direct product, metacyclic, nilpotent (class 2), monomial, 2-elementary
Aliases: C4⋊C4×C23, C4⋊C92, C92⋊3C4, C46.3Q8, C46.13D4, C2.(Q8×C23), (C2×C4).1C46, (C2×C92).2C2, C2.2(C2×C92), C2.2(D4×C23), C46.11(C2×C4), C22.3(C2×C46), (C2×C46).14C22, SmallGroup(368,21)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C4⋊C4×C23
G = < a,b,c | a23=b4=c4=1, ab=ba, ac=ca, cbc-1=b-1 >
Smallest permutation representation of C4⋊C4×C23
►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 86 102 319)(2 87 103 320)(3 88 104 321)(4 89 105 322)(5 90 106 300)(6 91 107 301)(7 92 108 302)(8 70 109 303)(9 71 110 304)(10 72 111 305)(11 73 112 306)(12 74 113 307)(13 75 114 308)(14 76 115 309)(15 77 93 310)(16 78 94 311)(17 79 95 312)(18 80 96 313)(19 81 97 314)(20 82 98 315)(21 83 99 316)(22 84 100 317)(23 85 101 318)(24 161 56 296)(25 139 57 297)(26 140 58 298)(27 141 59 299)(28 142 60 277)(29 143 61 278)(30 144 62 279)(31 145 63 280)(32 146 64 281)(33 147 65 282)(34 148 66 283)(35 149 67 284)(36 150 68 285)(37 151 69 286)(38 152 47 287)(39 153 48 288)(40 154 49 289)(41 155 50 290)(42 156 51 291)(43 157 52 292)(44 158 53 293)(45 159 54 294)(46 160 55 295)(116 338 186 224)(117 339 187 225)(118 340 188 226)(119 341 189 227)(120 342 190 228)(121 343 191 229)(122 344 192 230)(123 345 193 208)(124 323 194 209)(125 324 195 210)(126 325 196 211)(127 326 197 212)(128 327 198 213)(129 328 199 214)(130 329 200 215)(131 330 201 216)(132 331 202 217)(133 332 203 218)(134 333 204 219)(135 334 205 220)(136 335 206 221)(137 336 207 222)(138 337 185 223)(162 258 252 356)(163 259 253 357)(164 260 231 358)(165 261 232 359)(166 262 233 360)(167 263 234 361)(168 264 235 362)(169 265 236 363)(170 266 237 364)(171 267 238 365)(172 268 239 366)(173 269 240 367)(174 270 241 368)(175 271 242 346)(176 272 243 347)(177 273 244 348)(178 274 245 349)(179 275 246 350)(180 276 247 351)(181 254 248 352)(182 255 249 353)(183 256 250 354)(184 257 251 355)
(1 186 168 52)(2 187 169 53)(3 188 170 54)(4 189 171 55)(5 190 172 56)(6 191 173 57)(7 192 174 58)(8 193 175 59)(9 194 176 60)(10 195 177 61)(11 196 178 62)(12 197 179 63)(13 198 180 64)(14 199 181 65)(15 200 182 66)(16 201 183 67)(17 202 184 68)(18 203 162 69)(19 204 163 47)(20 205 164 48)(21 206 165 49)(22 207 166 50)(23 185 167 51)(24 106 120 239)(25 107 121 240)(26 108 122 241)(27 109 123 242)(28 110 124 243)(29 111 125 244)(30 112 126 245)(31 113 127 246)(32 114 128 247)(33 115 129 248)(34 93 130 249)(35 94 131 250)(36 95 132 251)(37 96 133 252)(38 97 134 253)(39 98 135 231)(40 99 136 232)(41 100 137 233)(42 101 138 234)(43 102 116 235)(44 103 117 236)(45 104 118 237)(46 105 119 238)(70 345 271 141)(71 323 272 142)(72 324 273 143)(73 325 274 144)(74 326 275 145)(75 327 276 146)(76 328 254 147)(77 329 255 148)(78 330 256 149)(79 331 257 150)(80 332 258 151)(81 333 259 152)(82 334 260 153)(83 335 261 154)(84 336 262 155)(85 337 263 156)(86 338 264 157)(87 339 265 158)(88 340 266 159)(89 341 267 160)(90 342 268 161)(91 343 269 139)(92 344 270 140)(208 346 299 303)(209 347 277 304)(210 348 278 305)(211 349 279 306)(212 350 280 307)(213 351 281 308)(214 352 282 309)(215 353 283 310)(216 354 284 311)(217 355 285 312)(218 356 286 313)(219 357 287 314)(220 358 288 315)(221 359 289 316)(222 360 290 317)(223 361 291 318)(224 362 292 319)(225 363 293 320)(226 364 294 321)(227 365 295 322)(228 366 296 300)(229 367 297 301)(230 368 298 302)
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), (1,86,102,319)(2,87,103,320)(3,88,104,321)(4,89,105,322)(5,90,106,300)(6,91,107,301)(7,92,108,302)(8,70,109,303)(9,71,110,304)(10,72,111,305)(11,73,112,306)(12,74,113,307)(13,75,114,308)(14,76,115,309)(15,77,93,310)(16,78,94,311)(17,79,95,312)(18,80,96,313)(19,81,97,314)(20,82,98,315)(21,83,99,316)(22,84,100,317)(23,85,101,318)(24,161,56,296)(25,139,57,297)(26,140,58,298)(27,141,59,299)(28,142,60,277)(29,143,61,278)(30,144,62,279)(31,145,63,280)(32,146,64,281)(33,147,65,282)(34,148,66,283)(35,149,67,284)(36,150,68,285)(37,151,69,286)(38,152,47,287)(39,153,48,288)(40,154,49,289)(41,155,50,290)(42,156,51,291)(43,157,52,292)(44,158,53,293)(45,159,54,294)(46,160,55,295)(116,338,186,224)(117,339,187,225)(118,340,188,226)(119,341,189,227)(120,342,190,228)(121,343,191,229)(122,344,192,230)(123,345,193,208)(124,323,194,209)(125,324,195,210)(126,325,196,211)(127,326,197,212)(128,327,198,213)(129,328,199,214)(130,329,200,215)(131,330,201,216)(132,331,202,217)(133,332,203,218)(134,333,204,219)(135,334,205,220)(136,335,206,221)(137,336,207,222)(138,337,185,223)(162,258,252,356)(163,259,253,357)(164,260,231,358)(165,261,232,359)(166,262,233,360)(167,263,234,361)(168,264,235,362)(169,265,236,363)(170,266,237,364)(171,267,238,365)(172,268,239,366)(173,269,240,367)(174,270,241,368)(175,271,242,346)(176,272,243,347)(177,273,244,348)(178,274,245,349)(179,275,246,350)(180,276,247,351)(181,254,248,352)(182,255,249,353)(183,256,250,354)(184,257,251,355), (1,186,168,52)(2,187,169,53)(3,188,170,54)(4,189,171,55)(5,190,172,56)(6,191,173,57)(7,192,174,58)(8,193,175,59)(9,194,176,60)(10,195,177,61)(11,196,178,62)(12,197,179,63)(13,198,180,64)(14,199,181,65)(15,200,182,66)(16,201,183,67)(17,202,184,68)(18,203,162,69)(19,204,163,47)(20,205,164,48)(21,206,165,49)(22,207,166,50)(23,185,167,51)(24,106,120,239)(25,107,121,240)(26,108,122,241)(27,109,123,242)(28,110,124,243)(29,111,125,244)(30,112,126,245)(31,113,127,246)(32,114,128,247)(33,115,129,248)(34,93,130,249)(35,94,131,250)(36,95,132,251)(37,96,133,252)(38,97,134,253)(39,98,135,231)(40,99,136,232)(41,100,137,233)(42,101,138,234)(43,102,116,235)(44,103,117,236)(45,104,118,237)(46,105,119,238)(70,345,271,141)(71,323,272,142)(72,324,273,143)(73,325,274,144)(74,326,275,145)(75,327,276,146)(76,328,254,147)(77,329,255,148)(78,330,256,149)(79,331,257,150)(80,332,258,151)(81,333,259,152)(82,334,260,153)(83,335,261,154)(84,336,262,155)(85,337,263,156)(86,338,264,157)(87,339,265,158)(88,340,266,159)(89,341,267,160)(90,342,268,161)(91,343,269,139)(92,344,270,140)(208,346,299,303)(209,347,277,304)(210,348,278,305)(211,349,279,306)(212,350,280,307)(213,351,281,308)(214,352,282,309)(215,353,283,310)(216,354,284,311)(217,355,285,312)(218,356,286,313)(219,357,287,314)(220,358,288,315)(221,359,289,316)(222,360,290,317)(223,361,291,318)(224,362,292,319)(225,363,293,320)(226,364,294,321)(227,365,295,322)(228,366,296,300)(229,367,297,301)(230,368,298,302)>;
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), (1,86,102,319)(2,87,103,320)(3,88,104,321)(4,89,105,322)(5,90,106,300)(6,91,107,301)(7,92,108,302)(8,70,109,303)(9,71,110,304)(10,72,111,305)(11,73,112,306)(12,74,113,307)(13,75,114,308)(14,76,115,309)(15,77,93,310)(16,78,94,311)(17,79,95,312)(18,80,96,313)(19,81,97,314)(20,82,98,315)(21,83,99,316)(22,84,100,317)(23,85,101,318)(24,161,56,296)(25,139,57,297)(26,140,58,298)(27,141,59,299)(28,142,60,277)(29,143,61,278)(30,144,62,279)(31,145,63,280)(32,146,64,281)(33,147,65,282)(34,148,66,283)(35,149,67,284)(36,150,68,285)(37,151,69,286)(38,152,47,287)(39,153,48,288)(40,154,49,289)(41,155,50,290)(42,156,51,291)(43,157,52,292)(44,158,53,293)(45,159,54,294)(46,160,55,295)(116,338,186,224)(117,339,187,225)(118,340,188,226)(119,341,189,227)(120,342,190,228)(121,343,191,229)(122,344,192,230)(123,345,193,208)(124,323,194,209)(125,324,195,210)(126,325,196,211)(127,326,197,212)(128,327,198,213)(129,328,199,214)(130,329,200,215)(131,330,201,216)(132,331,202,217)(133,332,203,218)(134,333,204,219)(135,334,205,220)(136,335,206,221)(137,336,207,222)(138,337,185,223)(162,258,252,356)(163,259,253,357)(164,260,231,358)(165,261,232,359)(166,262,233,360)(167,263,234,361)(168,264,235,362)(169,265,236,363)(170,266,237,364)(171,267,238,365)(172,268,239,366)(173,269,240,367)(174,270,241,368)(175,271,242,346)(176,272,243,347)(177,273,244,348)(178,274,245,349)(179,275,246,350)(180,276,247,351)(181,254,248,352)(182,255,249,353)(183,256,250,354)(184,257,251,355), (1,186,168,52)(2,187,169,53)(3,188,170,54)(4,189,171,55)(5,190,172,56)(6,191,173,57)(7,192,174,58)(8,193,175,59)(9,194,176,60)(10,195,177,61)(11,196,178,62)(12,197,179,63)(13,198,180,64)(14,199,181,65)(15,200,182,66)(16,201,183,67)(17,202,184,68)(18,203,162,69)(19,204,163,47)(20,205,164,48)(21,206,165,49)(22,207,166,50)(23,185,167,51)(24,106,120,239)(25,107,121,240)(26,108,122,241)(27,109,123,242)(28,110,124,243)(29,111,125,244)(30,112,126,245)(31,113,127,246)(32,114,128,247)(33,115,129,248)(34,93,130,249)(35,94,131,250)(36,95,132,251)(37,96,133,252)(38,97,134,253)(39,98,135,231)(40,99,136,232)(41,100,137,233)(42,101,138,234)(43,102,116,235)(44,103,117,236)(45,104,118,237)(46,105,119,238)(70,345,271,141)(71,323,272,142)(72,324,273,143)(73,325,274,144)(74,326,275,145)(75,327,276,146)(76,328,254,147)(77,329,255,148)(78,330,256,149)(79,331,257,150)(80,332,258,151)(81,333,259,152)(82,334,260,153)(83,335,261,154)(84,336,262,155)(85,337,263,156)(86,338,264,157)(87,339,265,158)(88,340,266,159)(89,341,267,160)(90,342,268,161)(91,343,269,139)(92,344,270,140)(208,346,299,303)(209,347,277,304)(210,348,278,305)(211,349,279,306)(212,350,280,307)(213,351,281,308)(214,352,282,309)(215,353,283,310)(216,354,284,311)(217,355,285,312)(218,356,286,313)(219,357,287,314)(220,358,288,315)(221,359,289,316)(222,360,290,317)(223,361,291,318)(224,362,292,319)(225,363,293,320)(226,364,294,321)(227,365,295,322)(228,366,296,300)(229,367,297,301)(230,368,298,302) );
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)], [(1,86,102,319),(2,87,103,320),(3,88,104,321),(4,89,105,322),(5,90,106,300),(6,91,107,301),(7,92,108,302),(8,70,109,303),(9,71,110,304),(10,72,111,305),(11,73,112,306),(12,74,113,307),(13,75,114,308),(14,76,115,309),(15,77,93,310),(16,78,94,311),(17,79,95,312),(18,80,96,313),(19,81,97,314),(20,82,98,315),(21,83,99,316),(22,84,100,317),(23,85,101,318),(24,161,56,296),(25,139,57,297),(26,140,58,298),(27,141,59,299),(28,142,60,277),(29,143,61,278),(30,144,62,279),(31,145,63,280),(32,146,64,281),(33,147,65,282),(34,148,66,283),(35,149,67,284),(36,150,68,285),(37,151,69,286),(38,152,47,287),(39,153,48,288),(40,154,49,289),(41,155,50,290),(42,156,51,291),(43,157,52,292),(44,158,53,293),(45,159,54,294),(46,160,55,295),(116,338,186,224),(117,339,187,225),(118,340,188,226),(119,341,189,227),(120,342,190,228),(121,343,191,229),(122,344,192,230),(123,345,193,208),(124,323,194,209),(125,324,195,210),(126,325,196,211),(127,326,197,212),(128,327,198,213),(129,328,199,214),(130,329,200,215),(131,330,201,216),(132,331,202,217),(133,332,203,218),(134,333,204,219),(135,334,205,220),(136,335,206,221),(137,336,207,222),(138,337,185,223),(162,258,252,356),(163,259,253,357),(164,260,231,358),(165,261,232,359),(166,262,233,360),(167,263,234,361),(168,264,235,362),(169,265,236,363),(170,266,237,364),(171,267,238,365),(172,268,239,366),(173,269,240,367),(174,270,241,368),(175,271,242,346),(176,272,243,347),(177,273,244,348),(178,274,245,349),(179,275,246,350),(180,276,247,351),(181,254,248,352),(182,255,249,353),(183,256,250,354),(184,257,251,355)], [(1,186,168,52),(2,187,169,53),(3,188,170,54),(4,189,171,55),(5,190,172,56),(6,191,173,57),(7,192,174,58),(8,193,175,59),(9,194,176,60),(10,195,177,61),(11,196,178,62),(12,197,179,63),(13,198,180,64),(14,199,181,65),(15,200,182,66),(16,201,183,67),(17,202,184,68),(18,203,162,69),(19,204,163,47),(20,205,164,48),(21,206,165,49),(22,207,166,50),(23,185,167,51),(24,106,120,239),(25,107,121,240),(26,108,122,241),(27,109,123,242),(28,110,124,243),(29,111,125,244),(30,112,126,245),(31,113,127,246),(32,114,128,247),(33,115,129,248),(34,93,130,249),(35,94,131,250),(36,95,132,251),(37,96,133,252),(38,97,134,253),(39,98,135,231),(40,99,136,232),(41,100,137,233),(42,101,138,234),(43,102,116,235),(44,103,117,236),(45,104,118,237),(46,105,119,238),(70,345,271,141),(71,323,272,142),(72,324,273,143),(73,325,274,144),(74,326,275,145),(75,327,276,146),(76,328,254,147),(77,329,255,148),(78,330,256,149),(79,331,257,150),(80,332,258,151),(81,333,259,152),(82,334,260,153),(83,335,261,154),(84,336,262,155),(85,337,263,156),(86,338,264,157),(87,339,265,158),(88,340,266,159),(89,341,267,160),(90,342,268,161),(91,343,269,139),(92,344,270,140),(208,346,299,303),(209,347,277,304),(210,348,278,305),(211,349,279,306),(212,350,280,307),(213,351,281,308),(214,352,282,309),(215,353,283,310),(216,354,284,311),(217,355,285,312),(218,356,286,313),(219,357,287,314),(220,358,288,315),(221,359,289,316),(222,360,290,317),(223,361,291,318),(224,362,292,319),(225,363,293,320),(226,364,294,321),(227,365,295,322),(228,366,296,300),(229,367,297,301),(230,368,298,302)]])
230 conjugacy classes
| class | 1 | 2A | 2B | 2C | 4A | ··· | 4F | 23A | ··· | 23V | 46A | ··· | 46BN | 92A | ··· | 92EB |
| order | 1 | 2 | 2 | 2 | 4 | ··· | 4 | 23 | ··· | 23 | 46 | ··· | 46 | 92 | ··· | 92 |
| size | 1 | 1 | 1 | 1 | 2 | ··· | 2 | 1 | ··· | 1 | 1 | ··· | 1 | 2 | ··· | 2 |
230 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 |
| type | + | + | + | - | ||||||
| image | C1 | C2 | C4 | C23 | C46 | C92 | D4 | Q8 | D4×C23 | Q8×C23 |
| kernel | C4⋊C4×C23 | C2×C92 | C92 | C4⋊C4 | C2×C4 | C4 | C46 | C46 | C2 | C2 |
| # reps | 1 | 3 | 4 | 22 | 66 | 88 | 1 | 1 | 22 | 22 |
Matrix representation of C4⋊C4×C23 ►in GL3(𝔽277) generated by
| 1 | 0 | 0 |
| 0 | 264 | 0 |
| 0 | 0 | 264 |
| 1 | 0 | 0 |
| 0 | 1 | 275 |
| 0 | 1 | 276 |
| 217 | 0 | 0 |
| 0 | 232 | 13 |
| 0 | 100 | 45 |
G:=sub<GL(3,GF(277))| [1,0,0,0,264,0,0,0,264],[1,0,0,0,1,1,0,275,276],[217,0,0,0,232,100,0,13,45] >;
C4⋊C4×C23 in GAP, Magma, Sage, TeX
C_4\rtimes C_4\times C_{23} % in TeX
G:=Group("C4:C4xC23"); // GroupNames label
G:=SmallGroup(368,21);
// by ID
G=gap.SmallGroup(368,21);
# by ID
G:=PCGroup([5,-2,-2,-23,-2,-2,920,941,466]);
// Polycyclic
G:=Group<a,b,c|a^23=b^4=c^4=1,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations
Export