direct product, metabelian, supersoluble, monomial, A-group, 2-hyperelementary
Aliases: C22×Dic23, C46.9C23, C23.2D23, C22.11D46, (C2×C46)⋊3C4, C46⋊2(C2×C4), C23⋊2(C22×C4), (C22×C46).3C2, C2.2(C22×D23), (C2×C46).12C22, SmallGroup(368,35)
Series: Derived ►Chief ►Lower central ►Upper central
| C23 — C22×Dic23 |
Generators and relations for C22×Dic23
G = < a,b,c,d | a2=b2=c46=1, d2=c23, ab=ba, ac=ca, ad=da, bc=cb, bd=db, dcd-1=c-1 >
Subgroups: 296 in 54 conjugacy classes, 43 normal (7 characteristic)
C1, C2, C2, C4, C22, C2×C4, C23, C22×C4, C23, C46, C46, Dic23, C2×C46, C2×Dic23, C22×C46, C22×Dic23
Quotients: C1, C2, C4, C22, C2×C4, C23, C22×C4, D23, Dic23, D46, C2×Dic23, C22×D23, C22×Dic23
►Regular action on 368 points
Generators in S368
(1 116)(2 117)(3 118)(4 119)(5 120)(6 121)(7 122)(8 123)(9 124)(10 125)(11 126)(12 127)(13 128)(14 129)(15 130)(16 131)(17 132)(18 133)(19 134)(20 135)(21 136)(22 137)(23 138)(24 93)(25 94)(26 95)(27 96)(28 97)(29 98)(30 99)(31 100)(32 101)(33 102)(34 103)(35 104)(36 105)(37 106)(38 107)(39 108)(40 109)(41 110)(42 111)(43 112)(44 113)(45 114)(46 115)(47 162)(48 163)(49 164)(50 165)(51 166)(52 167)(53 168)(54 169)(55 170)(56 171)(57 172)(58 173)(59 174)(60 175)(61 176)(62 177)(63 178)(64 179)(65 180)(66 181)(67 182)(68 183)(69 184)(70 139)(71 140)(72 141)(73 142)(74 143)(75 144)(76 145)(77 146)(78 147)(79 148)(80 149)(81 150)(82 151)(83 152)(84 153)(85 154)(86 155)(87 156)(88 157)(89 158)(90 159)(91 160)(92 161)(185 277)(186 278)(187 279)(188 280)(189 281)(190 282)(191 283)(192 284)(193 285)(194 286)(195 287)(196 288)(197 289)(198 290)(199 291)(200 292)(201 293)(202 294)(203 295)(204 296)(205 297)(206 298)(207 299)(208 300)(209 301)(210 302)(211 303)(212 304)(213 305)(214 306)(215 307)(216 308)(217 309)(218 310)(219 311)(220 312)(221 313)(222 314)(223 315)(224 316)(225 317)(226 318)(227 319)(228 320)(229 321)(230 322)(231 346)(232 347)(233 348)(234 349)(235 350)(236 351)(237 352)(238 353)(239 354)(240 355)(241 356)(242 357)(243 358)(244 359)(245 360)(246 361)(247 362)(248 363)(249 364)(250 365)(251 366)(252 367)(253 368)(254 323)(255 324)(256 325)(257 326)(258 327)(259 328)(260 329)(261 330)(262 331)(263 332)(264 333)(265 334)(266 335)(267 336)(268 337)(269 338)(270 339)(271 340)(272 341)(273 342)(274 343)(275 344)(276 345)
(1 65)(2 66)(3 67)(4 68)(5 69)(6 70)(7 71)(8 72)(9 73)(10 74)(11 75)(12 76)(13 77)(14 78)(15 79)(16 80)(17 81)(18 82)(19 83)(20 84)(21 85)(22 86)(23 87)(24 88)(25 89)(26 90)(27 91)(28 92)(29 47)(30 48)(31 49)(32 50)(33 51)(34 52)(35 53)(36 54)(37 55)(38 56)(39 57)(40 58)(41 59)(42 60)(43 61)(44 62)(45 63)(46 64)(93 157)(94 158)(95 159)(96 160)(97 161)(98 162)(99 163)(100 164)(101 165)(102 166)(103 167)(104 168)(105 169)(106 170)(107 171)(108 172)(109 173)(110 174)(111 175)(112 176)(113 177)(114 178)(115 179)(116 180)(117 181)(118 182)(119 183)(120 184)(121 139)(122 140)(123 141)(124 142)(125 143)(126 144)(127 145)(128 146)(129 147)(130 148)(131 149)(132 150)(133 151)(134 152)(135 153)(136 154)(137 155)(138 156)(185 231)(186 232)(187 233)(188 234)(189 235)(190 236)(191 237)(192 238)(193 239)(194 240)(195 241)(196 242)(197 243)(198 244)(199 245)(200 246)(201 247)(202 248)(203 249)(204 250)(205 251)(206 252)(207 253)(208 254)(209 255)(210 256)(211 257)(212 258)(213 259)(214 260)(215 261)(216 262)(217 263)(218 264)(219 265)(220 266)(221 267)(222 268)(223 269)(224 270)(225 271)(226 272)(227 273)(228 274)(229 275)(230 276)(277 346)(278 347)(279 348)(280 349)(281 350)(282 351)(283 352)(284 353)(285 354)(286 355)(287 356)(288 357)(289 358)(290 359)(291 360)(292 361)(293 362)(294 363)(295 364)(296 365)(297 366)(298 367)(299 368)(300 323)(301 324)(302 325)(303 326)(304 327)(305 328)(306 329)(307 330)(308 331)(309 332)(310 333)(311 334)(312 335)(313 336)(314 337)(315 338)(316 339)(317 340)(318 341)(319 342)(320 343)(321 344)(322 345)
(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)
(1 231 24 254)(2 276 25 253)(3 275 26 252)(4 274 27 251)(5 273 28 250)(6 272 29 249)(7 271 30 248)(8 270 31 247)(9 269 32 246)(10 268 33 245)(11 267 34 244)(12 266 35 243)(13 265 36 242)(14 264 37 241)(15 263 38 240)(16 262 39 239)(17 261 40 238)(18 260 41 237)(19 259 42 236)(20 258 43 235)(21 257 44 234)(22 256 45 233)(23 255 46 232)(47 203 70 226)(48 202 71 225)(49 201 72 224)(50 200 73 223)(51 199 74 222)(52 198 75 221)(53 197 76 220)(54 196 77 219)(55 195 78 218)(56 194 79 217)(57 193 80 216)(58 192 81 215)(59 191 82 214)(60 190 83 213)(61 189 84 212)(62 188 85 211)(63 187 86 210)(64 186 87 209)(65 185 88 208)(66 230 89 207)(67 229 90 206)(68 228 91 205)(69 227 92 204)(93 323 116 346)(94 368 117 345)(95 367 118 344)(96 366 119 343)(97 365 120 342)(98 364 121 341)(99 363 122 340)(100 362 123 339)(101 361 124 338)(102 360 125 337)(103 359 126 336)(104 358 127 335)(105 357 128 334)(106 356 129 333)(107 355 130 332)(108 354 131 331)(109 353 132 330)(110 352 133 329)(111 351 134 328)(112 350 135 327)(113 349 136 326)(114 348 137 325)(115 347 138 324)(139 318 162 295)(140 317 163 294)(141 316 164 293)(142 315 165 292)(143 314 166 291)(144 313 167 290)(145 312 168 289)(146 311 169 288)(147 310 170 287)(148 309 171 286)(149 308 172 285)(150 307 173 284)(151 306 174 283)(152 305 175 282)(153 304 176 281)(154 303 177 280)(155 302 178 279)(156 301 179 278)(157 300 180 277)(158 299 181 322)(159 298 182 321)(160 297 183 320)(161 296 184 319)
G:=sub<Sym(368)| (1,116)(2,117)(3,118)(4,119)(5,120)(6,121)(7,122)(8,123)(9,124)(10,125)(11,126)(12,127)(13,128)(14,129)(15,130)(16,131)(17,132)(18,133)(19,134)(20,135)(21,136)(22,137)(23,138)(24,93)(25,94)(26,95)(27,96)(28,97)(29,98)(30,99)(31,100)(32,101)(33,102)(34,103)(35,104)(36,105)(37,106)(38,107)(39,108)(40,109)(41,110)(42,111)(43,112)(44,113)(45,114)(46,115)(47,162)(48,163)(49,164)(50,165)(51,166)(52,167)(53,168)(54,169)(55,170)(56,171)(57,172)(58,173)(59,174)(60,175)(61,176)(62,177)(63,178)(64,179)(65,180)(66,181)(67,182)(68,183)(69,184)(70,139)(71,140)(72,141)(73,142)(74,143)(75,144)(76,145)(77,146)(78,147)(79,148)(80,149)(81,150)(82,151)(83,152)(84,153)(85,154)(86,155)(87,156)(88,157)(89,158)(90,159)(91,160)(92,161)(185,277)(186,278)(187,279)(188,280)(189,281)(190,282)(191,283)(192,284)(193,285)(194,286)(195,287)(196,288)(197,289)(198,290)(199,291)(200,292)(201,293)(202,294)(203,295)(204,296)(205,297)(206,298)(207,299)(208,300)(209,301)(210,302)(211,303)(212,304)(213,305)(214,306)(215,307)(216,308)(217,309)(218,310)(219,311)(220,312)(221,313)(222,314)(223,315)(224,316)(225,317)(226,318)(227,319)(228,320)(229,321)(230,322)(231,346)(232,347)(233,348)(234,349)(235,350)(236,351)(237,352)(238,353)(239,354)(240,355)(241,356)(242,357)(243,358)(244,359)(245,360)(246,361)(247,362)(248,363)(249,364)(250,365)(251,366)(252,367)(253,368)(254,323)(255,324)(256,325)(257,326)(258,327)(259,328)(260,329)(261,330)(262,331)(263,332)(264,333)(265,334)(266,335)(267,336)(268,337)(269,338)(270,339)(271,340)(272,341)(273,342)(274,343)(275,344)(276,345), (1,65)(2,66)(3,67)(4,68)(5,69)(6,70)(7,71)(8,72)(9,73)(10,74)(11,75)(12,76)(13,77)(14,78)(15,79)(16,80)(17,81)(18,82)(19,83)(20,84)(21,85)(22,86)(23,87)(24,88)(25,89)(26,90)(27,91)(28,92)(29,47)(30,48)(31,49)(32,50)(33,51)(34,52)(35,53)(36,54)(37,55)(38,56)(39,57)(40,58)(41,59)(42,60)(43,61)(44,62)(45,63)(46,64)(93,157)(94,158)(95,159)(96,160)(97,161)(98,162)(99,163)(100,164)(101,165)(102,166)(103,167)(104,168)(105,169)(106,170)(107,171)(108,172)(109,173)(110,174)(111,175)(112,176)(113,177)(114,178)(115,179)(116,180)(117,181)(118,182)(119,183)(120,184)(121,139)(122,140)(123,141)(124,142)(125,143)(126,144)(127,145)(128,146)(129,147)(130,148)(131,149)(132,150)(133,151)(134,152)(135,153)(136,154)(137,155)(138,156)(185,231)(186,232)(187,233)(188,234)(189,235)(190,236)(191,237)(192,238)(193,239)(194,240)(195,241)(196,242)(197,243)(198,244)(199,245)(200,246)(201,247)(202,248)(203,249)(204,250)(205,251)(206,252)(207,253)(208,254)(209,255)(210,256)(211,257)(212,258)(213,259)(214,260)(215,261)(216,262)(217,263)(218,264)(219,265)(220,266)(221,267)(222,268)(223,269)(224,270)(225,271)(226,272)(227,273)(228,274)(229,275)(230,276)(277,346)(278,347)(279,348)(280,349)(281,350)(282,351)(283,352)(284,353)(285,354)(286,355)(287,356)(288,357)(289,358)(290,359)(291,360)(292,361)(293,362)(294,363)(295,364)(296,365)(297,366)(298,367)(299,368)(300,323)(301,324)(302,325)(303,326)(304,327)(305,328)(306,329)(307,330)(308,331)(309,332)(310,333)(311,334)(312,335)(313,336)(314,337)(315,338)(316,339)(317,340)(318,341)(319,342)(320,343)(321,344)(322,345), (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), (1,231,24,254)(2,276,25,253)(3,275,26,252)(4,274,27,251)(5,273,28,250)(6,272,29,249)(7,271,30,248)(8,270,31,247)(9,269,32,246)(10,268,33,245)(11,267,34,244)(12,266,35,243)(13,265,36,242)(14,264,37,241)(15,263,38,240)(16,262,39,239)(17,261,40,238)(18,260,41,237)(19,259,42,236)(20,258,43,235)(21,257,44,234)(22,256,45,233)(23,255,46,232)(47,203,70,226)(48,202,71,225)(49,201,72,224)(50,200,73,223)(51,199,74,222)(52,198,75,221)(53,197,76,220)(54,196,77,219)(55,195,78,218)(56,194,79,217)(57,193,80,216)(58,192,81,215)(59,191,82,214)(60,190,83,213)(61,189,84,212)(62,188,85,211)(63,187,86,210)(64,186,87,209)(65,185,88,208)(66,230,89,207)(67,229,90,206)(68,228,91,205)(69,227,92,204)(93,323,116,346)(94,368,117,345)(95,367,118,344)(96,366,119,343)(97,365,120,342)(98,364,121,341)(99,363,122,340)(100,362,123,339)(101,361,124,338)(102,360,125,337)(103,359,126,336)(104,358,127,335)(105,357,128,334)(106,356,129,333)(107,355,130,332)(108,354,131,331)(109,353,132,330)(110,352,133,329)(111,351,134,328)(112,350,135,327)(113,349,136,326)(114,348,137,325)(115,347,138,324)(139,318,162,295)(140,317,163,294)(141,316,164,293)(142,315,165,292)(143,314,166,291)(144,313,167,290)(145,312,168,289)(146,311,169,288)(147,310,170,287)(148,309,171,286)(149,308,172,285)(150,307,173,284)(151,306,174,283)(152,305,175,282)(153,304,176,281)(154,303,177,280)(155,302,178,279)(156,301,179,278)(157,300,180,277)(158,299,181,322)(159,298,182,321)(160,297,183,320)(161,296,184,319)>;
G:=Group( (1,116)(2,117)(3,118)(4,119)(5,120)(6,121)(7,122)(8,123)(9,124)(10,125)(11,126)(12,127)(13,128)(14,129)(15,130)(16,131)(17,132)(18,133)(19,134)(20,135)(21,136)(22,137)(23,138)(24,93)(25,94)(26,95)(27,96)(28,97)(29,98)(30,99)(31,100)(32,101)(33,102)(34,103)(35,104)(36,105)(37,106)(38,107)(39,108)(40,109)(41,110)(42,111)(43,112)(44,113)(45,114)(46,115)(47,162)(48,163)(49,164)(50,165)(51,166)(52,167)(53,168)(54,169)(55,170)(56,171)(57,172)(58,173)(59,174)(60,175)(61,176)(62,177)(63,178)(64,179)(65,180)(66,181)(67,182)(68,183)(69,184)(70,139)(71,140)(72,141)(73,142)(74,143)(75,144)(76,145)(77,146)(78,147)(79,148)(80,149)(81,150)(82,151)(83,152)(84,153)(85,154)(86,155)(87,156)(88,157)(89,158)(90,159)(91,160)(92,161)(185,277)(186,278)(187,279)(188,280)(189,281)(190,282)(191,283)(192,284)(193,285)(194,286)(195,287)(196,288)(197,289)(198,290)(199,291)(200,292)(201,293)(202,294)(203,295)(204,296)(205,297)(206,298)(207,299)(208,300)(209,301)(210,302)(211,303)(212,304)(213,305)(214,306)(215,307)(216,308)(217,309)(218,310)(219,311)(220,312)(221,313)(222,314)(223,315)(224,316)(225,317)(226,318)(227,319)(228,320)(229,321)(230,322)(231,346)(232,347)(233,348)(234,349)(235,350)(236,351)(237,352)(238,353)(239,354)(240,355)(241,356)(242,357)(243,358)(244,359)(245,360)(246,361)(247,362)(248,363)(249,364)(250,365)(251,366)(252,367)(253,368)(254,323)(255,324)(256,325)(257,326)(258,327)(259,328)(260,329)(261,330)(262,331)(263,332)(264,333)(265,334)(266,335)(267,336)(268,337)(269,338)(270,339)(271,340)(272,341)(273,342)(274,343)(275,344)(276,345), (1,65)(2,66)(3,67)(4,68)(5,69)(6,70)(7,71)(8,72)(9,73)(10,74)(11,75)(12,76)(13,77)(14,78)(15,79)(16,80)(17,81)(18,82)(19,83)(20,84)(21,85)(22,86)(23,87)(24,88)(25,89)(26,90)(27,91)(28,92)(29,47)(30,48)(31,49)(32,50)(33,51)(34,52)(35,53)(36,54)(37,55)(38,56)(39,57)(40,58)(41,59)(42,60)(43,61)(44,62)(45,63)(46,64)(93,157)(94,158)(95,159)(96,160)(97,161)(98,162)(99,163)(100,164)(101,165)(102,166)(103,167)(104,168)(105,169)(106,170)(107,171)(108,172)(109,173)(110,174)(111,175)(112,176)(113,177)(114,178)(115,179)(116,180)(117,181)(118,182)(119,183)(120,184)(121,139)(122,140)(123,141)(124,142)(125,143)(126,144)(127,145)(128,146)(129,147)(130,148)(131,149)(132,150)(133,151)(134,152)(135,153)(136,154)(137,155)(138,156)(185,231)(186,232)(187,233)(188,234)(189,235)(190,236)(191,237)(192,238)(193,239)(194,240)(195,241)(196,242)(197,243)(198,244)(199,245)(200,246)(201,247)(202,248)(203,249)(204,250)(205,251)(206,252)(207,253)(208,254)(209,255)(210,256)(211,257)(212,258)(213,259)(214,260)(215,261)(216,262)(217,263)(218,264)(219,265)(220,266)(221,267)(222,268)(223,269)(224,270)(225,271)(226,272)(227,273)(228,274)(229,275)(230,276)(277,346)(278,347)(279,348)(280,349)(281,350)(282,351)(283,352)(284,353)(285,354)(286,355)(287,356)(288,357)(289,358)(290,359)(291,360)(292,361)(293,362)(294,363)(295,364)(296,365)(297,366)(298,367)(299,368)(300,323)(301,324)(302,325)(303,326)(304,327)(305,328)(306,329)(307,330)(308,331)(309,332)(310,333)(311,334)(312,335)(313,336)(314,337)(315,338)(316,339)(317,340)(318,341)(319,342)(320,343)(321,344)(322,345), (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), (1,231,24,254)(2,276,25,253)(3,275,26,252)(4,274,27,251)(5,273,28,250)(6,272,29,249)(7,271,30,248)(8,270,31,247)(9,269,32,246)(10,268,33,245)(11,267,34,244)(12,266,35,243)(13,265,36,242)(14,264,37,241)(15,263,38,240)(16,262,39,239)(17,261,40,238)(18,260,41,237)(19,259,42,236)(20,258,43,235)(21,257,44,234)(22,256,45,233)(23,255,46,232)(47,203,70,226)(48,202,71,225)(49,201,72,224)(50,200,73,223)(51,199,74,222)(52,198,75,221)(53,197,76,220)(54,196,77,219)(55,195,78,218)(56,194,79,217)(57,193,80,216)(58,192,81,215)(59,191,82,214)(60,190,83,213)(61,189,84,212)(62,188,85,211)(63,187,86,210)(64,186,87,209)(65,185,88,208)(66,230,89,207)(67,229,90,206)(68,228,91,205)(69,227,92,204)(93,323,116,346)(94,368,117,345)(95,367,118,344)(96,366,119,343)(97,365,120,342)(98,364,121,341)(99,363,122,340)(100,362,123,339)(101,361,124,338)(102,360,125,337)(103,359,126,336)(104,358,127,335)(105,357,128,334)(106,356,129,333)(107,355,130,332)(108,354,131,331)(109,353,132,330)(110,352,133,329)(111,351,134,328)(112,350,135,327)(113,349,136,326)(114,348,137,325)(115,347,138,324)(139,318,162,295)(140,317,163,294)(141,316,164,293)(142,315,165,292)(143,314,166,291)(144,313,167,290)(145,312,168,289)(146,311,169,288)(147,310,170,287)(148,309,171,286)(149,308,172,285)(150,307,173,284)(151,306,174,283)(152,305,175,282)(153,304,176,281)(154,303,177,280)(155,302,178,279)(156,301,179,278)(157,300,180,277)(158,299,181,322)(159,298,182,321)(160,297,183,320)(161,296,184,319) );
G=PermutationGroup([[(1,116),(2,117),(3,118),(4,119),(5,120),(6,121),(7,122),(8,123),(9,124),(10,125),(11,126),(12,127),(13,128),(14,129),(15,130),(16,131),(17,132),(18,133),(19,134),(20,135),(21,136),(22,137),(23,138),(24,93),(25,94),(26,95),(27,96),(28,97),(29,98),(30,99),(31,100),(32,101),(33,102),(34,103),(35,104),(36,105),(37,106),(38,107),(39,108),(40,109),(41,110),(42,111),(43,112),(44,113),(45,114),(46,115),(47,162),(48,163),(49,164),(50,165),(51,166),(52,167),(53,168),(54,169),(55,170),(56,171),(57,172),(58,173),(59,174),(60,175),(61,176),(62,177),(63,178),(64,179),(65,180),(66,181),(67,182),(68,183),(69,184),(70,139),(71,140),(72,141),(73,142),(74,143),(75,144),(76,145),(77,146),(78,147),(79,148),(80,149),(81,150),(82,151),(83,152),(84,153),(85,154),(86,155),(87,156),(88,157),(89,158),(90,159),(91,160),(92,161),(185,277),(186,278),(187,279),(188,280),(189,281),(190,282),(191,283),(192,284),(193,285),(194,286),(195,287),(196,288),(197,289),(198,290),(199,291),(200,292),(201,293),(202,294),(203,295),(204,296),(205,297),(206,298),(207,299),(208,300),(209,301),(210,302),(211,303),(212,304),(213,305),(214,306),(215,307),(216,308),(217,309),(218,310),(219,311),(220,312),(221,313),(222,314),(223,315),(224,316),(225,317),(226,318),(227,319),(228,320),(229,321),(230,322),(231,346),(232,347),(233,348),(234,349),(235,350),(236,351),(237,352),(238,353),(239,354),(240,355),(241,356),(242,357),(243,358),(244,359),(245,360),(246,361),(247,362),(248,363),(249,364),(250,365),(251,366),(252,367),(253,368),(254,323),(255,324),(256,325),(257,326),(258,327),(259,328),(260,329),(261,330),(262,331),(263,332),(264,333),(265,334),(266,335),(267,336),(268,337),(269,338),(270,339),(271,340),(272,341),(273,342),(274,343),(275,344),(276,345)], [(1,65),(2,66),(3,67),(4,68),(5,69),(6,70),(7,71),(8,72),(9,73),(10,74),(11,75),(12,76),(13,77),(14,78),(15,79),(16,80),(17,81),(18,82),(19,83),(20,84),(21,85),(22,86),(23,87),(24,88),(25,89),(26,90),(27,91),(28,92),(29,47),(30,48),(31,49),(32,50),(33,51),(34,52),(35,53),(36,54),(37,55),(38,56),(39,57),(40,58),(41,59),(42,60),(43,61),(44,62),(45,63),(46,64),(93,157),(94,158),(95,159),(96,160),(97,161),(98,162),(99,163),(100,164),(101,165),(102,166),(103,167),(104,168),(105,169),(106,170),(107,171),(108,172),(109,173),(110,174),(111,175),(112,176),(113,177),(114,178),(115,179),(116,180),(117,181),(118,182),(119,183),(120,184),(121,139),(122,140),(123,141),(124,142),(125,143),(126,144),(127,145),(128,146),(129,147),(130,148),(131,149),(132,150),(133,151),(134,152),(135,153),(136,154),(137,155),(138,156),(185,231),(186,232),(187,233),(188,234),(189,235),(190,236),(191,237),(192,238),(193,239),(194,240),(195,241),(196,242),(197,243),(198,244),(199,245),(200,246),(201,247),(202,248),(203,249),(204,250),(205,251),(206,252),(207,253),(208,254),(209,255),(210,256),(211,257),(212,258),(213,259),(214,260),(215,261),(216,262),(217,263),(218,264),(219,265),(220,266),(221,267),(222,268),(223,269),(224,270),(225,271),(226,272),(227,273),(228,274),(229,275),(230,276),(277,346),(278,347),(279,348),(280,349),(281,350),(282,351),(283,352),(284,353),(285,354),(286,355),(287,356),(288,357),(289,358),(290,359),(291,360),(292,361),(293,362),(294,363),(295,364),(296,365),(297,366),(298,367),(299,368),(300,323),(301,324),(302,325),(303,326),(304,327),(305,328),(306,329),(307,330),(308,331),(309,332),(310,333),(311,334),(312,335),(313,336),(314,337),(315,338),(316,339),(317,340),(318,341),(319,342),(320,343),(321,344),(322,345)], [(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)], [(1,231,24,254),(2,276,25,253),(3,275,26,252),(4,274,27,251),(5,273,28,250),(6,272,29,249),(7,271,30,248),(8,270,31,247),(9,269,32,246),(10,268,33,245),(11,267,34,244),(12,266,35,243),(13,265,36,242),(14,264,37,241),(15,263,38,240),(16,262,39,239),(17,261,40,238),(18,260,41,237),(19,259,42,236),(20,258,43,235),(21,257,44,234),(22,256,45,233),(23,255,46,232),(47,203,70,226),(48,202,71,225),(49,201,72,224),(50,200,73,223),(51,199,74,222),(52,198,75,221),(53,197,76,220),(54,196,77,219),(55,195,78,218),(56,194,79,217),(57,193,80,216),(58,192,81,215),(59,191,82,214),(60,190,83,213),(61,189,84,212),(62,188,85,211),(63,187,86,210),(64,186,87,209),(65,185,88,208),(66,230,89,207),(67,229,90,206),(68,228,91,205),(69,227,92,204),(93,323,116,346),(94,368,117,345),(95,367,118,344),(96,366,119,343),(97,365,120,342),(98,364,121,341),(99,363,122,340),(100,362,123,339),(101,361,124,338),(102,360,125,337),(103,359,126,336),(104,358,127,335),(105,357,128,334),(106,356,129,333),(107,355,130,332),(108,354,131,331),(109,353,132,330),(110,352,133,329),(111,351,134,328),(112,350,135,327),(113,349,136,326),(114,348,137,325),(115,347,138,324),(139,318,162,295),(140,317,163,294),(141,316,164,293),(142,315,165,292),(143,314,166,291),(144,313,167,290),(145,312,168,289),(146,311,169,288),(147,310,170,287),(148,309,171,286),(149,308,172,285),(150,307,173,284),(151,306,174,283),(152,305,175,282),(153,304,176,281),(154,303,177,280),(155,302,178,279),(156,301,179,278),(157,300,180,277),(158,299,181,322),(159,298,182,321),(160,297,183,320),(161,296,184,319)]])
104 conjugacy classes
| class | 1 | 2A | ··· | 2G | 4A | ··· | 4H | 23A | ··· | 23K | 46A | ··· | 46BY |
| order | 1 | 2 | ··· | 2 | 4 | ··· | 4 | 23 | ··· | 23 | 46 | ··· | 46 |
| size | 1 | 1 | ··· | 1 | 23 | ··· | 23 | 2 | ··· | 2 | 2 | ··· | 2 |
104 irreducible representations
| dim | 1 | 1 | 1 | 1 | 2 | 2 | 2 |
| type | + | + | + | + | - | + | |
| image | C1 | C2 | C2 | C4 | D23 | Dic23 | D46 |
| kernel | C22×Dic23 | C2×Dic23 | C22×C46 | C2×C46 | C23 | C22 | C22 |
| # reps | 1 | 6 | 1 | 8 | 11 | 44 | 33 |
Matrix representation of C22×Dic23 ►in GL4(𝔽277) generated by
| 276 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 276 | 0 |
| 0 | 0 | 0 | 276 |
| 276 | 0 | 0 | 0 |
| 0 | 276 | 0 | 0 |
| 0 | 0 | 276 | 0 |
| 0 | 0 | 0 | 276 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 276 |
| 0 | 0 | 1 | 77 |
| 1 | 0 | 0 | 0 |
| 0 | 276 | 0 | 0 |
| 0 | 0 | 254 | 186 |
| 0 | 0 | 18 | 23 |
G:=sub<GL(4,GF(277))| [276,0,0,0,0,1,0,0,0,0,276,0,0,0,0,276],[276,0,0,0,0,276,0,0,0,0,276,0,0,0,0,276],[1,0,0,0,0,1,0,0,0,0,0,1,0,0,276,77],[1,0,0,0,0,276,0,0,0,0,254,18,0,0,186,23] >;
C22×Dic23 in GAP, Magma, Sage, TeX
C_2^2\times {\rm Dic}_{23} % in TeX
G:=Group("C2^2xDic23"); // GroupNames label
G:=SmallGroup(368,35);
// by ID
G=gap.SmallGroup(368,35);
# by ID
G:=PCGroup([5,-2,-2,-2,-2,-23,40,8804]);
// Polycyclic
G:=Group<a,b,c,d|a^2=b^2=c^46=1,d^2=c^23,a*b=b*a,a*c=c*a,a*d=d*a,b*c=c*b,b*d=d*b,d*c*d^-1=c^-1>;
// generators/relations