direct product, metacyclic, supersoluble, monomial, A-group, 2-hyperelementary
Aliases: C4×Dic23, C23⋊C42, C92⋊2C4, C22.3D46, (C2×C92).7C2, C46.3(C2×C4), (C2×C4).6D23, C2.2(C4×D23), (C2×C46).3C22, C2.2(C2×Dic23), (C2×Dic23).4C2, SmallGroup(368,10)
Series: Derived ►Chief ►Lower central ►Upper central
| C23 — C4×Dic23 |
Generators and relations for C4×Dic23
G = < a,b,c | a4=b46=1, c2=b23, ab=ba, ac=ca, cbc-1=b-1 >
Smallest permutation representation of C4×Dic23
►Regular action on 368 points
Generators in S368
(1 156 199 96)(2 157 200 97)(3 158 201 98)(4 159 202 99)(5 160 203 100)(6 161 204 101)(7 162 205 102)(8 163 206 103)(9 164 207 104)(10 165 208 105)(11 166 209 106)(12 167 210 107)(13 168 211 108)(14 169 212 109)(15 170 213 110)(16 171 214 111)(17 172 215 112)(18 173 216 113)(19 174 217 114)(20 175 218 115)(21 176 219 116)(22 177 220 117)(23 178 221 118)(24 179 222 119)(25 180 223 120)(26 181 224 121)(27 182 225 122)(28 183 226 123)(29 184 227 124)(30 139 228 125)(31 140 229 126)(32 141 230 127)(33 142 185 128)(34 143 186 129)(35 144 187 130)(36 145 188 131)(37 146 189 132)(38 147 190 133)(39 148 191 134)(40 149 192 135)(41 150 193 136)(42 151 194 137)(43 152 195 138)(44 153 196 93)(45 154 197 94)(46 155 198 95)(47 294 328 268)(48 295 329 269)(49 296 330 270)(50 297 331 271)(51 298 332 272)(52 299 333 273)(53 300 334 274)(54 301 335 275)(55 302 336 276)(56 303 337 231)(57 304 338 232)(58 305 339 233)(59 306 340 234)(60 307 341 235)(61 308 342 236)(62 309 343 237)(63 310 344 238)(64 311 345 239)(65 312 346 240)(66 313 347 241)(67 314 348 242)(68 315 349 243)(69 316 350 244)(70 317 351 245)(71 318 352 246)(72 319 353 247)(73 320 354 248)(74 321 355 249)(75 322 356 250)(76 277 357 251)(77 278 358 252)(78 279 359 253)(79 280 360 254)(80 281 361 255)(81 282 362 256)(82 283 363 257)(83 284 364 258)(84 285 365 259)(85 286 366 260)(86 287 367 261)(87 288 368 262)(88 289 323 263)(89 290 324 264)(90 291 325 265)(91 292 326 266)(92 293 327 267)
(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 52 24 75)(2 51 25 74)(3 50 26 73)(4 49 27 72)(5 48 28 71)(6 47 29 70)(7 92 30 69)(8 91 31 68)(9 90 32 67)(10 89 33 66)(11 88 34 65)(12 87 35 64)(13 86 36 63)(14 85 37 62)(15 84 38 61)(16 83 39 60)(17 82 40 59)(18 81 41 58)(19 80 42 57)(20 79 43 56)(21 78 44 55)(22 77 45 54)(23 76 46 53)(93 276 116 253)(94 275 117 252)(95 274 118 251)(96 273 119 250)(97 272 120 249)(98 271 121 248)(99 270 122 247)(100 269 123 246)(101 268 124 245)(102 267 125 244)(103 266 126 243)(104 265 127 242)(105 264 128 241)(106 263 129 240)(107 262 130 239)(108 261 131 238)(109 260 132 237)(110 259 133 236)(111 258 134 235)(112 257 135 234)(113 256 136 233)(114 255 137 232)(115 254 138 231)(139 316 162 293)(140 315 163 292)(141 314 164 291)(142 313 165 290)(143 312 166 289)(144 311 167 288)(145 310 168 287)(146 309 169 286)(147 308 170 285)(148 307 171 284)(149 306 172 283)(150 305 173 282)(151 304 174 281)(152 303 175 280)(153 302 176 279)(154 301 177 278)(155 300 178 277)(156 299 179 322)(157 298 180 321)(158 297 181 320)(159 296 182 319)(160 295 183 318)(161 294 184 317)(185 347 208 324)(186 346 209 323)(187 345 210 368)(188 344 211 367)(189 343 212 366)(190 342 213 365)(191 341 214 364)(192 340 215 363)(193 339 216 362)(194 338 217 361)(195 337 218 360)(196 336 219 359)(197 335 220 358)(198 334 221 357)(199 333 222 356)(200 332 223 355)(201 331 224 354)(202 330 225 353)(203 329 226 352)(204 328 227 351)(205 327 228 350)(206 326 229 349)(207 325 230 348)
G:=sub<Sym(368)| (1,156,199,96)(2,157,200,97)(3,158,201,98)(4,159,202,99)(5,160,203,100)(6,161,204,101)(7,162,205,102)(8,163,206,103)(9,164,207,104)(10,165,208,105)(11,166,209,106)(12,167,210,107)(13,168,211,108)(14,169,212,109)(15,170,213,110)(16,171,214,111)(17,172,215,112)(18,173,216,113)(19,174,217,114)(20,175,218,115)(21,176,219,116)(22,177,220,117)(23,178,221,118)(24,179,222,119)(25,180,223,120)(26,181,224,121)(27,182,225,122)(28,183,226,123)(29,184,227,124)(30,139,228,125)(31,140,229,126)(32,141,230,127)(33,142,185,128)(34,143,186,129)(35,144,187,130)(36,145,188,131)(37,146,189,132)(38,147,190,133)(39,148,191,134)(40,149,192,135)(41,150,193,136)(42,151,194,137)(43,152,195,138)(44,153,196,93)(45,154,197,94)(46,155,198,95)(47,294,328,268)(48,295,329,269)(49,296,330,270)(50,297,331,271)(51,298,332,272)(52,299,333,273)(53,300,334,274)(54,301,335,275)(55,302,336,276)(56,303,337,231)(57,304,338,232)(58,305,339,233)(59,306,340,234)(60,307,341,235)(61,308,342,236)(62,309,343,237)(63,310,344,238)(64,311,345,239)(65,312,346,240)(66,313,347,241)(67,314,348,242)(68,315,349,243)(69,316,350,244)(70,317,351,245)(71,318,352,246)(72,319,353,247)(73,320,354,248)(74,321,355,249)(75,322,356,250)(76,277,357,251)(77,278,358,252)(78,279,359,253)(79,280,360,254)(80,281,361,255)(81,282,362,256)(82,283,363,257)(83,284,364,258)(84,285,365,259)(85,286,366,260)(86,287,367,261)(87,288,368,262)(88,289,323,263)(89,290,324,264)(90,291,325,265)(91,292,326,266)(92,293,327,267), (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), (1,52,24,75)(2,51,25,74)(3,50,26,73)(4,49,27,72)(5,48,28,71)(6,47,29,70)(7,92,30,69)(8,91,31,68)(9,90,32,67)(10,89,33,66)(11,88,34,65)(12,87,35,64)(13,86,36,63)(14,85,37,62)(15,84,38,61)(16,83,39,60)(17,82,40,59)(18,81,41,58)(19,80,42,57)(20,79,43,56)(21,78,44,55)(22,77,45,54)(23,76,46,53)(93,276,116,253)(94,275,117,252)(95,274,118,251)(96,273,119,250)(97,272,120,249)(98,271,121,248)(99,270,122,247)(100,269,123,246)(101,268,124,245)(102,267,125,244)(103,266,126,243)(104,265,127,242)(105,264,128,241)(106,263,129,240)(107,262,130,239)(108,261,131,238)(109,260,132,237)(110,259,133,236)(111,258,134,235)(112,257,135,234)(113,256,136,233)(114,255,137,232)(115,254,138,231)(139,316,162,293)(140,315,163,292)(141,314,164,291)(142,313,165,290)(143,312,166,289)(144,311,167,288)(145,310,168,287)(146,309,169,286)(147,308,170,285)(148,307,171,284)(149,306,172,283)(150,305,173,282)(151,304,174,281)(152,303,175,280)(153,302,176,279)(154,301,177,278)(155,300,178,277)(156,299,179,322)(157,298,180,321)(158,297,181,320)(159,296,182,319)(160,295,183,318)(161,294,184,317)(185,347,208,324)(186,346,209,323)(187,345,210,368)(188,344,211,367)(189,343,212,366)(190,342,213,365)(191,341,214,364)(192,340,215,363)(193,339,216,362)(194,338,217,361)(195,337,218,360)(196,336,219,359)(197,335,220,358)(198,334,221,357)(199,333,222,356)(200,332,223,355)(201,331,224,354)(202,330,225,353)(203,329,226,352)(204,328,227,351)(205,327,228,350)(206,326,229,349)(207,325,230,348)>;
G:=Group( (1,156,199,96)(2,157,200,97)(3,158,201,98)(4,159,202,99)(5,160,203,100)(6,161,204,101)(7,162,205,102)(8,163,206,103)(9,164,207,104)(10,165,208,105)(11,166,209,106)(12,167,210,107)(13,168,211,108)(14,169,212,109)(15,170,213,110)(16,171,214,111)(17,172,215,112)(18,173,216,113)(19,174,217,114)(20,175,218,115)(21,176,219,116)(22,177,220,117)(23,178,221,118)(24,179,222,119)(25,180,223,120)(26,181,224,121)(27,182,225,122)(28,183,226,123)(29,184,227,124)(30,139,228,125)(31,140,229,126)(32,141,230,127)(33,142,185,128)(34,143,186,129)(35,144,187,130)(36,145,188,131)(37,146,189,132)(38,147,190,133)(39,148,191,134)(40,149,192,135)(41,150,193,136)(42,151,194,137)(43,152,195,138)(44,153,196,93)(45,154,197,94)(46,155,198,95)(47,294,328,268)(48,295,329,269)(49,296,330,270)(50,297,331,271)(51,298,332,272)(52,299,333,273)(53,300,334,274)(54,301,335,275)(55,302,336,276)(56,303,337,231)(57,304,338,232)(58,305,339,233)(59,306,340,234)(60,307,341,235)(61,308,342,236)(62,309,343,237)(63,310,344,238)(64,311,345,239)(65,312,346,240)(66,313,347,241)(67,314,348,242)(68,315,349,243)(69,316,350,244)(70,317,351,245)(71,318,352,246)(72,319,353,247)(73,320,354,248)(74,321,355,249)(75,322,356,250)(76,277,357,251)(77,278,358,252)(78,279,359,253)(79,280,360,254)(80,281,361,255)(81,282,362,256)(82,283,363,257)(83,284,364,258)(84,285,365,259)(85,286,366,260)(86,287,367,261)(87,288,368,262)(88,289,323,263)(89,290,324,264)(90,291,325,265)(91,292,326,266)(92,293,327,267), (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), (1,52,24,75)(2,51,25,74)(3,50,26,73)(4,49,27,72)(5,48,28,71)(6,47,29,70)(7,92,30,69)(8,91,31,68)(9,90,32,67)(10,89,33,66)(11,88,34,65)(12,87,35,64)(13,86,36,63)(14,85,37,62)(15,84,38,61)(16,83,39,60)(17,82,40,59)(18,81,41,58)(19,80,42,57)(20,79,43,56)(21,78,44,55)(22,77,45,54)(23,76,46,53)(93,276,116,253)(94,275,117,252)(95,274,118,251)(96,273,119,250)(97,272,120,249)(98,271,121,248)(99,270,122,247)(100,269,123,246)(101,268,124,245)(102,267,125,244)(103,266,126,243)(104,265,127,242)(105,264,128,241)(106,263,129,240)(107,262,130,239)(108,261,131,238)(109,260,132,237)(110,259,133,236)(111,258,134,235)(112,257,135,234)(113,256,136,233)(114,255,137,232)(115,254,138,231)(139,316,162,293)(140,315,163,292)(141,314,164,291)(142,313,165,290)(143,312,166,289)(144,311,167,288)(145,310,168,287)(146,309,169,286)(147,308,170,285)(148,307,171,284)(149,306,172,283)(150,305,173,282)(151,304,174,281)(152,303,175,280)(153,302,176,279)(154,301,177,278)(155,300,178,277)(156,299,179,322)(157,298,180,321)(158,297,181,320)(159,296,182,319)(160,295,183,318)(161,294,184,317)(185,347,208,324)(186,346,209,323)(187,345,210,368)(188,344,211,367)(189,343,212,366)(190,342,213,365)(191,341,214,364)(192,340,215,363)(193,339,216,362)(194,338,217,361)(195,337,218,360)(196,336,219,359)(197,335,220,358)(198,334,221,357)(199,333,222,356)(200,332,223,355)(201,331,224,354)(202,330,225,353)(203,329,226,352)(204,328,227,351)(205,327,228,350)(206,326,229,349)(207,325,230,348) );
G=PermutationGroup([[(1,156,199,96),(2,157,200,97),(3,158,201,98),(4,159,202,99),(5,160,203,100),(6,161,204,101),(7,162,205,102),(8,163,206,103),(9,164,207,104),(10,165,208,105),(11,166,209,106),(12,167,210,107),(13,168,211,108),(14,169,212,109),(15,170,213,110),(16,171,214,111),(17,172,215,112),(18,173,216,113),(19,174,217,114),(20,175,218,115),(21,176,219,116),(22,177,220,117),(23,178,221,118),(24,179,222,119),(25,180,223,120),(26,181,224,121),(27,182,225,122),(28,183,226,123),(29,184,227,124),(30,139,228,125),(31,140,229,126),(32,141,230,127),(33,142,185,128),(34,143,186,129),(35,144,187,130),(36,145,188,131),(37,146,189,132),(38,147,190,133),(39,148,191,134),(40,149,192,135),(41,150,193,136),(42,151,194,137),(43,152,195,138),(44,153,196,93),(45,154,197,94),(46,155,198,95),(47,294,328,268),(48,295,329,269),(49,296,330,270),(50,297,331,271),(51,298,332,272),(52,299,333,273),(53,300,334,274),(54,301,335,275),(55,302,336,276),(56,303,337,231),(57,304,338,232),(58,305,339,233),(59,306,340,234),(60,307,341,235),(61,308,342,236),(62,309,343,237),(63,310,344,238),(64,311,345,239),(65,312,346,240),(66,313,347,241),(67,314,348,242),(68,315,349,243),(69,316,350,244),(70,317,351,245),(71,318,352,246),(72,319,353,247),(73,320,354,248),(74,321,355,249),(75,322,356,250),(76,277,357,251),(77,278,358,252),(78,279,359,253),(79,280,360,254),(80,281,361,255),(81,282,362,256),(82,283,363,257),(83,284,364,258),(84,285,365,259),(85,286,366,260),(86,287,367,261),(87,288,368,262),(88,289,323,263),(89,290,324,264),(90,291,325,265),(91,292,326,266),(92,293,327,267)], [(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)], [(1,52,24,75),(2,51,25,74),(3,50,26,73),(4,49,27,72),(5,48,28,71),(6,47,29,70),(7,92,30,69),(8,91,31,68),(9,90,32,67),(10,89,33,66),(11,88,34,65),(12,87,35,64),(13,86,36,63),(14,85,37,62),(15,84,38,61),(16,83,39,60),(17,82,40,59),(18,81,41,58),(19,80,42,57),(20,79,43,56),(21,78,44,55),(22,77,45,54),(23,76,46,53),(93,276,116,253),(94,275,117,252),(95,274,118,251),(96,273,119,250),(97,272,120,249),(98,271,121,248),(99,270,122,247),(100,269,123,246),(101,268,124,245),(102,267,125,244),(103,266,126,243),(104,265,127,242),(105,264,128,241),(106,263,129,240),(107,262,130,239),(108,261,131,238),(109,260,132,237),(110,259,133,236),(111,258,134,235),(112,257,135,234),(113,256,136,233),(114,255,137,232),(115,254,138,231),(139,316,162,293),(140,315,163,292),(141,314,164,291),(142,313,165,290),(143,312,166,289),(144,311,167,288),(145,310,168,287),(146,309,169,286),(147,308,170,285),(148,307,171,284),(149,306,172,283),(150,305,173,282),(151,304,174,281),(152,303,175,280),(153,302,176,279),(154,301,177,278),(155,300,178,277),(156,299,179,322),(157,298,180,321),(158,297,181,320),(159,296,182,319),(160,295,183,318),(161,294,184,317),(185,347,208,324),(186,346,209,323),(187,345,210,368),(188,344,211,367),(189,343,212,366),(190,342,213,365),(191,341,214,364),(192,340,215,363),(193,339,216,362),(194,338,217,361),(195,337,218,360),(196,336,219,359),(197,335,220,358),(198,334,221,357),(199,333,222,356),(200,332,223,355),(201,331,224,354),(202,330,225,353),(203,329,226,352),(204,328,227,351),(205,327,228,350),(206,326,229,349),(207,325,230,348)]])
104 conjugacy classes
| class | 1 | 2A | 2B | 2C | 4A | 4B | 4C | 4D | 4E | ··· | 4L | 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 | 1 | 1 | 1 | 1 | 23 | ··· | 23 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
104 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | - | + | |||
| image | C1 | C2 | C2 | C4 | C4 | D23 | Dic23 | D46 | C4×D23 |
| kernel | C4×Dic23 | C2×Dic23 | C2×C92 | Dic23 | C92 | C2×C4 | C4 | C22 | C2 |
| # reps | 1 | 2 | 1 | 8 | 4 | 11 | 22 | 11 | 44 |
Matrix representation of C4×Dic23 ►in GL4(𝔽277) generated by
| 60 | 0 | 0 | 0 |
| 0 | 276 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 |
| 0 | 276 | 0 | 0 |
| 0 | 0 | 0 | 1 |
| 0 | 0 | 276 | 88 |
| 276 | 0 | 0 | 0 |
| 0 | 60 | 0 | 0 |
| 0 | 0 | 167 | 49 |
| 0 | 0 | 64 | 110 |
G:=sub<GL(4,GF(277))| [60,0,0,0,0,276,0,0,0,0,1,0,0,0,0,1],[1,0,0,0,0,276,0,0,0,0,0,276,0,0,1,88],[276,0,0,0,0,60,0,0,0,0,167,64,0,0,49,110] >;
C4×Dic23 in GAP, Magma, Sage, TeX
C_4\times {\rm Dic}_{23} % in TeX
G:=Group("C4xDic23"); // GroupNames label
G:=SmallGroup(368,10);
// by ID
G=gap.SmallGroup(368,10);
# by ID
G:=PCGroup([5,-2,-2,-2,-2,-23,20,46,8804]);
// Polycyclic
G:=Group<a,b,c|a^4=b^46=1,c^2=b^23,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations
Export