direct product, metacyclic, supersoluble, monomial, 2-hyperelementary
Aliases: C7×Dic12, C21⋊6Q16, C56.3S3, C168.4C2, C24.1C14, C28.54D6, C42.30D4, C14.15D12, C84.70C22, Dic6.1C14, C8.(S3×C7), C3⋊1(C7×Q16), C6.3(C7×D4), C2.5(C7×D12), C4.10(S3×C14), C12.10(C2×C14), (C7×Dic6).3C2, SmallGroup(336,78)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C7×Dic12
G = < a,b,c | a7=b24=1, c2=b12, ab=ba, ac=ca, cbc-1=b-1 >
Smallest permutation representation of C7×Dic12
►Regular action on 336 points
Generators in S336
(1 252 75 42 135 201 103)(2 253 76 43 136 202 104)(3 254 77 44 137 203 105)(4 255 78 45 138 204 106)(5 256 79 46 139 205 107)(6 257 80 47 140 206 108)(7 258 81 48 141 207 109)(8 259 82 25 142 208 110)(9 260 83 26 143 209 111)(10 261 84 27 144 210 112)(11 262 85 28 121 211 113)(12 263 86 29 122 212 114)(13 264 87 30 123 213 115)(14 241 88 31 124 214 116)(15 242 89 32 125 215 117)(16 243 90 33 126 216 118)(17 244 91 34 127 193 119)(18 245 92 35 128 194 120)(19 246 93 36 129 195 97)(20 247 94 37 130 196 98)(21 248 95 38 131 197 99)(22 249 96 39 132 198 100)(23 250 73 40 133 199 101)(24 251 74 41 134 200 102)(49 192 225 277 325 303 148)(50 169 226 278 326 304 149)(51 170 227 279 327 305 150)(52 171 228 280 328 306 151)(53 172 229 281 329 307 152)(54 173 230 282 330 308 153)(55 174 231 283 331 309 154)(56 175 232 284 332 310 155)(57 176 233 285 333 311 156)(58 177 234 286 334 312 157)(59 178 235 287 335 289 158)(60 179 236 288 336 290 159)(61 180 237 265 313 291 160)(62 181 238 266 314 292 161)(63 182 239 267 315 293 162)(64 183 240 268 316 294 163)(65 184 217 269 317 295 164)(66 185 218 270 318 296 165)(67 186 219 271 319 297 166)(68 187 220 272 320 298 167)(69 188 221 273 321 299 168)(70 189 222 274 322 300 145)(71 190 223 275 323 301 146)(72 191 224 276 324 302 147)
(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)
(1 53 13 65)(2 52 14 64)(3 51 15 63)(4 50 16 62)(5 49 17 61)(6 72 18 60)(7 71 19 59)(8 70 20 58)(9 69 21 57)(10 68 22 56)(11 67 23 55)(12 66 24 54)(25 274 37 286)(26 273 38 285)(27 272 39 284)(28 271 40 283)(29 270 41 282)(30 269 42 281)(31 268 43 280)(32 267 44 279)(33 266 45 278)(34 265 46 277)(35 288 47 276)(36 287 48 275)(73 231 85 219)(74 230 86 218)(75 229 87 217)(76 228 88 240)(77 227 89 239)(78 226 90 238)(79 225 91 237)(80 224 92 236)(81 223 93 235)(82 222 94 234)(83 221 95 233)(84 220 96 232)(97 158 109 146)(98 157 110 145)(99 156 111 168)(100 155 112 167)(101 154 113 166)(102 153 114 165)(103 152 115 164)(104 151 116 163)(105 150 117 162)(106 149 118 161)(107 148 119 160)(108 147 120 159)(121 319 133 331)(122 318 134 330)(123 317 135 329)(124 316 136 328)(125 315 137 327)(126 314 138 326)(127 313 139 325)(128 336 140 324)(129 335 141 323)(130 334 142 322)(131 333 143 321)(132 332 144 320)(169 243 181 255)(170 242 182 254)(171 241 183 253)(172 264 184 252)(173 263 185 251)(174 262 186 250)(175 261 187 249)(176 260 188 248)(177 259 189 247)(178 258 190 246)(179 257 191 245)(180 256 192 244)(193 291 205 303)(194 290 206 302)(195 289 207 301)(196 312 208 300)(197 311 209 299)(198 310 210 298)(199 309 211 297)(200 308 212 296)(201 307 213 295)(202 306 214 294)(203 305 215 293)(204 304 216 292)
G:=sub<Sym(336)| (1,252,75,42,135,201,103)(2,253,76,43,136,202,104)(3,254,77,44,137,203,105)(4,255,78,45,138,204,106)(5,256,79,46,139,205,107)(6,257,80,47,140,206,108)(7,258,81,48,141,207,109)(8,259,82,25,142,208,110)(9,260,83,26,143,209,111)(10,261,84,27,144,210,112)(11,262,85,28,121,211,113)(12,263,86,29,122,212,114)(13,264,87,30,123,213,115)(14,241,88,31,124,214,116)(15,242,89,32,125,215,117)(16,243,90,33,126,216,118)(17,244,91,34,127,193,119)(18,245,92,35,128,194,120)(19,246,93,36,129,195,97)(20,247,94,37,130,196,98)(21,248,95,38,131,197,99)(22,249,96,39,132,198,100)(23,250,73,40,133,199,101)(24,251,74,41,134,200,102)(49,192,225,277,325,303,148)(50,169,226,278,326,304,149)(51,170,227,279,327,305,150)(52,171,228,280,328,306,151)(53,172,229,281,329,307,152)(54,173,230,282,330,308,153)(55,174,231,283,331,309,154)(56,175,232,284,332,310,155)(57,176,233,285,333,311,156)(58,177,234,286,334,312,157)(59,178,235,287,335,289,158)(60,179,236,288,336,290,159)(61,180,237,265,313,291,160)(62,181,238,266,314,292,161)(63,182,239,267,315,293,162)(64,183,240,268,316,294,163)(65,184,217,269,317,295,164)(66,185,218,270,318,296,165)(67,186,219,271,319,297,166)(68,187,220,272,320,298,167)(69,188,221,273,321,299,168)(70,189,222,274,322,300,145)(71,190,223,275,323,301,146)(72,191,224,276,324,302,147), (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), (1,53,13,65)(2,52,14,64)(3,51,15,63)(4,50,16,62)(5,49,17,61)(6,72,18,60)(7,71,19,59)(8,70,20,58)(9,69,21,57)(10,68,22,56)(11,67,23,55)(12,66,24,54)(25,274,37,286)(26,273,38,285)(27,272,39,284)(28,271,40,283)(29,270,41,282)(30,269,42,281)(31,268,43,280)(32,267,44,279)(33,266,45,278)(34,265,46,277)(35,288,47,276)(36,287,48,275)(73,231,85,219)(74,230,86,218)(75,229,87,217)(76,228,88,240)(77,227,89,239)(78,226,90,238)(79,225,91,237)(80,224,92,236)(81,223,93,235)(82,222,94,234)(83,221,95,233)(84,220,96,232)(97,158,109,146)(98,157,110,145)(99,156,111,168)(100,155,112,167)(101,154,113,166)(102,153,114,165)(103,152,115,164)(104,151,116,163)(105,150,117,162)(106,149,118,161)(107,148,119,160)(108,147,120,159)(121,319,133,331)(122,318,134,330)(123,317,135,329)(124,316,136,328)(125,315,137,327)(126,314,138,326)(127,313,139,325)(128,336,140,324)(129,335,141,323)(130,334,142,322)(131,333,143,321)(132,332,144,320)(169,243,181,255)(170,242,182,254)(171,241,183,253)(172,264,184,252)(173,263,185,251)(174,262,186,250)(175,261,187,249)(176,260,188,248)(177,259,189,247)(178,258,190,246)(179,257,191,245)(180,256,192,244)(193,291,205,303)(194,290,206,302)(195,289,207,301)(196,312,208,300)(197,311,209,299)(198,310,210,298)(199,309,211,297)(200,308,212,296)(201,307,213,295)(202,306,214,294)(203,305,215,293)(204,304,216,292)>;
G:=Group( (1,252,75,42,135,201,103)(2,253,76,43,136,202,104)(3,254,77,44,137,203,105)(4,255,78,45,138,204,106)(5,256,79,46,139,205,107)(6,257,80,47,140,206,108)(7,258,81,48,141,207,109)(8,259,82,25,142,208,110)(9,260,83,26,143,209,111)(10,261,84,27,144,210,112)(11,262,85,28,121,211,113)(12,263,86,29,122,212,114)(13,264,87,30,123,213,115)(14,241,88,31,124,214,116)(15,242,89,32,125,215,117)(16,243,90,33,126,216,118)(17,244,91,34,127,193,119)(18,245,92,35,128,194,120)(19,246,93,36,129,195,97)(20,247,94,37,130,196,98)(21,248,95,38,131,197,99)(22,249,96,39,132,198,100)(23,250,73,40,133,199,101)(24,251,74,41,134,200,102)(49,192,225,277,325,303,148)(50,169,226,278,326,304,149)(51,170,227,279,327,305,150)(52,171,228,280,328,306,151)(53,172,229,281,329,307,152)(54,173,230,282,330,308,153)(55,174,231,283,331,309,154)(56,175,232,284,332,310,155)(57,176,233,285,333,311,156)(58,177,234,286,334,312,157)(59,178,235,287,335,289,158)(60,179,236,288,336,290,159)(61,180,237,265,313,291,160)(62,181,238,266,314,292,161)(63,182,239,267,315,293,162)(64,183,240,268,316,294,163)(65,184,217,269,317,295,164)(66,185,218,270,318,296,165)(67,186,219,271,319,297,166)(68,187,220,272,320,298,167)(69,188,221,273,321,299,168)(70,189,222,274,322,300,145)(71,190,223,275,323,301,146)(72,191,224,276,324,302,147), (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), (1,53,13,65)(2,52,14,64)(3,51,15,63)(4,50,16,62)(5,49,17,61)(6,72,18,60)(7,71,19,59)(8,70,20,58)(9,69,21,57)(10,68,22,56)(11,67,23,55)(12,66,24,54)(25,274,37,286)(26,273,38,285)(27,272,39,284)(28,271,40,283)(29,270,41,282)(30,269,42,281)(31,268,43,280)(32,267,44,279)(33,266,45,278)(34,265,46,277)(35,288,47,276)(36,287,48,275)(73,231,85,219)(74,230,86,218)(75,229,87,217)(76,228,88,240)(77,227,89,239)(78,226,90,238)(79,225,91,237)(80,224,92,236)(81,223,93,235)(82,222,94,234)(83,221,95,233)(84,220,96,232)(97,158,109,146)(98,157,110,145)(99,156,111,168)(100,155,112,167)(101,154,113,166)(102,153,114,165)(103,152,115,164)(104,151,116,163)(105,150,117,162)(106,149,118,161)(107,148,119,160)(108,147,120,159)(121,319,133,331)(122,318,134,330)(123,317,135,329)(124,316,136,328)(125,315,137,327)(126,314,138,326)(127,313,139,325)(128,336,140,324)(129,335,141,323)(130,334,142,322)(131,333,143,321)(132,332,144,320)(169,243,181,255)(170,242,182,254)(171,241,183,253)(172,264,184,252)(173,263,185,251)(174,262,186,250)(175,261,187,249)(176,260,188,248)(177,259,189,247)(178,258,190,246)(179,257,191,245)(180,256,192,244)(193,291,205,303)(194,290,206,302)(195,289,207,301)(196,312,208,300)(197,311,209,299)(198,310,210,298)(199,309,211,297)(200,308,212,296)(201,307,213,295)(202,306,214,294)(203,305,215,293)(204,304,216,292) );
G=PermutationGroup([[(1,252,75,42,135,201,103),(2,253,76,43,136,202,104),(3,254,77,44,137,203,105),(4,255,78,45,138,204,106),(5,256,79,46,139,205,107),(6,257,80,47,140,206,108),(7,258,81,48,141,207,109),(8,259,82,25,142,208,110),(9,260,83,26,143,209,111),(10,261,84,27,144,210,112),(11,262,85,28,121,211,113),(12,263,86,29,122,212,114),(13,264,87,30,123,213,115),(14,241,88,31,124,214,116),(15,242,89,32,125,215,117),(16,243,90,33,126,216,118),(17,244,91,34,127,193,119),(18,245,92,35,128,194,120),(19,246,93,36,129,195,97),(20,247,94,37,130,196,98),(21,248,95,38,131,197,99),(22,249,96,39,132,198,100),(23,250,73,40,133,199,101),(24,251,74,41,134,200,102),(49,192,225,277,325,303,148),(50,169,226,278,326,304,149),(51,170,227,279,327,305,150),(52,171,228,280,328,306,151),(53,172,229,281,329,307,152),(54,173,230,282,330,308,153),(55,174,231,283,331,309,154),(56,175,232,284,332,310,155),(57,176,233,285,333,311,156),(58,177,234,286,334,312,157),(59,178,235,287,335,289,158),(60,179,236,288,336,290,159),(61,180,237,265,313,291,160),(62,181,238,266,314,292,161),(63,182,239,267,315,293,162),(64,183,240,268,316,294,163),(65,184,217,269,317,295,164),(66,185,218,270,318,296,165),(67,186,219,271,319,297,166),(68,187,220,272,320,298,167),(69,188,221,273,321,299,168),(70,189,222,274,322,300,145),(71,190,223,275,323,301,146),(72,191,224,276,324,302,147)], [(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)], [(1,53,13,65),(2,52,14,64),(3,51,15,63),(4,50,16,62),(5,49,17,61),(6,72,18,60),(7,71,19,59),(8,70,20,58),(9,69,21,57),(10,68,22,56),(11,67,23,55),(12,66,24,54),(25,274,37,286),(26,273,38,285),(27,272,39,284),(28,271,40,283),(29,270,41,282),(30,269,42,281),(31,268,43,280),(32,267,44,279),(33,266,45,278),(34,265,46,277),(35,288,47,276),(36,287,48,275),(73,231,85,219),(74,230,86,218),(75,229,87,217),(76,228,88,240),(77,227,89,239),(78,226,90,238),(79,225,91,237),(80,224,92,236),(81,223,93,235),(82,222,94,234),(83,221,95,233),(84,220,96,232),(97,158,109,146),(98,157,110,145),(99,156,111,168),(100,155,112,167),(101,154,113,166),(102,153,114,165),(103,152,115,164),(104,151,116,163),(105,150,117,162),(106,149,118,161),(107,148,119,160),(108,147,120,159),(121,319,133,331),(122,318,134,330),(123,317,135,329),(124,316,136,328),(125,315,137,327),(126,314,138,326),(127,313,139,325),(128,336,140,324),(129,335,141,323),(130,334,142,322),(131,333,143,321),(132,332,144,320),(169,243,181,255),(170,242,182,254),(171,241,183,253),(172,264,184,252),(173,263,185,251),(174,262,186,250),(175,261,187,249),(176,260,188,248),(177,259,189,247),(178,258,190,246),(179,257,191,245),(180,256,192,244),(193,291,205,303),(194,290,206,302),(195,289,207,301),(196,312,208,300),(197,311,209,299),(198,310,210,298),(199,309,211,297),(200,308,212,296),(201,307,213,295),(202,306,214,294),(203,305,215,293),(204,304,216,292)]])
105 conjugacy classes
| class | 1 | 2 | 3 | 4A | 4B | 4C | 6 | 7A | ··· | 7F | 8A | 8B | 12A | 12B | 14A | ··· | 14F | 21A | ··· | 21F | 24A | 24B | 24C | 24D | 28A | ··· | 28F | 28G | ··· | 28R | 42A | ··· | 42F | 56A | ··· | 56L | 84A | ··· | 84L | 168A | ··· | 168X |
| order | 1 | 2 | 3 | 4 | 4 | 4 | 6 | 7 | ··· | 7 | 8 | 8 | 12 | 12 | 14 | ··· | 14 | 21 | ··· | 21 | 24 | 24 | 24 | 24 | 28 | ··· | 28 | 28 | ··· | 28 | 42 | ··· | 42 | 56 | ··· | 56 | 84 | ··· | 84 | 168 | ··· | 168 |
| size | 1 | 1 | 2 | 2 | 12 | 12 | 2 | 1 | ··· | 1 | 2 | 2 | 2 | 2 | 1 | ··· | 1 | 2 | ··· | 2 | 2 | 2 | 2 | 2 | 2 | ··· | 2 | 12 | ··· | 12 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
105 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | + | - | + | - | |||||||||
| image | C1 | C2 | C2 | C7 | C14 | C14 | S3 | D4 | D6 | Q16 | D12 | S3×C7 | Dic12 | C7×D4 | S3×C14 | C7×Q16 | C7×D12 | C7×Dic12 |
| kernel | C7×Dic12 | C168 | C7×Dic6 | Dic12 | C24 | Dic6 | C56 | C42 | C28 | C21 | C14 | C8 | C7 | C6 | C4 | C3 | C2 | C1 |
| # reps | 1 | 1 | 2 | 6 | 6 | 12 | 1 | 1 | 1 | 2 | 2 | 6 | 4 | 6 | 6 | 12 | 12 | 24 |
Matrix representation of C7×Dic12 ►in GL2(𝔽337) generated by
| 8 | 0 |
| 0 | 8 |
| 129 | 155 |
| 182 | 284 |
| 241 | 91 |
| 332 | 96 |
G:=sub<GL(2,GF(337))| [8,0,0,8],[129,182,155,284],[241,332,91,96] >;
C7×Dic12 in GAP, Magma, Sage, TeX
C_7\times {\rm Dic}_{12} % in TeX
G:=Group("C7xDic12"); // GroupNames label
G:=SmallGroup(336,78);
// by ID
G=gap.SmallGroup(336,78);
# by ID
G:=PCGroup([6,-2,-2,-7,-2,-2,-3,336,361,511,2019,69,8069]);
// Polycyclic
G:=Group<a,b,c|a^7=b^24=1,c^2=b^12,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations
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