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## G = C2×C142order 392 = 23·72

### Abelian group of type [2,14,14]

Aliases: C2×C142, SmallGroup(392,44)

Series: Derived Chief Lower central Upper central

 Derived series C1 — C2×C142
 Chief series C1 — C7 — C72 — C7×C14 — C142 — C2×C142
 Lower central C1 — C2×C142
 Upper central 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, C22, C7, C23, C14, C2×C14, C72, C22×C14, C7×C14, C142, C2×C142
Quotients: C1, C2, C22, C7, C23, C14, C2×C14, C72, C22×C14, C7×C14, C142, C2×C142

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

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

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

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

392 conjugacy classes

 class 1 2A ··· 2G 7A ··· 7AV 14A ··· 14LX order 1 2 ··· 2 7 ··· 7 14 ··· 14 size 1 1 ··· 1 1 ··· 1 1 ··· 1

392 irreducible representations

 dim 1 1 1 1 type + + image C1 C2 C7 C14 kernel C2×C142 C142 C22×C14 C2×C14 # reps 1 7 48 336

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

 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
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