Copied to
clipboard

G = C2×C142order 392 = 23·72

Abelian group of type [2,14,14]

direct product, abelian, monomial

Aliases: C2×C142, SmallGroup(392,44)

Series: Derived Chief Lower central Upper central

C1 — C2×C142
C1C7C72C7×C14C142 — C2×C142
C1 — C2×C142
C1 — C2×C142

Generators and relations for C2×C142
 G = < a,b,c | a2=b14=c14=1, ab=ba, ac=ca, bc=cb >

Subgroups: 160, all normal (4 characteristic)
C1, C2 [×7], C22 [×7], C7 [×8], C23, C14 [×56], C2×C14 [×56], C72, C22×C14 [×8], C7×C14 [×7], C142 [×7], C2×C142
Quotients: C1, C2 [×7], C22 [×7], C7 [×8], C23, C14 [×56], C2×C14 [×56], C72, C22×C14 [×8], C7×C14 [×7], C142 [×7], C2×C142

Smallest permutation representation of C2×C142
Regular action on 392 points
Generators in S392
(1 216)(2 217)(3 218)(4 219)(5 220)(6 221)(7 222)(8 223)(9 224)(10 211)(11 212)(12 213)(13 214)(14 215)(15 119)(16 120)(17 121)(18 122)(19 123)(20 124)(21 125)(22 126)(23 113)(24 114)(25 115)(26 116)(27 117)(28 118)(29 342)(30 343)(31 344)(32 345)(33 346)(34 347)(35 348)(36 349)(37 350)(38 337)(39 338)(40 339)(41 340)(42 341)(43 60)(44 61)(45 62)(46 63)(47 64)(48 65)(49 66)(50 67)(51 68)(52 69)(53 70)(54 57)(55 58)(56 59)(71 150)(72 151)(73 152)(74 153)(75 154)(76 141)(77 142)(78 143)(79 144)(80 145)(81 146)(82 147)(83 148)(84 149)(85 325)(86 326)(87 327)(88 328)(89 329)(90 330)(91 331)(92 332)(93 333)(94 334)(95 335)(96 336)(97 323)(98 324)(99 206)(100 207)(101 208)(102 209)(103 210)(104 197)(105 198)(106 199)(107 200)(108 201)(109 202)(110 203)(111 204)(112 205)(127 164)(128 165)(129 166)(130 167)(131 168)(132 155)(133 156)(134 157)(135 158)(136 159)(137 160)(138 161)(139 162)(140 163)(169 193)(170 194)(171 195)(172 196)(173 183)(174 184)(175 185)(176 186)(177 187)(178 188)(179 189)(180 190)(181 191)(182 192)(225 320)(226 321)(227 322)(228 309)(229 310)(230 311)(231 312)(232 313)(233 314)(234 315)(235 316)(236 317)(237 318)(238 319)(239 359)(240 360)(241 361)(242 362)(243 363)(244 364)(245 351)(246 352)(247 353)(248 354)(249 355)(250 356)(251 357)(252 358)(253 379)(254 380)(255 381)(256 382)(257 383)(258 384)(259 385)(260 386)(261 387)(262 388)(263 389)(264 390)(265 391)(266 392)(267 298)(268 299)(269 300)(270 301)(271 302)(272 303)(273 304)(274 305)(275 306)(276 307)(277 308)(278 295)(279 296)(280 297)(281 371)(282 372)(283 373)(284 374)(285 375)(286 376)(287 377)(288 378)(289 365)(290 366)(291 367)(292 368)(293 369)(294 370)
(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)
(1 329 359 171 235 20 209 379 136 282 42 70 267 149)(2 330 360 172 236 21 210 380 137 283 29 57 268 150)(3 331 361 173 237 22 197 381 138 284 30 58 269 151)(4 332 362 174 238 23 198 382 139 285 31 59 270 152)(5 333 363 175 225 24 199 383 140 286 32 60 271 153)(6 334 364 176 226 25 200 384 127 287 33 61 272 154)(7 335 351 177 227 26 201 385 128 288 34 62 273 141)(8 336 352 178 228 27 202 386 129 289 35 63 274 142)(9 323 353 179 229 28 203 387 130 290 36 64 275 143)(10 324 354 180 230 15 204 388 131 291 37 65 276 144)(11 325 355 181 231 16 205 389 132 292 38 66 277 145)(12 326 356 182 232 17 206 390 133 293 39 67 278 146)(13 327 357 169 233 18 207 391 134 294 40 68 279 147)(14 328 358 170 234 19 208 392 135 281 41 69 280 148)(43 302 74 220 93 243 185 320 114 106 257 163 376 345)(44 303 75 221 94 244 186 321 115 107 258 164 377 346)(45 304 76 222 95 245 187 322 116 108 259 165 378 347)(46 305 77 223 96 246 188 309 117 109 260 166 365 348)(47 306 78 224 97 247 189 310 118 110 261 167 366 349)(48 307 79 211 98 248 190 311 119 111 262 168 367 350)(49 308 80 212 85 249 191 312 120 112 263 155 368 337)(50 295 81 213 86 250 192 313 121 99 264 156 369 338)(51 296 82 214 87 251 193 314 122 100 265 157 370 339)(52 297 83 215 88 252 194 315 123 101 266 158 371 340)(53 298 84 216 89 239 195 316 124 102 253 159 372 341)(54 299 71 217 90 240 196 317 125 103 254 160 373 342)(55 300 72 218 91 241 183 318 126 104 255 161 374 343)(56 301 73 219 92 242 184 319 113 105 256 162 375 344)

G:=sub<Sym(392)| (1,216)(2,217)(3,218)(4,219)(5,220)(6,221)(7,222)(8,223)(9,224)(10,211)(11,212)(12,213)(13,214)(14,215)(15,119)(16,120)(17,121)(18,122)(19,123)(20,124)(21,125)(22,126)(23,113)(24,114)(25,115)(26,116)(27,117)(28,118)(29,342)(30,343)(31,344)(32,345)(33,346)(34,347)(35,348)(36,349)(37,350)(38,337)(39,338)(40,339)(41,340)(42,341)(43,60)(44,61)(45,62)(46,63)(47,64)(48,65)(49,66)(50,67)(51,68)(52,69)(53,70)(54,57)(55,58)(56,59)(71,150)(72,151)(73,152)(74,153)(75,154)(76,141)(77,142)(78,143)(79,144)(80,145)(81,146)(82,147)(83,148)(84,149)(85,325)(86,326)(87,327)(88,328)(89,329)(90,330)(91,331)(92,332)(93,333)(94,334)(95,335)(96,336)(97,323)(98,324)(99,206)(100,207)(101,208)(102,209)(103,210)(104,197)(105,198)(106,199)(107,200)(108,201)(109,202)(110,203)(111,204)(112,205)(127,164)(128,165)(129,166)(130,167)(131,168)(132,155)(133,156)(134,157)(135,158)(136,159)(137,160)(138,161)(139,162)(140,163)(169,193)(170,194)(171,195)(172,196)(173,183)(174,184)(175,185)(176,186)(177,187)(178,188)(179,189)(180,190)(181,191)(182,192)(225,320)(226,321)(227,322)(228,309)(229,310)(230,311)(231,312)(232,313)(233,314)(234,315)(235,316)(236,317)(237,318)(238,319)(239,359)(240,360)(241,361)(242,362)(243,363)(244,364)(245,351)(246,352)(247,353)(248,354)(249,355)(250,356)(251,357)(252,358)(253,379)(254,380)(255,381)(256,382)(257,383)(258,384)(259,385)(260,386)(261,387)(262,388)(263,389)(264,390)(265,391)(266,392)(267,298)(268,299)(269,300)(270,301)(271,302)(272,303)(273,304)(274,305)(275,306)(276,307)(277,308)(278,295)(279,296)(280,297)(281,371)(282,372)(283,373)(284,374)(285,375)(286,376)(287,377)(288,378)(289,365)(290,366)(291,367)(292,368)(293,369)(294,370), (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), (1,329,359,171,235,20,209,379,136,282,42,70,267,149)(2,330,360,172,236,21,210,380,137,283,29,57,268,150)(3,331,361,173,237,22,197,381,138,284,30,58,269,151)(4,332,362,174,238,23,198,382,139,285,31,59,270,152)(5,333,363,175,225,24,199,383,140,286,32,60,271,153)(6,334,364,176,226,25,200,384,127,287,33,61,272,154)(7,335,351,177,227,26,201,385,128,288,34,62,273,141)(8,336,352,178,228,27,202,386,129,289,35,63,274,142)(9,323,353,179,229,28,203,387,130,290,36,64,275,143)(10,324,354,180,230,15,204,388,131,291,37,65,276,144)(11,325,355,181,231,16,205,389,132,292,38,66,277,145)(12,326,356,182,232,17,206,390,133,293,39,67,278,146)(13,327,357,169,233,18,207,391,134,294,40,68,279,147)(14,328,358,170,234,19,208,392,135,281,41,69,280,148)(43,302,74,220,93,243,185,320,114,106,257,163,376,345)(44,303,75,221,94,244,186,321,115,107,258,164,377,346)(45,304,76,222,95,245,187,322,116,108,259,165,378,347)(46,305,77,223,96,246,188,309,117,109,260,166,365,348)(47,306,78,224,97,247,189,310,118,110,261,167,366,349)(48,307,79,211,98,248,190,311,119,111,262,168,367,350)(49,308,80,212,85,249,191,312,120,112,263,155,368,337)(50,295,81,213,86,250,192,313,121,99,264,156,369,338)(51,296,82,214,87,251,193,314,122,100,265,157,370,339)(52,297,83,215,88,252,194,315,123,101,266,158,371,340)(53,298,84,216,89,239,195,316,124,102,253,159,372,341)(54,299,71,217,90,240,196,317,125,103,254,160,373,342)(55,300,72,218,91,241,183,318,126,104,255,161,374,343)(56,301,73,219,92,242,184,319,113,105,256,162,375,344)>;

G:=Group( (1,216)(2,217)(3,218)(4,219)(5,220)(6,221)(7,222)(8,223)(9,224)(10,211)(11,212)(12,213)(13,214)(14,215)(15,119)(16,120)(17,121)(18,122)(19,123)(20,124)(21,125)(22,126)(23,113)(24,114)(25,115)(26,116)(27,117)(28,118)(29,342)(30,343)(31,344)(32,345)(33,346)(34,347)(35,348)(36,349)(37,350)(38,337)(39,338)(40,339)(41,340)(42,341)(43,60)(44,61)(45,62)(46,63)(47,64)(48,65)(49,66)(50,67)(51,68)(52,69)(53,70)(54,57)(55,58)(56,59)(71,150)(72,151)(73,152)(74,153)(75,154)(76,141)(77,142)(78,143)(79,144)(80,145)(81,146)(82,147)(83,148)(84,149)(85,325)(86,326)(87,327)(88,328)(89,329)(90,330)(91,331)(92,332)(93,333)(94,334)(95,335)(96,336)(97,323)(98,324)(99,206)(100,207)(101,208)(102,209)(103,210)(104,197)(105,198)(106,199)(107,200)(108,201)(109,202)(110,203)(111,204)(112,205)(127,164)(128,165)(129,166)(130,167)(131,168)(132,155)(133,156)(134,157)(135,158)(136,159)(137,160)(138,161)(139,162)(140,163)(169,193)(170,194)(171,195)(172,196)(173,183)(174,184)(175,185)(176,186)(177,187)(178,188)(179,189)(180,190)(181,191)(182,192)(225,320)(226,321)(227,322)(228,309)(229,310)(230,311)(231,312)(232,313)(233,314)(234,315)(235,316)(236,317)(237,318)(238,319)(239,359)(240,360)(241,361)(242,362)(243,363)(244,364)(245,351)(246,352)(247,353)(248,354)(249,355)(250,356)(251,357)(252,358)(253,379)(254,380)(255,381)(256,382)(257,383)(258,384)(259,385)(260,386)(261,387)(262,388)(263,389)(264,390)(265,391)(266,392)(267,298)(268,299)(269,300)(270,301)(271,302)(272,303)(273,304)(274,305)(275,306)(276,307)(277,308)(278,295)(279,296)(280,297)(281,371)(282,372)(283,373)(284,374)(285,375)(286,376)(287,377)(288,378)(289,365)(290,366)(291,367)(292,368)(293,369)(294,370), (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), (1,329,359,171,235,20,209,379,136,282,42,70,267,149)(2,330,360,172,236,21,210,380,137,283,29,57,268,150)(3,331,361,173,237,22,197,381,138,284,30,58,269,151)(4,332,362,174,238,23,198,382,139,285,31,59,270,152)(5,333,363,175,225,24,199,383,140,286,32,60,271,153)(6,334,364,176,226,25,200,384,127,287,33,61,272,154)(7,335,351,177,227,26,201,385,128,288,34,62,273,141)(8,336,352,178,228,27,202,386,129,289,35,63,274,142)(9,323,353,179,229,28,203,387,130,290,36,64,275,143)(10,324,354,180,230,15,204,388,131,291,37,65,276,144)(11,325,355,181,231,16,205,389,132,292,38,66,277,145)(12,326,356,182,232,17,206,390,133,293,39,67,278,146)(13,327,357,169,233,18,207,391,134,294,40,68,279,147)(14,328,358,170,234,19,208,392,135,281,41,69,280,148)(43,302,74,220,93,243,185,320,114,106,257,163,376,345)(44,303,75,221,94,244,186,321,115,107,258,164,377,346)(45,304,76,222,95,245,187,322,116,108,259,165,378,347)(46,305,77,223,96,246,188,309,117,109,260,166,365,348)(47,306,78,224,97,247,189,310,118,110,261,167,366,349)(48,307,79,211,98,248,190,311,119,111,262,168,367,350)(49,308,80,212,85,249,191,312,120,112,263,155,368,337)(50,295,81,213,86,250,192,313,121,99,264,156,369,338)(51,296,82,214,87,251,193,314,122,100,265,157,370,339)(52,297,83,215,88,252,194,315,123,101,266,158,371,340)(53,298,84,216,89,239,195,316,124,102,253,159,372,341)(54,299,71,217,90,240,196,317,125,103,254,160,373,342)(55,300,72,218,91,241,183,318,126,104,255,161,374,343)(56,301,73,219,92,242,184,319,113,105,256,162,375,344) );

G=PermutationGroup([(1,216),(2,217),(3,218),(4,219),(5,220),(6,221),(7,222),(8,223),(9,224),(10,211),(11,212),(12,213),(13,214),(14,215),(15,119),(16,120),(17,121),(18,122),(19,123),(20,124),(21,125),(22,126),(23,113),(24,114),(25,115),(26,116),(27,117),(28,118),(29,342),(30,343),(31,344),(32,345),(33,346),(34,347),(35,348),(36,349),(37,350),(38,337),(39,338),(40,339),(41,340),(42,341),(43,60),(44,61),(45,62),(46,63),(47,64),(48,65),(49,66),(50,67),(51,68),(52,69),(53,70),(54,57),(55,58),(56,59),(71,150),(72,151),(73,152),(74,153),(75,154),(76,141),(77,142),(78,143),(79,144),(80,145),(81,146),(82,147),(83,148),(84,149),(85,325),(86,326),(87,327),(88,328),(89,329),(90,330),(91,331),(92,332),(93,333),(94,334),(95,335),(96,336),(97,323),(98,324),(99,206),(100,207),(101,208),(102,209),(103,210),(104,197),(105,198),(106,199),(107,200),(108,201),(109,202),(110,203),(111,204),(112,205),(127,164),(128,165),(129,166),(130,167),(131,168),(132,155),(133,156),(134,157),(135,158),(136,159),(137,160),(138,161),(139,162),(140,163),(169,193),(170,194),(171,195),(172,196),(173,183),(174,184),(175,185),(176,186),(177,187),(178,188),(179,189),(180,190),(181,191),(182,192),(225,320),(226,321),(227,322),(228,309),(229,310),(230,311),(231,312),(232,313),(233,314),(234,315),(235,316),(236,317),(237,318),(238,319),(239,359),(240,360),(241,361),(242,362),(243,363),(244,364),(245,351),(246,352),(247,353),(248,354),(249,355),(250,356),(251,357),(252,358),(253,379),(254,380),(255,381),(256,382),(257,383),(258,384),(259,385),(260,386),(261,387),(262,388),(263,389),(264,390),(265,391),(266,392),(267,298),(268,299),(269,300),(270,301),(271,302),(272,303),(273,304),(274,305),(275,306),(276,307),(277,308),(278,295),(279,296),(280,297),(281,371),(282,372),(283,373),(284,374),(285,375),(286,376),(287,377),(288,378),(289,365),(290,366),(291,367),(292,368),(293,369),(294,370)], [(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)], [(1,329,359,171,235,20,209,379,136,282,42,70,267,149),(2,330,360,172,236,21,210,380,137,283,29,57,268,150),(3,331,361,173,237,22,197,381,138,284,30,58,269,151),(4,332,362,174,238,23,198,382,139,285,31,59,270,152),(5,333,363,175,225,24,199,383,140,286,32,60,271,153),(6,334,364,176,226,25,200,384,127,287,33,61,272,154),(7,335,351,177,227,26,201,385,128,288,34,62,273,141),(8,336,352,178,228,27,202,386,129,289,35,63,274,142),(9,323,353,179,229,28,203,387,130,290,36,64,275,143),(10,324,354,180,230,15,204,388,131,291,37,65,276,144),(11,325,355,181,231,16,205,389,132,292,38,66,277,145),(12,326,356,182,232,17,206,390,133,293,39,67,278,146),(13,327,357,169,233,18,207,391,134,294,40,68,279,147),(14,328,358,170,234,19,208,392,135,281,41,69,280,148),(43,302,74,220,93,243,185,320,114,106,257,163,376,345),(44,303,75,221,94,244,186,321,115,107,258,164,377,346),(45,304,76,222,95,245,187,322,116,108,259,165,378,347),(46,305,77,223,96,246,188,309,117,109,260,166,365,348),(47,306,78,224,97,247,189,310,118,110,261,167,366,349),(48,307,79,211,98,248,190,311,119,111,262,168,367,350),(49,308,80,212,85,249,191,312,120,112,263,155,368,337),(50,295,81,213,86,250,192,313,121,99,264,156,369,338),(51,296,82,214,87,251,193,314,122,100,265,157,370,339),(52,297,83,215,88,252,194,315,123,101,266,158,371,340),(53,298,84,216,89,239,195,316,124,102,253,159,372,341),(54,299,71,217,90,240,196,317,125,103,254,160,373,342),(55,300,72,218,91,241,183,318,126,104,255,161,374,343),(56,301,73,219,92,242,184,319,113,105,256,162,375,344)])

392 conjugacy classes

class 1 2A···2G7A···7AV14A···14LX
order12···27···714···14
size11···11···11···1

392 irreducible representations

dim1111
type++
imageC1C2C7C14
kernelC2×C142C142C22×C14C2×C14
# reps1748336

Matrix representation of C2×C142 in GL3(𝔽29) generated by

100
010
0028
,
100
060
0016
,
2800
060
001
G:=sub<GL(3,GF(29))| [1,0,0,0,1,0,0,0,28],[1,0,0,0,6,0,0,0,16],[28,0,0,0,6,0,0,0,1] >;

C2×C142 in GAP, Magma, Sage, TeX

C_2\times C_{14}^2
% in TeX

G:=Group("C2xC14^2");
// GroupNames label

G:=SmallGroup(392,44);
// by ID

G=gap.SmallGroup(392,44);
# by ID

G:=PCGroup([5,-2,-2,-2,-7,-7]);
// Polycyclic

G:=Group<a,b,c|a^2=b^14=c^14=1,a*b=b*a,a*c=c*a,b*c=c*b>;
// generators/relations

׿
×
𝔽