)(89 258 133 214)(90 257 134 213)(91 256 135 212)(92 255 136 211)(93 254 137 210)(94 253 138 209)(95 252 139 208)(96 251 140 207)(97 250 141 206)(98 249 142 205)(99 248 143 204)(100 247 144 203)(101 246 145 202)(102 245 146 201)(103 244 147 200)(104 243 148 199)(105 242 149 198)(106 241 150 197)(107 240 151 196)(108 239 152 195)(109 238 153 194)(110 237 154 193)(111 236 155 192)(112 235 156 191)(113 234 157 190)(114 233 158 189)(115 232 159 188)(116 231 160 187)(117 230 161 186)(118 229 162 185)(119 228 163 184)(120 227 164 183)(121 226 165 182)(122 225 166 181)(123 224 167 180)(124 223 168 179)(125 222 169 178)(126 221 170 177)(127 220 171 264)(128 219 172 263)(129 218 173 262)(130 217 174 261)(131 216 175 260)(132 215 176 259)
G:=sub<Sym(352)| (1,251)(2,252)(3,253)(4,254)(5,255)(6,256)(7,257)(8,258)(9,259)(10,260)(11,261)(12,262)(13,263)(14,264)(15,177)(16,178)(17,179)(18,180)(19,181)(20,182)(21,183)(22,184)(23,185)(24,186)(25,187)(26,188)(27,189)(28,190)(29,191)(30,192)(31,193)(32,194)(33,195)(34,196)(35,197)(36,198)(37,199)(38,200)(39,201)(40,202)(41,203)(42,204)(43,205)(44,206)(45,207)(46,208)(47,209)(48,210)(49,211)(50,212)(51,213)(52,214)(53,215)(54,216)(55,217)(56,218)(57,219)(58,220)(59,221)(60,222)(61,223)(62,224)(63,225)(64,226)(65,227)(66,228)(67,229)(68,230)(69,231)(70,232)(71,233)(72,234)(73,235)(74,236)(75,237)(76,238)(77,239)(78,240)(79,241)(80,242)(81,243)(82,244)(83,245)(84,246)(85,247)(86,248)(87,249)(88,250)(89,272)(90,273)(91,274)(92,275)(93,276)(94,277)(95,278)(96,279)(97,280)(98,281)(99,282)(100,283)(101,284)(102,285)(103,286)(104,287)(105,288)(106,289)(107,290)(108,291)(109,292)(110,293)(111,294)(112,295)(113,296)(114,297)(115,298)(116,299)(117,300)(118,301)(119,302)(120,303)(121,304)(122,305)(123,306)(124,307)(125,308)(126,309)(127,310)(128,311)(129,312)(130,313)(131,314)(132,315)(133,316)(134,317)(135,318)(136,319)(137,320)(138,321)(139,322)(140,323)(141,324)(142,325)(143,326)(144,327)(145,328)(146,329)(147,330)(148,331)(149,332)(150,333)(151,334)(152,335)(153,336)(154,337)(155,338)(156,339)(157,340)(158,341)(159,342)(160,343)(161,344)(162,345)(163,346)(164,347)(165,348)(166,349)(167,350)(168,351)(169,352)(170,265)(171,266)(172,267)(173,268)(174,269)(175,270)(176,271), (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), (1,323,45,279)(2,322,46,278)(3,321,47,277)(4,320,48,276)(5,319,49,275)(6,318,50,274)(7,317,51,273)(8,316,52,272)(9,315,53,271)(10,314,54,270)(11,313,55,269)(12,312,56,268)(13,311,57,267)(14,310,58,266)(15,309,59,265)(16,308,60,352)(17,307,61,351)(18,306,62,350)(19,305,63,349)(20,304,64,348)(21,303,65,347)(22,302,66,346)(23,301,67,345)(24,300,68,344)(25,299,69,343)(26,298,70,342)(27,297,71,341)(28,296,72,340)(29,295,73,339)(30,294,74,338)(31,293,75,337)(32,292,76,336)(33,291,77,335)(34,290,78,334)(35,289,79,333)(36,288,80,332)(37,287,81,331)(38,286,82,330)(39,285,83,329)(40,284,84,328)(41,283,85,327)(42,282,86,326)(43,281,87,325)(44,280,88,324)(89,258,133,214)(90,257,134,213)(91,256,135,212)(92,255,136,211)(93,254,137,210)(94,253,138,209)(95,252,139,208)(96,251,140,207)(97,250,141,206)(98,249,142,205)(99,248,143,204)(100,247,144,203)(101,246,145,202)(102,245,146,201)(103,244,147,200)(104,243,148,199)(105,242,149,198)(106,241,150,197)(107,240,151,196)(108,239,152,195)(109,238,153,194)(110,237,154,193)(111,236,155,192)(112,235,156,191)(113,234,157,190)(114,233,158,189)(115,232,159,188)(116,231,160,187)(117,230,161,186)(118,229,162,185)(119,228,163,184)(120,227,164,183)(121,226,165,182)(122,225,166,181)(123,224,167,180)(124,223,168,179)(125,222,169,178)(126,221,170,177)(127,220,171,264)(128,219,172,263)(129,218,173,262)(130,217,174,261)(131,216,175,260)(132,215,176,259)>;
G:=Group( (1,251)(2,252)(3,253)(4,254)(5,255)(6,256)(7,257)(8,258)(9,259)(10,260)(11,261)(12,262)(13,263)(14,264)(15,177)(16,178)(17,179)(18,180)(19,181)(20,182)(21,183)(22,184)(23,185)(24,186)(25,187)(26,188)(27,189)(28,190)(29,191)(30,192)(31,193)(32,194)(33,195)(34,196)(35,197)(36,198)(37,199)(38,200)(39,201)(40,202)(41,203)(42,204)(43,205)(44,206)(45,207)(46,208)(47,209)(48,210)(49,211)(50,212)(51,213)(52,214)(53,215)(54,216)(55,217)(56,218)(57,219)(58,220)(59,221)(60,222)(61,223)(62,224)(63,225)(64,226)(65,227)(66,228)(67,229)(68,230)(69,231)(70,232)(71,233)(72,234)(73,235)(74,236)(75,237)(76,238)(77,239)(78,240)(79,241)(80,242)(81,243)(82,244)(83,245)(84,246)(85,247)(86,248)(87,249)(88,250)(89,272)(90,273)(91,274)(92,275)(93,276)(94,277)(95,278)(96,279)(97,280)(98,281)(99,282)(100,283)(101,284)(102,285)(103,286)(104,287)(105,288)(106,289)(107,290)(108,291)(109,292)(110,293)(111,294)(112,295)(113,296)(114,297)(115,298)(116,299)(117,300)(118,301)(119,302)(120,303)(121,304)(122,305)(123,306)(124,307)(125,308)(126,309)(127,310)(128,311)(129,312)(130,313)(131,314)(132,315)(133,316)(134,317)(135,318)(136,319)(137,320)(138,321)(139,322)(140,323)(141,324)(142,325)(143,326)(144,327)(145,328)(146,329)(147,330)(148,331)(149,332)(150,333)(151,334)(152,335)(153,336)(154,337)(155,338)(156,339)(157,340)(158,341)(159,342)(160,343)(161,344)(162,345)(163,346)(164,347)(165,348)(166,349)(167,350)(168,351)(169,352)(170,265)(171,266)(172,267)(173,268)(174,269)(175,270)(176,271), (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), (1,323,45,279)(2,322,46,278)(3,321,47,277)(4,320,48,276)(5,319,49,275)(6,318,50,274)(7,317,51,273)(8,316,52,272)(9,315,53,271)(10,314,54,270)(11,313,55,269)(12,312,56,268)(13,311,57,267)(14,310,58,266)(15,309,59,265)(16,308,60,352)(17,307,61,351)(18,306,62,350)(19,305,63,349)(20,304,64,348)(21,303,65,347)(22,302,66,346)(23,301,67,345)(24,300,68,344)(25,299,69,343)(26,298,70,342)(27,297,71,341)(28,296,72,340)(29,295,73,339)(30,294,74,338)(31,293,75,337)(32,292,76,336)(33,291,77,335)(34,290,78,334)(35,289,79,333)(36,288,80,332)(37,287,81,331)(38,286,82,330)(39,285,83,329)(40,284,84,328)(41,283,85,327)(42,282,86,326)(43,281,87,325)(44,280,88,324)(89,258,133,214)(90,257,134,213)(91,256,135,212)(92,255,136,211)(93,254,137,210)(94,253,138,209)(95,252,139,208)(96,251,140,207)(97,250,141,206)(98,249,142,205)(99,248,143,204)(100,247,144,203)(101,246,145,202)(102,245,146,201)(103,244,147,200)(104,243,148,199)(105,242,149,198)(106,241,150,197)(107,240,151,196)(108,239,152,195)(109,238,153,194)(110,237,154,193)(111,236,155,192)(112,235,156,191)(113,234,157,190)(114,233,158,189)(115,232,159,188)(116,231,160,187)(117,230,161,186)(118,229,162,185)(119,228,163,184)(120,227,164,183)(121,226,165,182)(122,225,166,181)(123,224,167,180)(124,223,168,179)(125,222,169,178)(126,221,170,177)(127,220,171,264)(128,219,172,263)(129,218,173,262)(130,217,174,261)(131,216,175,260)(132,215,176,259) );
G=PermutationGroup([[(1,251),(2,252),(3,253),(4,254),(5,255),(6,256),(7,257),(8,258),(9,259),(10,260),(11,261),(12,262),(13,263),(14,264),(15,177),(16,178),(17,179),(18,180),(19,181),(20,182),(21,183),(22,184),(23,185),(24,186),(25,187),(26,188),(27,189),(28,190),(29,191),(30,192),(31,193),(32,194),(33,195),(34,196),(35,197),(36,198),(37,199),(38,200),(39,201),(40,202),(41,203),(42,204),(43,205),(44,206),(45,207),(46,208),(47,209),(48,210),(49,211),(50,212),(51,213),(52,214),(53,215),(54,216),(55,217),(56,218),(57,219),(58,220),(59,221),(60,222),(61,223),(62,224),(63,225),(64,226),(65,227),(66,228),(67,229),(68,230),(69,231),(70,232),(71,233),(72,234),(73,235),(74,236),(75,237),(76,238),(77,239),(78,240),(79,241),(80,242),(81,243),(82,244),(83,245),(84,246),(85,247),(86,248),(87,249),(88,250),(89,272),(90,273),(91,274),(92,275),(93,276),(94,277),(95,278),(96,279),(97,280),(98,281),(99,282),(100,283),(101,284),(102,285),(103,286),(104,287),(105,288),(106,289),(107,290),(108,291),(109,292),(110,293),(111,294),(112,295),(113,296),(114,297),(115,298),(116,299),(117,300),(118,301),(119,302),(120,303),(121,304),(122,305),(123,306),(124,307),(125,308),(126,309),(127,310),(128,311),(129,312),(130,313),(131,314),(132,315),(133,316),(134,317),(135,318),(136,319),(137,320),(138,321),(139,322),(140,323),(141,324),(142,325),(143,326),(144,327),(145,328),(146,329),(147,330),(148,331),(149,332),(150,333),(151,334),(152,335),(153,336),(154,337),(155,338),(156,339),(157,340),(158,341),(159,342),(160,343),(161,344),(162,345),(163,346),(164,347),(165,348),(166,349),(167,350),(168,351),(169,352),(170,265),(171,266),(172,267),(173,268),(174,269),(175,270),(176,271)], [(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)], [(1,323,45,279),(2,322,46,278),(3,321,47,277),(4,320,48,276),(5,319,49,275),(6,318,50,274),(7,317,51,273),(8,316,52,272),(9,315,53,271),(10,314,54,270),(11,313,55,269),(12,312,56,268),(13,311,57,267),(14,310,58,266),(15,309,59,265),(16,308,60,352),(17,307,61,351),(18,306,62,350),(19,305,63,349),(20,304,64,348),(21,303,65,347),(22,302,66,346),(23,301,67,345),(24,300,68,344),(25,299,69,343),(26,298,70,342),(27,297,71,341),(28,296,72,340),(29,295,73,339),(30,294,74,338),(31,293,75,337),(32,292,76,336),(33,291,77,335),(34,290,78,334),(35,289,79,333),(36,288,80,332),(37,287,81,331),(38,286,82,330),(39,285,83,329),(40,284,84,328),(41,283,85,327),(42,282,86,326),(43,281,87,325),(44,280,88,324),(89,258,133,214),(90,257,134,213),(91,256,135,212),(92,255,136,211),(93,254,137,210),(94,253,138,209),(95,252,139,208),(96,251,140,207),(97,250,141,206),(98,249,142,205),(99,248,143,204),(100,247,144,203),(101,246,145,202),(102,245,146,201),(103,244,147,200),(104,243,148,199),(105,242,149,198),(106,241,150,197),(107,240,151,196),(108,239,152,195),(109,238,153,194),(110,237,154,193),(111,236,155,192),(112,235,156,191),(113,234,157,190),(114,233,158,189),(115,232,159,188),(116,231,160,187),(117,230,161,186),(118,229,162,185),(119,228,163,184),(120,227,164,183),(121,226,165,182),(122,225,166,181),(123,224,167,180),(124,223,168,179),(125,222,169,178),(126,221,170,177),(127,220,171,264),(128,219,172,263),(129,218,173,262),(130,217,174,261),(131,216,175,260),(132,215,176,259)]])
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 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | + | - | + | + | + | + | + | - |
| image | C1 | C2 | C2 | C2 | D4 | D4 | Q16 | D11 | D22 | D22 | D44 | D44 | Dic44 |
| kernel | C2×Dic44 | Dic44 | C2×C88 | C2×Dic22 | C44 | C2×C22 | C22 | C2×C8 | C8 | C2×C4 | C4 | C22 | C2 |
| # reps | 1 | 4 | 1 | 2 | 1 | 1 | 4 | 5 | 10 | 5 | 10 | 10 | 40 |
Matrix representation of C2×Dic44 ►in GL3(𝔽89) generated by
| 88 | 0 | 0 |
| 0 | 88 | 0 |
| 0 | 0 | 88 |
| 88 | 0 | 0 |
| 0 | 62 | 0 |
| 0 | 0 | 56 |
| 1 | 0 | 0 |
| 0 | 0 | 37 |
| 0 | 12 | 0 |
G:=sub<GL(3,GF(89))| [88,0,0,0,88,0,0,0,88],[88,0,0,0,62,0,0,0,56],[1,0,0,0,0,12,0,37,0] >;
C2×Dic44 in GAP, Magma, Sage, TeX
C_2\times {\rm Dic}_{44} % in TeX
G:=Group("C2xDic44"); // GroupNames label
G:=SmallGroup(352,100);
// by ID
G=gap.SmallGroup(352,100);
# by ID
G:=PCGroup([6,-2,-2,-2,-2,-2,-11,96,218,122,579,69,11525]);
// Polycyclic
G:=Group<a,b,c|a^2=b^88=1,c^2=b^44,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations