metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: Dic23⋊C4, C46.5D4, C46.1Q8, C2.1Dic46, C22.4D46, C23⋊1(C4⋊C4), (C2×C92).1C2, C46.4(C2×C4), C2.4(C4×D23), (C2×C4).1D23, C2.1(C23⋊D4), (C2×C46).4C22, (C2×Dic23).1C2, SmallGroup(368,11)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for Dic23⋊C4
G = < a,b,c | a46=c4=1, b2=a23, bab-1=a-1, ac=ca, cbc-1=a23b >
Smallest permutation representation of Dic23⋊C4
►Regular action on 368 points
Generators in S368
(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)(323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368)
(1 254 24 231)(2 253 25 276)(3 252 26 275)(4 251 27 274)(5 250 28 273)(6 249 29 272)(7 248 30 271)(8 247 31 270)(9 246 32 269)(10 245 33 268)(11 244 34 267)(12 243 35 266)(13 242 36 265)(14 241 37 264)(15 240 38 263)(16 239 39 262)(17 238 40 261)(18 237 41 260)(19 236 42 259)(20 235 43 258)(21 234 44 257)(22 233 45 256)(23 232 46 255)(47 195 70 218)(48 194 71 217)(49 193 72 216)(50 192 73 215)(51 191 74 214)(52 190 75 213)(53 189 76 212)(54 188 77 211)(55 187 78 210)(56 186 79 209)(57 185 80 208)(58 230 81 207)(59 229 82 206)(60 228 83 205)(61 227 84 204)(62 226 85 203)(63 225 86 202)(64 224 87 201)(65 223 88 200)(66 222 89 199)(67 221 90 198)(68 220 91 197)(69 219 92 196)(93 339 116 362)(94 338 117 361)(95 337 118 360)(96 336 119 359)(97 335 120 358)(98 334 121 357)(99 333 122 356)(100 332 123 355)(101 331 124 354)(102 330 125 353)(103 329 126 352)(104 328 127 351)(105 327 128 350)(106 326 129 349)(107 325 130 348)(108 324 131 347)(109 323 132 346)(110 368 133 345)(111 367 134 344)(112 366 135 343)(113 365 136 342)(114 364 137 341)(115 363 138 340)(139 319 162 296)(140 318 163 295)(141 317 164 294)(142 316 165 293)(143 315 166 292)(144 314 167 291)(145 313 168 290)(146 312 169 289)(147 311 170 288)(148 310 171 287)(149 309 172 286)(150 308 173 285)(151 307 174 284)(152 306 175 283)(153 305 176 282)(154 304 177 281)(155 303 178 280)(156 302 179 279)(157 301 180 278)(158 300 181 277)(159 299 182 322)(160 298 183 321)(161 297 184 320)
(1 158 80 109)(2 159 81 110)(3 160 82 111)(4 161 83 112)(5 162 84 113)(6 163 85 114)(7 164 86 115)(8 165 87 116)(9 166 88 117)(10 167 89 118)(11 168 90 119)(12 169 91 120)(13 170 92 121)(14 171 47 122)(15 172 48 123)(16 173 49 124)(17 174 50 125)(18 175 51 126)(19 176 52 127)(20 177 53 128)(21 178 54 129)(22 179 55 130)(23 180 56 131)(24 181 57 132)(25 182 58 133)(26 183 59 134)(27 184 60 135)(28 139 61 136)(29 140 62 137)(30 141 63 138)(31 142 64 93)(32 143 65 94)(33 144 66 95)(34 145 67 96)(35 146 68 97)(36 147 69 98)(37 148 70 99)(38 149 71 100)(39 150 72 101)(40 151 73 102)(41 152 74 103)(42 153 75 104)(43 154 76 105)(44 155 77 106)(45 156 78 107)(46 157 79 108)(185 323 231 300)(186 324 232 301)(187 325 233 302)(188 326 234 303)(189 327 235 304)(190 328 236 305)(191 329 237 306)(192 330 238 307)(193 331 239 308)(194 332 240 309)(195 333 241 310)(196 334 242 311)(197 335 243 312)(198 336 244 313)(199 337 245 314)(200 338 246 315)(201 339 247 316)(202 340 248 317)(203 341 249 318)(204 342 250 319)(205 343 251 320)(206 344 252 321)(207 345 253 322)(208 346 254 277)(209 347 255 278)(210 348 256 279)(211 349 257 280)(212 350 258 281)(213 351 259 282)(214 352 260 283)(215 353 261 284)(216 354 262 285)(217 355 263 286)(218 356 264 287)(219 357 265 288)(220 358 266 289)(221 359 267 290)(222 360 268 291)(223 361 269 292)(224 362 270 293)(225 363 271 294)(226 364 272 295)(227 365 273 296)(228 366 274 297)(229 367 275 298)(230 368 276 299)
G:=sub<Sym(368)| (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)(323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368), (1,254,24,231)(2,253,25,276)(3,252,26,275)(4,251,27,274)(5,250,28,273)(6,249,29,272)(7,248,30,271)(8,247,31,270)(9,246,32,269)(10,245,33,268)(11,244,34,267)(12,243,35,266)(13,242,36,265)(14,241,37,264)(15,240,38,263)(16,239,39,262)(17,238,40,261)(18,237,41,260)(19,236,42,259)(20,235,43,258)(21,234,44,257)(22,233,45,256)(23,232,46,255)(47,195,70,218)(48,194,71,217)(49,193,72,216)(50,192,73,215)(51,191,74,214)(52,190,75,213)(53,189,76,212)(54,188,77,211)(55,187,78,210)(56,186,79,209)(57,185,80,208)(58,230,81,207)(59,229,82,206)(60,228,83,205)(61,227,84,204)(62,226,85,203)(63,225,86,202)(64,224,87,201)(65,223,88,200)(66,222,89,199)(67,221,90,198)(68,220,91,197)(69,219,92,196)(93,339,116,362)(94,338,117,361)(95,337,118,360)(96,336,119,359)(97,335,120,358)(98,334,121,357)(99,333,122,356)(100,332,123,355)(101,331,124,354)(102,330,125,353)(103,329,126,352)(104,328,127,351)(105,327,128,350)(106,326,129,349)(107,325,130,348)(108,324,131,347)(109,323,132,346)(110,368,133,345)(111,367,134,344)(112,366,135,343)(113,365,136,342)(114,364,137,341)(115,363,138,340)(139,319,162,296)(140,318,163,295)(141,317,164,294)(142,316,165,293)(143,315,166,292)(144,314,167,291)(145,313,168,290)(146,312,169,289)(147,311,170,288)(148,310,171,287)(149,309,172,286)(150,308,173,285)(151,307,174,284)(152,306,175,283)(153,305,176,282)(154,304,177,281)(155,303,178,280)(156,302,179,279)(157,301,180,278)(158,300,181,277)(159,299,182,322)(160,298,183,321)(161,297,184,320), (1,158,80,109)(2,159,81,110)(3,160,82,111)(4,161,83,112)(5,162,84,113)(6,163,85,114)(7,164,86,115)(8,165,87,116)(9,166,88,117)(10,167,89,118)(11,168,90,119)(12,169,91,120)(13,170,92,121)(14,171,47,122)(15,172,48,123)(16,173,49,124)(17,174,50,125)(18,175,51,126)(19,176,52,127)(20,177,53,128)(21,178,54,129)(22,179,55,130)(23,180,56,131)(24,181,57,132)(25,182,58,133)(26,183,59,134)(27,184,60,135)(28,139,61,136)(29,140,62,137)(30,141,63,138)(31,142,64,93)(32,143,65,94)(33,144,66,95)(34,145,67,96)(35,146,68,97)(36,147,69,98)(37,148,70,99)(38,149,71,100)(39,150,72,101)(40,151,73,102)(41,152,74,103)(42,153,75,104)(43,154,76,105)(44,155,77,106)(45,156,78,107)(46,157,79,108)(185,323,231,300)(186,324,232,301)(187,325,233,302)(188,326,234,303)(189,327,235,304)(190,328,236,305)(191,329,237,306)(192,330,238,307)(193,331,239,308)(194,332,240,309)(195,333,241,310)(196,334,242,311)(197,335,243,312)(198,336,244,313)(199,337,245,314)(200,338,246,315)(201,339,247,316)(202,340,248,317)(203,341,249,318)(204,342,250,319)(205,343,251,320)(206,344,252,321)(207,345,253,322)(208,346,254,277)(209,347,255,278)(210,348,256,279)(211,349,257,280)(212,350,258,281)(213,351,259,282)(214,352,260,283)(215,353,261,284)(216,354,262,285)(217,355,263,286)(218,356,264,287)(219,357,265,288)(220,358,266,289)(221,359,267,290)(222,360,268,291)(223,361,269,292)(224,362,270,293)(225,363,271,294)(226,364,272,295)(227,365,273,296)(228,366,274,297)(229,367,275,298)(230,368,276,299)>;
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)(323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368), (1,254,24,231)(2,253,25,276)(3,252,26,275)(4,251,27,274)(5,250,28,273)(6,249,29,272)(7,248,30,271)(8,247,31,270)(9,246,32,269)(10,245,33,268)(11,244,34,267)(12,243,35,266)(13,242,36,265)(14,241,37,264)(15,240,38,263)(16,239,39,262)(17,238,40,261)(18,237,41,260)(19,236,42,259)(20,235,43,258)(21,234,44,257)(22,233,45,256)(23,232,46,255)(47,195,70,218)(48,194,71,217)(49,193,72,216)(50,192,73,215)(51,191,74,214)(52,190,75,213)(53,189,76,212)(54,188,77,211)(55,187,78,210)(56,186,79,209)(57,185,80,208)(58,230,81,207)(59,229,82,206)(60,228,83,205)(61,227,84,204)(62,226,85,203)(63,225,86,202)(64,224,87,201)(65,223,88,200)(66,222,89,199)(67,221,90,198)(68,220,91,197)(69,219,92,196)(93,339,116,362)(94,338,117,361)(95,337,118,360)(96,336,119,359)(97,335,120,358)(98,334,121,357)(99,333,122,356)(100,332,123,355)(101,331,124,354)(102,330,125,353)(103,329,126,352)(104,328,127,351)(105,327,128,350)(106,326,129,349)(107,325,130,348)(108,324,131,347)(109,323,132,346)(110,368,133,345)(111,367,134,344)(112,366,135,343)(113,365,136,342)(114,364,137,341)(115,363,138,340)(139,319,162,296)(140,318,163,295)(141,317,164,294)(142,316,165,293)(143,315,166,292)(144,314,167,291)(145,313,168,290)(146,312,169,289)(147,311,170,288)(148,310,171,287)(149,309,172,286)(150,308,173,285)(151,307,174,284)(152,306,175,283)(153,305,176,282)(154,304,177,281)(155,303,178,280)(156,302,179,279)(157,301,180,278)(158,300,181,277)(159,299,182,322)(160,298,183,321)(161,297,184,320), (1,158,80,109)(2,159,81,110)(3,160,82,111)(4,161,83,112)(5,162,84,113)(6,163,85,114)(7,164,86,115)(8,165,87,116)(9,166,88,117)(10,167,89,118)(11,168,90,119)(12,169,91,120)(13,170,92,121)(14,171,47,122)(15,172,48,123)(16,173,49,124)(17,174,50,125)(18,175,51,126)(19,176,52,127)(20,177,53,128)(21,178,54,129)(22,179,55,130)(23,180,56,131)(24,181,57,132)(25,182,58,133)(26,183,59,134)(27,184,60,135)(28,139,61,136)(29,140,62,137)(30,141,63,138)(31,142,64,93)(32,143,65,94)(33,144,66,95)(34,145,67,96)(35,146,68,97)(36,147,69,98)(37,148,70,99)(38,149,71,100)(39,150,72,101)(40,151,73,102)(41,152,74,103)(42,153,75,104)(43,154,76,105)(44,155,77,106)(45,156,78,107)(46,157,79,108)(185,323,231,300)(186,324,232,301)(187,325,233,302)(188,326,234,303)(189,327,235,304)(190,328,236,305)(191,329,237,306)(192,330,238,307)(193,331,239,308)(194,332,240,309)(195,333,241,310)(196,334,242,311)(197,335,243,312)(198,336,244,313)(199,337,245,314)(200,338,246,315)(201,339,247,316)(202,340,248,317)(203,341,249,318)(204,342,250,319)(205,343,251,320)(206,344,252,321)(207,345,253,322)(208,346,254,277)(209,347,255,278)(210,348,256,279)(211,349,257,280)(212,350,258,281)(213,351,259,282)(214,352,260,283)(215,353,261,284)(216,354,262,285)(217,355,263,286)(218,356,264,287)(219,357,265,288)(220,358,266,289)(221,359,267,290)(222,360,268,291)(223,361,269,292)(224,362,270,293)(225,363,271,294)(226,364,272,295)(227,365,273,296)(228,366,274,297)(229,367,275,298)(230,368,276,299) );
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),(323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368)], [(1,254,24,231),(2,253,25,276),(3,252,26,275),(4,251,27,274),(5,250,28,273),(6,249,29,272),(7,248,30,271),(8,247,31,270),(9,246,32,269),(10,245,33,268),(11,244,34,267),(12,243,35,266),(13,242,36,265),(14,241,37,264),(15,240,38,263),(16,239,39,262),(17,238,40,261),(18,237,41,260),(19,236,42,259),(20,235,43,258),(21,234,44,257),(22,233,45,256),(23,232,46,255),(47,195,70,218),(48,194,71,217),(49,193,72,216),(50,192,73,215),(51,191,74,214),(52,190,75,213),(53,189,76,212),(54,188,77,211),(55,187,78,210),(56,186,79,209),(57,185,80,208),(58,230,81,207),(59,229,82,206),(60,228,83,205),(61,227,84,204),(62,226,85,203),(63,225,86,202),(64,224,87,201),(65,223,88,200),(66,222,89,199),(67,221,90,198),(68,220,91,197),(69,219,92,196),(93,339,116,362),(94,338,117,361),(95,337,118,360),(96,336,119,359),(97,335,120,358),(98,334,121,357),(99,333,122,356),(100,332,123,355),(101,331,124,354),(102,330,125,353),(103,329,126,352),(104,328,127,351),(105,327,128,350),(106,326,129,349),(107,325,130,348),(108,324,131,347),(109,323,132,346),(110,368,133,345),(111,367,134,344),(112,366,135,343),(113,365,136,342),(114,364,137,341),(115,363,138,340),(139,319,162,296),(140,318,163,295),(141,317,164,294),(142,316,165,293),(143,315,166,292),(144,314,167,291),(145,313,168,290),(146,312,169,289),(147,311,170,288),(148,310,171,287),(149,309,172,286),(150,308,173,285),(151,307,174,284),(152,306,175,283),(153,305,176,282),(154,304,177,281),(155,303,178,280),(156,302,179,279),(157,301,180,278),(158,300,181,277),(159,299,182,322),(160,298,183,321),(161,297,184,320)], [(1,158,80,109),(2,159,81,110),(3,160,82,111),(4,161,83,112),(5,162,84,113),(6,163,85,114),(7,164,86,115),(8,165,87,116),(9,166,88,117),(10,167,89,118),(11,168,90,119),(12,169,91,120),(13,170,92,121),(14,171,47,122),(15,172,48,123),(16,173,49,124),(17,174,50,125),(18,175,51,126),(19,176,52,127),(20,177,53,128),(21,178,54,129),(22,179,55,130),(23,180,56,131),(24,181,57,132),(25,182,58,133),(26,183,59,134),(27,184,60,135),(28,139,61,136),(29,140,62,137),(30,141,63,138),(31,142,64,93),(32,143,65,94),(33,144,66,95),(34,145,67,96),(35,146,68,97),(36,147,69,98),(37,148,70,99),(38,149,71,100),(39,150,72,101),(40,151,73,102),(41,152,74,103),(42,153,75,104),(43,154,76,105),(44,155,77,106),(45,156,78,107),(46,157,79,108),(185,323,231,300),(186,324,232,301),(187,325,233,302),(188,326,234,303),(189,327,235,304),(190,328,236,305),(191,329,237,306),(192,330,238,307),(193,331,239,308),(194,332,240,309),(195,333,241,310),(196,334,242,311),(197,335,243,312),(198,336,244,313),(199,337,245,314),(200,338,246,315),(201,339,247,316),(202,340,248,317),(203,341,249,318),(204,342,250,319),(205,343,251,320),(206,344,252,321),(207,345,253,322),(208,346,254,277),(209,347,255,278),(210,348,256,279),(211,349,257,280),(212,350,258,281),(213,351,259,282),(214,352,260,283),(215,353,261,284),(216,354,262,285),(217,355,263,286),(218,356,264,287),(219,357,265,288),(220,358,266,289),(221,359,267,290),(222,360,268,291),(223,361,269,292),(224,362,270,293),(225,363,271,294),(226,364,272,295),(227,365,273,296),(228,366,274,297),(229,367,275,298),(230,368,276,299)]])
98 conjugacy classes
| class | 1 | 2A | 2B | 2C | 4A | 4B | 4C | 4D | 4E | 4F | 23A | ··· | 23K | 46A | ··· | 46AG | 92A | ··· | 92AR |
| order | 1 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 23 | ··· | 23 | 46 | ··· | 46 | 92 | ··· | 92 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 46 | 46 | 46 | 46 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
98 irreducible representations
| dim | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | - | + | + | - | |||
| image | C1 | C2 | C2 | C4 | D4 | Q8 | D23 | D46 | Dic46 | C4×D23 | C23⋊D4 |
| kernel | Dic23⋊C4 | C2×Dic23 | C2×C92 | Dic23 | C46 | C46 | C2×C4 | C22 | C2 | C2 | C2 |
| # reps | 1 | 2 | 1 | 4 | 1 | 1 | 11 | 11 | 22 | 22 | 22 |
Matrix representation of Dic23⋊C4 ►in GL3(𝔽277) generated by
| 1 | 0 | 0 |
| 0 | 0 | 276 |
| 0 | 1 | 83 |
| 276 | 0 | 0 |
| 0 | 187 | 27 |
| 0 | 18 | 90 |
| 217 | 0 | 0 |
| 0 | 258 | 103 |
| 0 | 174 | 19 |
G:=sub<GL(3,GF(277))| [1,0,0,0,0,1,0,276,83],[276,0,0,0,187,18,0,27,90],[217,0,0,0,258,174,0,103,19] >;
Dic23⋊C4 in GAP, Magma, Sage, TeX
{\rm Dic}_{23}\rtimes C_4 % in TeX
G:=Group("Dic23:C4"); // GroupNames label
G:=SmallGroup(368,11);
// by ID
G=gap.SmallGroup(368,11);
# by ID
G:=PCGroup([5,-2,-2,-2,-2,-23,40,101,26,8804]);
// Polycyclic
G:=Group<a,b,c|a^46=c^4=1,b^2=a^23,b*a*b^-1=a^-1,a*c=c*a,c*b*c^-1=a^23*b>;
// generators/relations
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