direct product, metacyclic, supersoluble, monomial, A-group, 2-hyperelementary
Aliases: C2×Dic53, C106⋊2C4, C22.D53, C2.2D106, C106.4C22, C53⋊3(C2×C4), (C2×C106).C2, SmallGroup(424,7)
Series: Derived ►Chief ►Lower central ►Upper central
| C53 — C2×Dic53 |
Generators and relations for C2×Dic53
G = < a,b,c | a2=b106=1, c2=b53, ab=ba, ac=ca, cbc-1=b-1 >
Smallest permutation representation of C2×Dic53
►Regular action on 424 points
Generators in S424
(1 167)(2 168)(3 169)(4 170)(5 171)(6 172)(7 173)(8 174)(9 175)(10 176)(11 177)(12 178)(13 179)(14 180)(15 181)(16 182)(17 183)(18 184)(19 185)(20 186)(21 187)(22 188)(23 189)(24 190)(25 191)(26 192)(27 193)(28 194)(29 195)(30 196)(31 197)(32 198)(33 199)(34 200)(35 201)(36 202)(37 203)(38 204)(39 205)(40 206)(41 207)(42 208)(43 209)(44 210)(45 211)(46 212)(47 107)(48 108)(49 109)(50 110)(51 111)(52 112)(53 113)(54 114)(55 115)(56 116)(57 117)(58 118)(59 119)(60 120)(61 121)(62 122)(63 123)(64 124)(65 125)(66 126)(67 127)(68 128)(69 129)(70 130)(71 131)(72 132)(73 133)(74 134)(75 135)(76 136)(77 137)(78 138)(79 139)(80 140)(81 141)(82 142)(83 143)(84 144)(85 145)(86 146)(87 147)(88 148)(89 149)(90 150)(91 151)(92 152)(93 153)(94 154)(95 155)(96 156)(97 157)(98 158)(99 159)(100 160)(101 161)(102 162)(103 163)(104 164)(105 165)(106 166)(213 372)(214 373)(215 374)(216 375)(217 376)(218 377)(219 378)(220 379)(221 380)(222 381)(223 382)(224 383)(225 384)(226 385)(227 386)(228 387)(229 388)(230 389)(231 390)(232 391)(233 392)(234 393)(235 394)(236 395)(237 396)(238 397)(239 398)(240 399)(241 400)(242 401)(243 402)(244 403)(245 404)(246 405)(247 406)(248 407)(249 408)(250 409)(251 410)(252 411)(253 412)(254 413)(255 414)(256 415)(257 416)(258 417)(259 418)(260 419)(261 420)(262 421)(263 422)(264 423)(265 424)(266 319)(267 320)(268 321)(269 322)(270 323)(271 324)(272 325)(273 326)(274 327)(275 328)(276 329)(277 330)(278 331)(279 332)(280 333)(281 334)(282 335)(283 336)(284 337)(285 338)(286 339)(287 340)(288 341)(289 342)(290 343)(291 344)(292 345)(293 346)(294 347)(295 348)(296 349)(297 350)(298 351)(299 352)(300 353)(301 354)(302 355)(303 356)(304 357)(305 358)(306 359)(307 360)(308 361)(309 362)(310 363)(311 364)(312 365)(313 366)(314 367)(315 368)(316 369)(317 370)(318 371)
(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)(319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424)
(1 266 54 213)(2 265 55 318)(3 264 56 317)(4 263 57 316)(5 262 58 315)(6 261 59 314)(7 260 60 313)(8 259 61 312)(9 258 62 311)(10 257 63 310)(11 256 64 309)(12 255 65 308)(13 254 66 307)(14 253 67 306)(15 252 68 305)(16 251 69 304)(17 250 70 303)(18 249 71 302)(19 248 72 301)(20 247 73 300)(21 246 74 299)(22 245 75 298)(23 244 76 297)(24 243 77 296)(25 242 78 295)(26 241 79 294)(27 240 80 293)(28 239 81 292)(29 238 82 291)(30 237 83 290)(31 236 84 289)(32 235 85 288)(33 234 86 287)(34 233 87 286)(35 232 88 285)(36 231 89 284)(37 230 90 283)(38 229 91 282)(39 228 92 281)(40 227 93 280)(41 226 94 279)(42 225 95 278)(43 224 96 277)(44 223 97 276)(45 222 98 275)(46 221 99 274)(47 220 100 273)(48 219 101 272)(49 218 102 271)(50 217 103 270)(51 216 104 269)(52 215 105 268)(53 214 106 267)(107 379 160 326)(108 378 161 325)(109 377 162 324)(110 376 163 323)(111 375 164 322)(112 374 165 321)(113 373 166 320)(114 372 167 319)(115 371 168 424)(116 370 169 423)(117 369 170 422)(118 368 171 421)(119 367 172 420)(120 366 173 419)(121 365 174 418)(122 364 175 417)(123 363 176 416)(124 362 177 415)(125 361 178 414)(126 360 179 413)(127 359 180 412)(128 358 181 411)(129 357 182 410)(130 356 183 409)(131 355 184 408)(132 354 185 407)(133 353 186 406)(134 352 187 405)(135 351 188 404)(136 350 189 403)(137 349 190 402)(138 348 191 401)(139 347 192 400)(140 346 193 399)(141 345 194 398)(142 344 195 397)(143 343 196 396)(144 342 197 395)(145 341 198 394)(146 340 199 393)(147 339 200 392)(148 338 201 391)(149 337 202 390)(150 336 203 389)(151 335 204 388)(152 334 205 387)(153 333 206 386)(154 332 207 385)(155 331 208 384)(156 330 209 383)(157 329 210 382)(158 328 211 381)(159 327 212 380)
G:=sub<Sym(424)| (1,167)(2,168)(3,169)(4,170)(5,171)(6,172)(7,173)(8,174)(9,175)(10,176)(11,177)(12,178)(13,179)(14,180)(15,181)(16,182)(17,183)(18,184)(19,185)(20,186)(21,187)(22,188)(23,189)(24,190)(25,191)(26,192)(27,193)(28,194)(29,195)(30,196)(31,197)(32,198)(33,199)(34,200)(35,201)(36,202)(37,203)(38,204)(39,205)(40,206)(41,207)(42,208)(43,209)(44,210)(45,211)(46,212)(47,107)(48,108)(49,109)(50,110)(51,111)(52,112)(53,113)(54,114)(55,115)(56,116)(57,117)(58,118)(59,119)(60,120)(61,121)(62,122)(63,123)(64,124)(65,125)(66,126)(67,127)(68,128)(69,129)(70,130)(71,131)(72,132)(73,133)(74,134)(75,135)(76,136)(77,137)(78,138)(79,139)(80,140)(81,141)(82,142)(83,143)(84,144)(85,145)(86,146)(87,147)(88,148)(89,149)(90,150)(91,151)(92,152)(93,153)(94,154)(95,155)(96,156)(97,157)(98,158)(99,159)(100,160)(101,161)(102,162)(103,163)(104,164)(105,165)(106,166)(213,372)(214,373)(215,374)(216,375)(217,376)(218,377)(219,378)(220,379)(221,380)(222,381)(223,382)(224,383)(225,384)(226,385)(227,386)(228,387)(229,388)(230,389)(231,390)(232,391)(233,392)(234,393)(235,394)(236,395)(237,396)(238,397)(239,398)(240,399)(241,400)(242,401)(243,402)(244,403)(245,404)(246,405)(247,406)(248,407)(249,408)(250,409)(251,410)(252,411)(253,412)(254,413)(255,414)(256,415)(257,416)(258,417)(259,418)(260,419)(261,420)(262,421)(263,422)(264,423)(265,424)(266,319)(267,320)(268,321)(269,322)(270,323)(271,324)(272,325)(273,326)(274,327)(275,328)(276,329)(277,330)(278,331)(279,332)(280,333)(281,334)(282,335)(283,336)(284,337)(285,338)(286,339)(287,340)(288,341)(289,342)(290,343)(291,344)(292,345)(293,346)(294,347)(295,348)(296,349)(297,350)(298,351)(299,352)(300,353)(301,354)(302,355)(303,356)(304,357)(305,358)(306,359)(307,360)(308,361)(309,362)(310,363)(311,364)(312,365)(313,366)(314,367)(315,368)(316,369)(317,370)(318,371), (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)(319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424), (1,266,54,213)(2,265,55,318)(3,264,56,317)(4,263,57,316)(5,262,58,315)(6,261,59,314)(7,260,60,313)(8,259,61,312)(9,258,62,311)(10,257,63,310)(11,256,64,309)(12,255,65,308)(13,254,66,307)(14,253,67,306)(15,252,68,305)(16,251,69,304)(17,250,70,303)(18,249,71,302)(19,248,72,301)(20,247,73,300)(21,246,74,299)(22,245,75,298)(23,244,76,297)(24,243,77,296)(25,242,78,295)(26,241,79,294)(27,240,80,293)(28,239,81,292)(29,238,82,291)(30,237,83,290)(31,236,84,289)(32,235,85,288)(33,234,86,287)(34,233,87,286)(35,232,88,285)(36,231,89,284)(37,230,90,283)(38,229,91,282)(39,228,92,281)(40,227,93,280)(41,226,94,279)(42,225,95,278)(43,224,96,277)(44,223,97,276)(45,222,98,275)(46,221,99,274)(47,220,100,273)(48,219,101,272)(49,218,102,271)(50,217,103,270)(51,216,104,269)(52,215,105,268)(53,214,106,267)(107,379,160,326)(108,378,161,325)(109,377,162,324)(110,376,163,323)(111,375,164,322)(112,374,165,321)(113,373,166,320)(114,372,167,319)(115,371,168,424)(116,370,169,423)(117,369,170,422)(118,368,171,421)(119,367,172,420)(120,366,173,419)(121,365,174,418)(122,364,175,417)(123,363,176,416)(124,362,177,415)(125,361,178,414)(126,360,179,413)(127,359,180,412)(128,358,181,411)(129,357,182,410)(130,356,183,409)(131,355,184,408)(132,354,185,407)(133,353,186,406)(134,352,187,405)(135,351,188,404)(136,350,189,403)(137,349,190,402)(138,348,191,401)(139,347,192,400)(140,346,193,399)(141,345,194,398)(142,344,195,397)(143,343,196,396)(144,342,197,395)(145,341,198,394)(146,340,199,393)(147,339,200,392)(148,338,201,391)(149,337,202,390)(150,336,203,389)(151,335,204,388)(152,334,205,387)(153,333,206,386)(154,332,207,385)(155,331,208,384)(156,330,209,383)(157,329,210,382)(158,328,211,381)(159,327,212,380)>;
G:=Group( (1,167)(2,168)(3,169)(4,170)(5,171)(6,172)(7,173)(8,174)(9,175)(10,176)(11,177)(12,178)(13,179)(14,180)(15,181)(16,182)(17,183)(18,184)(19,185)(20,186)(21,187)(22,188)(23,189)(24,190)(25,191)(26,192)(27,193)(28,194)(29,195)(30,196)(31,197)(32,198)(33,199)(34,200)(35,201)(36,202)(37,203)(38,204)(39,205)(40,206)(41,207)(42,208)(43,209)(44,210)(45,211)(46,212)(47,107)(48,108)(49,109)(50,110)(51,111)(52,112)(53,113)(54,114)(55,115)(56,116)(57,117)(58,118)(59,119)(60,120)(61,121)(62,122)(63,123)(64,124)(65,125)(66,126)(67,127)(68,128)(69,129)(70,130)(71,131)(72,132)(73,133)(74,134)(75,135)(76,136)(77,137)(78,138)(79,139)(80,140)(81,141)(82,142)(83,143)(84,144)(85,145)(86,146)(87,147)(88,148)(89,149)(90,150)(91,151)(92,152)(93,153)(94,154)(95,155)(96,156)(97,157)(98,158)(99,159)(100,160)(101,161)(102,162)(103,163)(104,164)(105,165)(106,166)(213,372)(214,373)(215,374)(216,375)(217,376)(218,377)(219,378)(220,379)(221,380)(222,381)(223,382)(224,383)(225,384)(226,385)(227,386)(228,387)(229,388)(230,389)(231,390)(232,391)(233,392)(234,393)(235,394)(236,395)(237,396)(238,397)(239,398)(240,399)(241,400)(242,401)(243,402)(244,403)(245,404)(246,405)(247,406)(248,407)(249,408)(250,409)(251,410)(252,411)(253,412)(254,413)(255,414)(256,415)(257,416)(258,417)(259,418)(260,419)(261,420)(262,421)(263,422)(264,423)(265,424)(266,319)(267,320)(268,321)(269,322)(270,323)(271,324)(272,325)(273,326)(274,327)(275,328)(276,329)(277,330)(278,331)(279,332)(280,333)(281,334)(282,335)(283,336)(284,337)(285,338)(286,339)(287,340)(288,341)(289,342)(290,343)(291,344)(292,345)(293,346)(294,347)(295,348)(296,349)(297,350)(298,351)(299,352)(300,353)(301,354)(302,355)(303,356)(304,357)(305,358)(306,359)(307,360)(308,361)(309,362)(310,363)(311,364)(312,365)(313,366)(314,367)(315,368)(316,369)(317,370)(318,371), (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)(319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424), (1,266,54,213)(2,265,55,318)(3,264,56,317)(4,263,57,316)(5,262,58,315)(6,261,59,314)(7,260,60,313)(8,259,61,312)(9,258,62,311)(10,257,63,310)(11,256,64,309)(12,255,65,308)(13,254,66,307)(14,253,67,306)(15,252,68,305)(16,251,69,304)(17,250,70,303)(18,249,71,302)(19,248,72,301)(20,247,73,300)(21,246,74,299)(22,245,75,298)(23,244,76,297)(24,243,77,296)(25,242,78,295)(26,241,79,294)(27,240,80,293)(28,239,81,292)(29,238,82,291)(30,237,83,290)(31,236,84,289)(32,235,85,288)(33,234,86,287)(34,233,87,286)(35,232,88,285)(36,231,89,284)(37,230,90,283)(38,229,91,282)(39,228,92,281)(40,227,93,280)(41,226,94,279)(42,225,95,278)(43,224,96,277)(44,223,97,276)(45,222,98,275)(46,221,99,274)(47,220,100,273)(48,219,101,272)(49,218,102,271)(50,217,103,270)(51,216,104,269)(52,215,105,268)(53,214,106,267)(107,379,160,326)(108,378,161,325)(109,377,162,324)(110,376,163,323)(111,375,164,322)(112,374,165,321)(113,373,166,320)(114,372,167,319)(115,371,168,424)(116,370,169,423)(117,369,170,422)(118,368,171,421)(119,367,172,420)(120,366,173,419)(121,365,174,418)(122,364,175,417)(123,363,176,416)(124,362,177,415)(125,361,178,414)(126,360,179,413)(127,359,180,412)(128,358,181,411)(129,357,182,410)(130,356,183,409)(131,355,184,408)(132,354,185,407)(133,353,186,406)(134,352,187,405)(135,351,188,404)(136,350,189,403)(137,349,190,402)(138,348,191,401)(139,347,192,400)(140,346,193,399)(141,345,194,398)(142,344,195,397)(143,343,196,396)(144,342,197,395)(145,341,198,394)(146,340,199,393)(147,339,200,392)(148,338,201,391)(149,337,202,390)(150,336,203,389)(151,335,204,388)(152,334,205,387)(153,333,206,386)(154,332,207,385)(155,331,208,384)(156,330,209,383)(157,329,210,382)(158,328,211,381)(159,327,212,380) );
G=PermutationGroup([[(1,167),(2,168),(3,169),(4,170),(5,171),(6,172),(7,173),(8,174),(9,175),(10,176),(11,177),(12,178),(13,179),(14,180),(15,181),(16,182),(17,183),(18,184),(19,185),(20,186),(21,187),(22,188),(23,189),(24,190),(25,191),(26,192),(27,193),(28,194),(29,195),(30,196),(31,197),(32,198),(33,199),(34,200),(35,201),(36,202),(37,203),(38,204),(39,205),(40,206),(41,207),(42,208),(43,209),(44,210),(45,211),(46,212),(47,107),(48,108),(49,109),(50,110),(51,111),(52,112),(53,113),(54,114),(55,115),(56,116),(57,117),(58,118),(59,119),(60,120),(61,121),(62,122),(63,123),(64,124),(65,125),(66,126),(67,127),(68,128),(69,129),(70,130),(71,131),(72,132),(73,133),(74,134),(75,135),(76,136),(77,137),(78,138),(79,139),(80,140),(81,141),(82,142),(83,143),(84,144),(85,145),(86,146),(87,147),(88,148),(89,149),(90,150),(91,151),(92,152),(93,153),(94,154),(95,155),(96,156),(97,157),(98,158),(99,159),(100,160),(101,161),(102,162),(103,163),(104,164),(105,165),(106,166),(213,372),(214,373),(215,374),(216,375),(217,376),(218,377),(219,378),(220,379),(221,380),(222,381),(223,382),(224,383),(225,384),(226,385),(227,386),(228,387),(229,388),(230,389),(231,390),(232,391),(233,392),(234,393),(235,394),(236,395),(237,396),(238,397),(239,398),(240,399),(241,400),(242,401),(243,402),(244,403),(245,404),(246,405),(247,406),(248,407),(249,408),(250,409),(251,410),(252,411),(253,412),(254,413),(255,414),(256,415),(257,416),(258,417),(259,418),(260,419),(261,420),(262,421),(263,422),(264,423),(265,424),(266,319),(267,320),(268,321),(269,322),(270,323),(271,324),(272,325),(273,326),(274,327),(275,328),(276,329),(277,330),(278,331),(279,332),(280,333),(281,334),(282,335),(283,336),(284,337),(285,338),(286,339),(287,340),(288,341),(289,342),(290,343),(291,344),(292,345),(293,346),(294,347),(295,348),(296,349),(297,350),(298,351),(299,352),(300,353),(301,354),(302,355),(303,356),(304,357),(305,358),(306,359),(307,360),(308,361),(309,362),(310,363),(311,364),(312,365),(313,366),(314,367),(315,368),(316,369),(317,370),(318,371)], [(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),(319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424)], [(1,266,54,213),(2,265,55,318),(3,264,56,317),(4,263,57,316),(5,262,58,315),(6,261,59,314),(7,260,60,313),(8,259,61,312),(9,258,62,311),(10,257,63,310),(11,256,64,309),(12,255,65,308),(13,254,66,307),(14,253,67,306),(15,252,68,305),(16,251,69,304),(17,250,70,303),(18,249,71,302),(19,248,72,301),(20,247,73,300),(21,246,74,299),(22,245,75,298),(23,244,76,297),(24,243,77,296),(25,242,78,295),(26,241,79,294),(27,240,80,293),(28,239,81,292),(29,238,82,291),(30,237,83,290),(31,236,84,289),(32,235,85,288),(33,234,86,287),(34,233,87,286),(35,232,88,285),(36,231,89,284),(37,230,90,283),(38,229,91,282),(39,228,92,281),(40,227,93,280),(41,226,94,279),(42,225,95,278),(43,224,96,277),(44,223,97,276),(45,222,98,275),(46,221,99,274),(47,220,100,273),(48,219,101,272),(49,218,102,271),(50,217,103,270),(51,216,104,269),(52,215,105,268),(53,214,106,267),(107,379,160,326),(108,378,161,325),(109,377,162,324),(110,376,163,323),(111,375,164,322),(112,374,165,321),(113,373,166,320),(114,372,167,319),(115,371,168,424),(116,370,169,423),(117,369,170,422),(118,368,171,421),(119,367,172,420),(120,366,173,419),(121,365,174,418),(122,364,175,417),(123,363,176,416),(124,362,177,415),(125,361,178,414),(126,360,179,413),(127,359,180,412),(128,358,181,411),(129,357,182,410),(130,356,183,409),(131,355,184,408),(132,354,185,407),(133,353,186,406),(134,352,187,405),(135,351,188,404),(136,350,189,403),(137,349,190,402),(138,348,191,401),(139,347,192,400),(140,346,193,399),(141,345,194,398),(142,344,195,397),(143,343,196,396),(144,342,197,395),(145,341,198,394),(146,340,199,393),(147,339,200,392),(148,338,201,391),(149,337,202,390),(150,336,203,389),(151,335,204,388),(152,334,205,387),(153,333,206,386),(154,332,207,385),(155,331,208,384),(156,330,209,383),(157,329,210,382),(158,328,211,381),(159,327,212,380)]])
112 conjugacy classes
| class | 1 | 2A | 2B | 2C | 4A | 4B | 4C | 4D | 53A | ··· | 53Z | 106A | ··· | 106BZ |
| order | 1 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 53 | ··· | 53 | 106 | ··· | 106 |
| size | 1 | 1 | 1 | 1 | 53 | 53 | 53 | 53 | 2 | ··· | 2 | 2 | ··· | 2 |
112 irreducible representations
| dim | 1 | 1 | 1 | 1 | 2 | 2 | 2 |
| type | + | + | + | + | - | + | |
| image | C1 | C2 | C2 | C4 | D53 | Dic53 | D106 |
| kernel | C2×Dic53 | Dic53 | C2×C106 | C106 | C22 | C2 | C2 |
| # reps | 1 | 2 | 1 | 4 | 26 | 52 | 26 |
Matrix representation of C2×Dic53 ►in GL4(𝔽1061) generated by
| 1 | 0 | 0 | 0 |
| 0 | 1060 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 1060 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 1 |
| 0 | 0 | 1060 | 786 |
| 103 | 0 | 0 | 0 |
| 0 | 1060 | 0 | 0 |
| 0 | 0 | 704 | 755 |
| 0 | 0 | 257 | 357 |
G:=sub<GL(4,GF(1061))| [1,0,0,0,0,1060,0,0,0,0,1,0,0,0,0,1],[1060,0,0,0,0,1,0,0,0,0,0,1060,0,0,1,786],[103,0,0,0,0,1060,0,0,0,0,704,257,0,0,755,357] >;
C2×Dic53 in GAP, Magma, Sage, TeX
C_2\times {\rm Dic}_{53} % in TeX
G:=Group("C2xDic53"); // GroupNames label
G:=SmallGroup(424,7);
// by ID
G=gap.SmallGroup(424,7);
# by ID
G:=PCGroup([4,-2,-2,-2,-53,16,6659]);
// Polycyclic
G:=Group<a,b,c|a^2=b^106=1,c^2=b^53,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations
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