direct product, metacyclic, supersoluble, monomial, A-group, 2-hyperelementary
Aliases: C2×Dic49, C98⋊C4, C2.2D98, C22.D49, C14.9D14, C98.4C22, C14.2Dic7, C49⋊2(C2×C4), (C2×C98).C2, C7.(C2×Dic7), (C2×C14).1D7, SmallGroup(392,6)
Series: Derived ►Chief ►Lower central ►Upper central
| C49 — C2×Dic49 |
Generators and relations for C2×Dic49
G = < a,b,c | a2=b98=1, c2=b49, ab=ba, ac=ca, cbc-1=b-1 >
Smallest permutation representation of C2×Dic49
►Regular action on 392 points
Generators in S392
(1 120)(2 121)(3 122)(4 123)(5 124)(6 125)(7 126)(8 127)(9 128)(10 129)(11 130)(12 131)(13 132)(14 133)(15 134)(16 135)(17 136)(18 137)(19 138)(20 139)(21 140)(22 141)(23 142)(24 143)(25 144)(26 145)(27 146)(28 147)(29 148)(30 149)(31 150)(32 151)(33 152)(34 153)(35 154)(36 155)(37 156)(38 157)(39 158)(40 159)(41 160)(42 161)(43 162)(44 163)(45 164)(46 165)(47 166)(48 167)(49 168)(50 169)(51 170)(52 171)(53 172)(54 173)(55 174)(56 175)(57 176)(58 177)(59 178)(60 179)(61 180)(62 181)(63 182)(64 183)(65 184)(66 185)(67 186)(68 187)(69 188)(70 189)(71 190)(72 191)(73 192)(74 193)(75 194)(76 195)(77 196)(78 99)(79 100)(80 101)(81 102)(82 103)(83 104)(84 105)(85 106)(86 107)(87 108)(88 109)(89 110)(90 111)(91 112)(92 113)(93 114)(94 115)(95 116)(96 117)(97 118)(98 119)(197 362)(198 363)(199 364)(200 365)(201 366)(202 367)(203 368)(204 369)(205 370)(206 371)(207 372)(208 373)(209 374)(210 375)(211 376)(212 377)(213 378)(214 379)(215 380)(216 381)(217 382)(218 383)(219 384)(220 385)(221 386)(222 387)(223 388)(224 389)(225 390)(226 391)(227 392)(228 295)(229 296)(230 297)(231 298)(232 299)(233 300)(234 301)(235 302)(236 303)(237 304)(238 305)(239 306)(240 307)(241 308)(242 309)(243 310)(244 311)(245 312)(246 313)(247 314)(248 315)(249 316)(250 317)(251 318)(252 319)(253 320)(254 321)(255 322)(256 323)(257 324)(258 325)(259 326)(260 327)(261 328)(262 329)(263 330)(264 331)(265 332)(266 333)(267 334)(268 335)(269 336)(270 337)(271 338)(272 339)(273 340)(274 341)(275 342)(276 343)(277 344)(278 345)(279 346)(280 347)(281 348)(282 349)(283 350)(284 351)(285 352)(286 353)(287 354)(288 355)(289 356)(290 357)(291 358)(292 359)(293 360)(294 361)
(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)
(1 290 50 241)(2 289 51 240)(3 288 52 239)(4 287 53 238)(5 286 54 237)(6 285 55 236)(7 284 56 235)(8 283 57 234)(9 282 58 233)(10 281 59 232)(11 280 60 231)(12 279 61 230)(13 278 62 229)(14 277 63 228)(15 276 64 227)(16 275 65 226)(17 274 66 225)(18 273 67 224)(19 272 68 223)(20 271 69 222)(21 270 70 221)(22 269 71 220)(23 268 72 219)(24 267 73 218)(25 266 74 217)(26 265 75 216)(27 264 76 215)(28 263 77 214)(29 262 78 213)(30 261 79 212)(31 260 80 211)(32 259 81 210)(33 258 82 209)(34 257 83 208)(35 256 84 207)(36 255 85 206)(37 254 86 205)(38 253 87 204)(39 252 88 203)(40 251 89 202)(41 250 90 201)(42 249 91 200)(43 248 92 199)(44 247 93 198)(45 246 94 197)(46 245 95 294)(47 244 96 293)(48 243 97 292)(49 242 98 291)(99 378 148 329)(100 377 149 328)(101 376 150 327)(102 375 151 326)(103 374 152 325)(104 373 153 324)(105 372 154 323)(106 371 155 322)(107 370 156 321)(108 369 157 320)(109 368 158 319)(110 367 159 318)(111 366 160 317)(112 365 161 316)(113 364 162 315)(114 363 163 314)(115 362 164 313)(116 361 165 312)(117 360 166 311)(118 359 167 310)(119 358 168 309)(120 357 169 308)(121 356 170 307)(122 355 171 306)(123 354 172 305)(124 353 173 304)(125 352 174 303)(126 351 175 302)(127 350 176 301)(128 349 177 300)(129 348 178 299)(130 347 179 298)(131 346 180 297)(132 345 181 296)(133 344 182 295)(134 343 183 392)(135 342 184 391)(136 341 185 390)(137 340 186 389)(138 339 187 388)(139 338 188 387)(140 337 189 386)(141 336 190 385)(142 335 191 384)(143 334 192 383)(144 333 193 382)(145 332 194 381)(146 331 195 380)(147 330 196 379)
G:=sub<Sym(392)| (1,120)(2,121)(3,122)(4,123)(5,124)(6,125)(7,126)(8,127)(9,128)(10,129)(11,130)(12,131)(13,132)(14,133)(15,134)(16,135)(17,136)(18,137)(19,138)(20,139)(21,140)(22,141)(23,142)(24,143)(25,144)(26,145)(27,146)(28,147)(29,148)(30,149)(31,150)(32,151)(33,152)(34,153)(35,154)(36,155)(37,156)(38,157)(39,158)(40,159)(41,160)(42,161)(43,162)(44,163)(45,164)(46,165)(47,166)(48,167)(49,168)(50,169)(51,170)(52,171)(53,172)(54,173)(55,174)(56,175)(57,176)(58,177)(59,178)(60,179)(61,180)(62,181)(63,182)(64,183)(65,184)(66,185)(67,186)(68,187)(69,188)(70,189)(71,190)(72,191)(73,192)(74,193)(75,194)(76,195)(77,196)(78,99)(79,100)(80,101)(81,102)(82,103)(83,104)(84,105)(85,106)(86,107)(87,108)(88,109)(89,110)(90,111)(91,112)(92,113)(93,114)(94,115)(95,116)(96,117)(97,118)(98,119)(197,362)(198,363)(199,364)(200,365)(201,366)(202,367)(203,368)(204,369)(205,370)(206,371)(207,372)(208,373)(209,374)(210,375)(211,376)(212,377)(213,378)(214,379)(215,380)(216,381)(217,382)(218,383)(219,384)(220,385)(221,386)(222,387)(223,388)(224,389)(225,390)(226,391)(227,392)(228,295)(229,296)(230,297)(231,298)(232,299)(233,300)(234,301)(235,302)(236,303)(237,304)(238,305)(239,306)(240,307)(241,308)(242,309)(243,310)(244,311)(245,312)(246,313)(247,314)(248,315)(249,316)(250,317)(251,318)(252,319)(253,320)(254,321)(255,322)(256,323)(257,324)(258,325)(259,326)(260,327)(261,328)(262,329)(263,330)(264,331)(265,332)(266,333)(267,334)(268,335)(269,336)(270,337)(271,338)(272,339)(273,340)(274,341)(275,342)(276,343)(277,344)(278,345)(279,346)(280,347)(281,348)(282,349)(283,350)(284,351)(285,352)(286,353)(287,354)(288,355)(289,356)(290,357)(291,358)(292,359)(293,360)(294,361), (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), (1,290,50,241)(2,289,51,240)(3,288,52,239)(4,287,53,238)(5,286,54,237)(6,285,55,236)(7,284,56,235)(8,283,57,234)(9,282,58,233)(10,281,59,232)(11,280,60,231)(12,279,61,230)(13,278,62,229)(14,277,63,228)(15,276,64,227)(16,275,65,226)(17,274,66,225)(18,273,67,224)(19,272,68,223)(20,271,69,222)(21,270,70,221)(22,269,71,220)(23,268,72,219)(24,267,73,218)(25,266,74,217)(26,265,75,216)(27,264,76,215)(28,263,77,214)(29,262,78,213)(30,261,79,212)(31,260,80,211)(32,259,81,210)(33,258,82,209)(34,257,83,208)(35,256,84,207)(36,255,85,206)(37,254,86,205)(38,253,87,204)(39,252,88,203)(40,251,89,202)(41,250,90,201)(42,249,91,200)(43,248,92,199)(44,247,93,198)(45,246,94,197)(46,245,95,294)(47,244,96,293)(48,243,97,292)(49,242,98,291)(99,378,148,329)(100,377,149,328)(101,376,150,327)(102,375,151,326)(103,374,152,325)(104,373,153,324)(105,372,154,323)(106,371,155,322)(107,370,156,321)(108,369,157,320)(109,368,158,319)(110,367,159,318)(111,366,160,317)(112,365,161,316)(113,364,162,315)(114,363,163,314)(115,362,164,313)(116,361,165,312)(117,360,166,311)(118,359,167,310)(119,358,168,309)(120,357,169,308)(121,356,170,307)(122,355,171,306)(123,354,172,305)(124,353,173,304)(125,352,174,303)(126,351,175,302)(127,350,176,301)(128,349,177,300)(129,348,178,299)(130,347,179,298)(131,346,180,297)(132,345,181,296)(133,344,182,295)(134,343,183,392)(135,342,184,391)(136,341,185,390)(137,340,186,389)(138,339,187,388)(139,338,188,387)(140,337,189,386)(141,336,190,385)(142,335,191,384)(143,334,192,383)(144,333,193,382)(145,332,194,381)(146,331,195,380)(147,330,196,379)>;
G:=Group( (1,120)(2,121)(3,122)(4,123)(5,124)(6,125)(7,126)(8,127)(9,128)(10,129)(11,130)(12,131)(13,132)(14,133)(15,134)(16,135)(17,136)(18,137)(19,138)(20,139)(21,140)(22,141)(23,142)(24,143)(25,144)(26,145)(27,146)(28,147)(29,148)(30,149)(31,150)(32,151)(33,152)(34,153)(35,154)(36,155)(37,156)(38,157)(39,158)(40,159)(41,160)(42,161)(43,162)(44,163)(45,164)(46,165)(47,166)(48,167)(49,168)(50,169)(51,170)(52,171)(53,172)(54,173)(55,174)(56,175)(57,176)(58,177)(59,178)(60,179)(61,180)(62,181)(63,182)(64,183)(65,184)(66,185)(67,186)(68,187)(69,188)(70,189)(71,190)(72,191)(73,192)(74,193)(75,194)(76,195)(77,196)(78,99)(79,100)(80,101)(81,102)(82,103)(83,104)(84,105)(85,106)(86,107)(87,108)(88,109)(89,110)(90,111)(91,112)(92,113)(93,114)(94,115)(95,116)(96,117)(97,118)(98,119)(197,362)(198,363)(199,364)(200,365)(201,366)(202,367)(203,368)(204,369)(205,370)(206,371)(207,372)(208,373)(209,374)(210,375)(211,376)(212,377)(213,378)(214,379)(215,380)(216,381)(217,382)(218,383)(219,384)(220,385)(221,386)(222,387)(223,388)(224,389)(225,390)(226,391)(227,392)(228,295)(229,296)(230,297)(231,298)(232,299)(233,300)(234,301)(235,302)(236,303)(237,304)(238,305)(239,306)(240,307)(241,308)(242,309)(243,310)(244,311)(245,312)(246,313)(247,314)(248,315)(249,316)(250,317)(251,318)(252,319)(253,320)(254,321)(255,322)(256,323)(257,324)(258,325)(259,326)(260,327)(261,328)(262,329)(263,330)(264,331)(265,332)(266,333)(267,334)(268,335)(269,336)(270,337)(271,338)(272,339)(273,340)(274,341)(275,342)(276,343)(277,344)(278,345)(279,346)(280,347)(281,348)(282,349)(283,350)(284,351)(285,352)(286,353)(287,354)(288,355)(289,356)(290,357)(291,358)(292,359)(293,360)(294,361), (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), (1,290,50,241)(2,289,51,240)(3,288,52,239)(4,287,53,238)(5,286,54,237)(6,285,55,236)(7,284,56,235)(8,283,57,234)(9,282,58,233)(10,281,59,232)(11,280,60,231)(12,279,61,230)(13,278,62,229)(14,277,63,228)(15,276,64,227)(16,275,65,226)(17,274,66,225)(18,273,67,224)(19,272,68,223)(20,271,69,222)(21,270,70,221)(22,269,71,220)(23,268,72,219)(24,267,73,218)(25,266,74,217)(26,265,75,216)(27,264,76,215)(28,263,77,214)(29,262,78,213)(30,261,79,212)(31,260,80,211)(32,259,81,210)(33,258,82,209)(34,257,83,208)(35,256,84,207)(36,255,85,206)(37,254,86,205)(38,253,87,204)(39,252,88,203)(40,251,89,202)(41,250,90,201)(42,249,91,200)(43,248,92,199)(44,247,93,198)(45,246,94,197)(46,245,95,294)(47,244,96,293)(48,243,97,292)(49,242,98,291)(99,378,148,329)(100,377,149,328)(101,376,150,327)(102,375,151,326)(103,374,152,325)(104,373,153,324)(105,372,154,323)(106,371,155,322)(107,370,156,321)(108,369,157,320)(109,368,158,319)(110,367,159,318)(111,366,160,317)(112,365,161,316)(113,364,162,315)(114,363,163,314)(115,362,164,313)(116,361,165,312)(117,360,166,311)(118,359,167,310)(119,358,168,309)(120,357,169,308)(121,356,170,307)(122,355,171,306)(123,354,172,305)(124,353,173,304)(125,352,174,303)(126,351,175,302)(127,350,176,301)(128,349,177,300)(129,348,178,299)(130,347,179,298)(131,346,180,297)(132,345,181,296)(133,344,182,295)(134,343,183,392)(135,342,184,391)(136,341,185,390)(137,340,186,389)(138,339,187,388)(139,338,188,387)(140,337,189,386)(141,336,190,385)(142,335,191,384)(143,334,192,383)(144,333,193,382)(145,332,194,381)(146,331,195,380)(147,330,196,379) );
G=PermutationGroup([[(1,120),(2,121),(3,122),(4,123),(5,124),(6,125),(7,126),(8,127),(9,128),(10,129),(11,130),(12,131),(13,132),(14,133),(15,134),(16,135),(17,136),(18,137),(19,138),(20,139),(21,140),(22,141),(23,142),(24,143),(25,144),(26,145),(27,146),(28,147),(29,148),(30,149),(31,150),(32,151),(33,152),(34,153),(35,154),(36,155),(37,156),(38,157),(39,158),(40,159),(41,160),(42,161),(43,162),(44,163),(45,164),(46,165),(47,166),(48,167),(49,168),(50,169),(51,170),(52,171),(53,172),(54,173),(55,174),(56,175),(57,176),(58,177),(59,178),(60,179),(61,180),(62,181),(63,182),(64,183),(65,184),(66,185),(67,186),(68,187),(69,188),(70,189),(71,190),(72,191),(73,192),(74,193),(75,194),(76,195),(77,196),(78,99),(79,100),(80,101),(81,102),(82,103),(83,104),(84,105),(85,106),(86,107),(87,108),(88,109),(89,110),(90,111),(91,112),(92,113),(93,114),(94,115),(95,116),(96,117),(97,118),(98,119),(197,362),(198,363),(199,364),(200,365),(201,366),(202,367),(203,368),(204,369),(205,370),(206,371),(207,372),(208,373),(209,374),(210,375),(211,376),(212,377),(213,378),(214,379),(215,380),(216,381),(217,382),(218,383),(219,384),(220,385),(221,386),(222,387),(223,388),(224,389),(225,390),(226,391),(227,392),(228,295),(229,296),(230,297),(231,298),(232,299),(233,300),(234,301),(235,302),(236,303),(237,304),(238,305),(239,306),(240,307),(241,308),(242,309),(243,310),(244,311),(245,312),(246,313),(247,314),(248,315),(249,316),(250,317),(251,318),(252,319),(253,320),(254,321),(255,322),(256,323),(257,324),(258,325),(259,326),(260,327),(261,328),(262,329),(263,330),(264,331),(265,332),(266,333),(267,334),(268,335),(269,336),(270,337),(271,338),(272,339),(273,340),(274,341),(275,342),(276,343),(277,344),(278,345),(279,346),(280,347),(281,348),(282,349),(283,350),(284,351),(285,352),(286,353),(287,354),(288,355),(289,356),(290,357),(291,358),(292,359),(293,360),(294,361)], [(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)], [(1,290,50,241),(2,289,51,240),(3,288,52,239),(4,287,53,238),(5,286,54,237),(6,285,55,236),(7,284,56,235),(8,283,57,234),(9,282,58,233),(10,281,59,232),(11,280,60,231),(12,279,61,230),(13,278,62,229),(14,277,63,228),(15,276,64,227),(16,275,65,226),(17,274,66,225),(18,273,67,224),(19,272,68,223),(20,271,69,222),(21,270,70,221),(22,269,71,220),(23,268,72,219),(24,267,73,218),(25,266,74,217),(26,265,75,216),(27,264,76,215),(28,263,77,214),(29,262,78,213),(30,261,79,212),(31,260,80,211),(32,259,81,210),(33,258,82,209),(34,257,83,208),(35,256,84,207),(36,255,85,206),(37,254,86,205),(38,253,87,204),(39,252,88,203),(40,251,89,202),(41,250,90,201),(42,249,91,200),(43,248,92,199),(44,247,93,198),(45,246,94,197),(46,245,95,294),(47,244,96,293),(48,243,97,292),(49,242,98,291),(99,378,148,329),(100,377,149,328),(101,376,150,327),(102,375,151,326),(103,374,152,325),(104,373,153,324),(105,372,154,323),(106,371,155,322),(107,370,156,321),(108,369,157,320),(109,368,158,319),(110,367,159,318),(111,366,160,317),(112,365,161,316),(113,364,162,315),(114,363,163,314),(115,362,164,313),(116,361,165,312),(117,360,166,311),(118,359,167,310),(119,358,168,309),(120,357,169,308),(121,356,170,307),(122,355,171,306),(123,354,172,305),(124,353,173,304),(125,352,174,303),(126,351,175,302),(127,350,176,301),(128,349,177,300),(129,348,178,299),(130,347,179,298),(131,346,180,297),(132,345,181,296),(133,344,182,295),(134,343,183,392),(135,342,184,391),(136,341,185,390),(137,340,186,389),(138,339,187,388),(139,338,188,387),(140,337,189,386),(141,336,190,385),(142,335,191,384),(143,334,192,383),(144,333,193,382),(145,332,194,381),(146,331,195,380),(147,330,196,379)]])
104 conjugacy classes
| class | 1 | 2A | 2B | 2C | 4A | 4B | 4C | 4D | 7A | 7B | 7C | 14A | ··· | 14I | 49A | ··· | 49U | 98A | ··· | 98BK |
| order | 1 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 49 | ··· | 49 | 98 | ··· | 98 |
| size | 1 | 1 | 1 | 1 | 49 | 49 | 49 | 49 | 2 | 2 | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
104 irreducible representations
| dim | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | - | + | + | - | + | |
| image | C1 | C2 | C2 | C4 | D7 | Dic7 | D14 | D49 | Dic49 | D98 |
| kernel | C2×Dic49 | Dic49 | C2×C98 | C98 | C2×C14 | C14 | C14 | C22 | C2 | C2 |
| # reps | 1 | 2 | 1 | 4 | 3 | 6 | 3 | 21 | 42 | 21 |
Matrix representation of C2×Dic49 ►in GL5(𝔽197)
| 196 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 196 | 0 | 0 |
| 0 | 1 | 39 | 0 | 0 |
| 0 | 0 | 0 | 99 | 44 |
| 0 | 0 | 0 | 52 | 47 |
| 196 | 0 | 0 | 0 | 0 |
| 0 | 104 | 186 | 0 | 0 |
| 0 | 70 | 93 | 0 | 0 |
| 0 | 0 | 0 | 114 | 164 |
| 0 | 0 | 0 | 155 | 83 |
G:=sub<GL(5,GF(197))| [196,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1],[1,0,0,0,0,0,0,1,0,0,0,196,39,0,0,0,0,0,99,52,0,0,0,44,47],[196,0,0,0,0,0,104,70,0,0,0,186,93,0,0,0,0,0,114,155,0,0,0,164,83] >;
C2×Dic49 in GAP, Magma, Sage, TeX
C_2\times {\rm Dic}_{49} % in TeX
G:=Group("C2xDic49"); // GroupNames label
G:=SmallGroup(392,6);
// by ID
G=gap.SmallGroup(392,6);
# by ID
G:=PCGroup([5,-2,-2,-2,-7,-7,20,2083,858,8404]);
// Polycyclic
G:=Group<a,b,c|a^2=b^98=1,c^2=b^49,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations
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