metabelian, supersoluble, monomial
Aliases: C12⋊2Dic6, C62.232C23, (C3×C12)⋊6Q8, C3⋊4(C12⋊Q8), C3⋊Dic3⋊8Q8, C6.43(S3×Q8), C6.112(S3×D4), (C2×C12).31D6, C32⋊12(C4⋊Q8), C3⋊Dic3.47D4, C6.42(C2×Dic6), C4⋊1(C32⋊4Q8), (C6×C12).134C22, C6.Dic6.2C2, C12⋊Dic3.18C2, C2.4(Q8×C3⋊S3), C2.11(D4×C3⋊S3), C4⋊C4.4(C3⋊S3), (C3×C4⋊C4).21S3, (C3×C6).56(C2×Q8), (C3×C6).234(C2×D4), (C4×C3⋊Dic3).5C2, C2.7(C2×C32⋊4Q8), (C32×C4⋊C4).12C2, (C2×C32⋊4Q8).5C2, (C2×C6).249(C22×S3), C22.46(C22×C3⋊S3), (C2×C3⋊Dic3).157C22, (C2×C4).8(C2×C3⋊S3), SmallGroup(288,745)
Series: Derived ►Chief ►Lower central ►Upper central
| C1 — C3 — C32 — C3×C6 — C62 — C2×C3⋊Dic3 — C4×C3⋊Dic3 — C12⋊2Dic6 |
Generators and relations for C12⋊2Dic6
G = < a,b,c | a12=b12=1, c2=b6, bab-1=a7, cac-1=a5, cbc-1=b-1 >
Subgroups: 684 in 204 conjugacy classes, 81 normal (19 characteristic)
C1, C2, C3, C4, C4, C22, C6, C2×C4, C2×C4, C2×C4, Q8, C32, Dic3, C12, C12, C2×C6, C42, C4⋊C4, C4⋊C4, C2×Q8, C3×C6, Dic6, C2×Dic3, C2×C12, C4⋊Q8, C3⋊Dic3, C3⋊Dic3, C3×C12, C3×C12, C62, C4×Dic3, Dic3⋊C4, C4⋊Dic3, C3×C4⋊C4, C2×Dic6, C32⋊4Q8, C2×C3⋊Dic3, C2×C3⋊Dic3, C6×C12, C6×C12, C12⋊Q8, C4×C3⋊Dic3, C6.Dic6, C12⋊Dic3, C32×C4⋊C4, C2×C32⋊4Q8, C12⋊2Dic6
Quotients: C1, C2, C22, S3, D4, Q8, C23, D6, C2×D4, C2×Q8, C3⋊S3, Dic6, C22×S3, C4⋊Q8, C2×C3⋊S3, C2×Dic6, S3×D4, S3×Q8, C32⋊4Q8, C22×C3⋊S3, C12⋊Q8, C2×C32⋊4Q8, D4×C3⋊S3, Q8×C3⋊S3, C12⋊2Dic6
►Regular action on 288 points
Generators in S288
(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)
(1 14 98 86 151 169 205 166 247 190 26 59)(2 21 99 93 152 176 206 161 248 185 27 54)(3 16 100 88 153 171 207 168 249 192 28 49)(4 23 101 95 154 178 208 163 250 187 29 56)(5 18 102 90 155 173 209 158 251 182 30 51)(6 13 103 85 156 180 210 165 252 189 31 58)(7 20 104 92 145 175 211 160 241 184 32 53)(8 15 105 87 146 170 212 167 242 191 33 60)(9 22 106 94 147 177 213 162 243 186 34 55)(10 17 107 89 148 172 214 157 244 181 35 50)(11 24 108 96 149 179 215 164 245 188 36 57)(12 19 97 91 150 174 216 159 246 183 25 52)(37 229 130 228 280 267 137 83 63 253 109 199)(38 236 131 223 281 274 138 78 64 260 110 194)(39 231 132 218 282 269 139 73 65 255 111 201)(40 238 121 225 283 276 140 80 66 262 112 196)(41 233 122 220 284 271 141 75 67 257 113 203)(42 240 123 227 285 266 142 82 68 264 114 198)(43 235 124 222 286 273 143 77 69 259 115 193)(44 230 125 217 287 268 144 84 70 254 116 200)(45 237 126 224 288 275 133 79 71 261 117 195)(46 232 127 219 277 270 134 74 72 256 118 202)(47 239 128 226 278 265 135 81 61 263 119 197)(48 234 129 221 279 272 136 76 62 258 120 204)
(1 126 205 71)(2 131 206 64)(3 124 207 69)(4 129 208 62)(5 122 209 67)(6 127 210 72)(7 132 211 65)(8 125 212 70)(9 130 213 63)(10 123 214 68)(11 128 215 61)(12 121 216 66)(13 232 165 74)(14 237 166 79)(15 230 167 84)(16 235 168 77)(17 240 157 82)(18 233 158 75)(19 238 159 80)(20 231 160 73)(21 236 161 78)(22 229 162 83)(23 234 163 76)(24 239 164 81)(25 283 150 112)(26 288 151 117)(27 281 152 110)(28 286 153 115)(29 279 154 120)(30 284 155 113)(31 277 156 118)(32 282 145 111)(33 287 146 116)(34 280 147 109)(35 285 148 114)(36 278 149 119)(37 243 137 106)(38 248 138 99)(39 241 139 104)(40 246 140 97)(41 251 141 102)(42 244 142 107)(43 249 143 100)(44 242 144 105)(45 247 133 98)(46 252 134 103)(47 245 135 108)(48 250 136 101)(49 222 171 259)(50 227 172 264)(51 220 173 257)(52 225 174 262)(53 218 175 255)(54 223 176 260)(55 228 177 253)(56 221 178 258)(57 226 179 263)(58 219 180 256)(59 224 169 261)(60 217 170 254)(85 202 189 270)(86 195 190 275)(87 200 191 268)(88 193 192 273)(89 198 181 266)(90 203 182 271)(91 196 183 276)(92 201 184 269)(93 194 185 274)(94 199 186 267)(95 204 187 272)(96 197 188 265)
G:=sub<Sym(288)| (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), (1,14,98,86,151,169,205,166,247,190,26,59)(2,21,99,93,152,176,206,161,248,185,27,54)(3,16,100,88,153,171,207,168,249,192,28,49)(4,23,101,95,154,178,208,163,250,187,29,56)(5,18,102,90,155,173,209,158,251,182,30,51)(6,13,103,85,156,180,210,165,252,189,31,58)(7,20,104,92,145,175,211,160,241,184,32,53)(8,15,105,87,146,170,212,167,242,191,33,60)(9,22,106,94,147,177,213,162,243,186,34,55)(10,17,107,89,148,172,214,157,244,181,35,50)(11,24,108,96,149,179,215,164,245,188,36,57)(12,19,97,91,150,174,216,159,246,183,25,52)(37,229,130,228,280,267,137,83,63,253,109,199)(38,236,131,223,281,274,138,78,64,260,110,194)(39,231,132,218,282,269,139,73,65,255,111,201)(40,238,121,225,283,276,140,80,66,262,112,196)(41,233,122,220,284,271,141,75,67,257,113,203)(42,240,123,227,285,266,142,82,68,264,114,198)(43,235,124,222,286,273,143,77,69,259,115,193)(44,230,125,217,287,268,144,84,70,254,116,200)(45,237,126,224,288,275,133,79,71,261,117,195)(46,232,127,219,277,270,134,74,72,256,118,202)(47,239,128,226,278,265,135,81,61,263,119,197)(48,234,129,221,279,272,136,76,62,258,120,204), (1,126,205,71)(2,131,206,64)(3,124,207,69)(4,129,208,62)(5,122,209,67)(6,127,210,72)(7,132,211,65)(8,125,212,70)(9,130,213,63)(10,123,214,68)(11,128,215,61)(12,121,216,66)(13,232,165,74)(14,237,166,79)(15,230,167,84)(16,235,168,77)(17,240,157,82)(18,233,158,75)(19,238,159,80)(20,231,160,73)(21,236,161,78)(22,229,162,83)(23,234,163,76)(24,239,164,81)(25,283,150,112)(26,288,151,117)(27,281,152,110)(28,286,153,115)(29,279,154,120)(30,284,155,113)(31,277,156,118)(32,282,145,111)(33,287,146,116)(34,280,147,109)(35,285,148,114)(36,278,149,119)(37,243,137,106)(38,248,138,99)(39,241,139,104)(40,246,140,97)(41,251,141,102)(42,244,142,107)(43,249,143,100)(44,242,144,105)(45,247,133,98)(46,252,134,103)(47,245,135,108)(48,250,136,101)(49,222,171,259)(50,227,172,264)(51,220,173,257)(52,225,174,262)(53,218,175,255)(54,223,176,260)(55,228,177,253)(56,221,178,258)(57,226,179,263)(58,219,180,256)(59,224,169,261)(60,217,170,254)(85,202,189,270)(86,195,190,275)(87,200,191,268)(88,193,192,273)(89,198,181,266)(90,203,182,271)(91,196,183,276)(92,201,184,269)(93,194,185,274)(94,199,186,267)(95,204,187,272)(96,197,188,265)>;
G:=Group( (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), (1,14,98,86,151,169,205,166,247,190,26,59)(2,21,99,93,152,176,206,161,248,185,27,54)(3,16,100,88,153,171,207,168,249,192,28,49)(4,23,101,95,154,178,208,163,250,187,29,56)(5,18,102,90,155,173,209,158,251,182,30,51)(6,13,103,85,156,180,210,165,252,189,31,58)(7,20,104,92,145,175,211,160,241,184,32,53)(8,15,105,87,146,170,212,167,242,191,33,60)(9,22,106,94,147,177,213,162,243,186,34,55)(10,17,107,89,148,172,214,157,244,181,35,50)(11,24,108,96,149,179,215,164,245,188,36,57)(12,19,97,91,150,174,216,159,246,183,25,52)(37,229,130,228,280,267,137,83,63,253,109,199)(38,236,131,223,281,274,138,78,64,260,110,194)(39,231,132,218,282,269,139,73,65,255,111,201)(40,238,121,225,283,276,140,80,66,262,112,196)(41,233,122,220,284,271,141,75,67,257,113,203)(42,240,123,227,285,266,142,82,68,264,114,198)(43,235,124,222,286,273,143,77,69,259,115,193)(44,230,125,217,287,268,144,84,70,254,116,200)(45,237,126,224,288,275,133,79,71,261,117,195)(46,232,127,219,277,270,134,74,72,256,118,202)(47,239,128,226,278,265,135,81,61,263,119,197)(48,234,129,221,279,272,136,76,62,258,120,204), (1,126,205,71)(2,131,206,64)(3,124,207,69)(4,129,208,62)(5,122,209,67)(6,127,210,72)(7,132,211,65)(8,125,212,70)(9,130,213,63)(10,123,214,68)(11,128,215,61)(12,121,216,66)(13,232,165,74)(14,237,166,79)(15,230,167,84)(16,235,168,77)(17,240,157,82)(18,233,158,75)(19,238,159,80)(20,231,160,73)(21,236,161,78)(22,229,162,83)(23,234,163,76)(24,239,164,81)(25,283,150,112)(26,288,151,117)(27,281,152,110)(28,286,153,115)(29,279,154,120)(30,284,155,113)(31,277,156,118)(32,282,145,111)(33,287,146,116)(34,280,147,109)(35,285,148,114)(36,278,149,119)(37,243,137,106)(38,248,138,99)(39,241,139,104)(40,246,140,97)(41,251,141,102)(42,244,142,107)(43,249,143,100)(44,242,144,105)(45,247,133,98)(46,252,134,103)(47,245,135,108)(48,250,136,101)(49,222,171,259)(50,227,172,264)(51,220,173,257)(52,225,174,262)(53,218,175,255)(54,223,176,260)(55,228,177,253)(56,221,178,258)(57,226,179,263)(58,219,180,256)(59,224,169,261)(60,217,170,254)(85,202,189,270)(86,195,190,275)(87,200,191,268)(88,193,192,273)(89,198,181,266)(90,203,182,271)(91,196,183,276)(92,201,184,269)(93,194,185,274)(94,199,186,267)(95,204,187,272)(96,197,188,265) );
G=PermutationGroup([[(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)], [(1,14,98,86,151,169,205,166,247,190,26,59),(2,21,99,93,152,176,206,161,248,185,27,54),(3,16,100,88,153,171,207,168,249,192,28,49),(4,23,101,95,154,178,208,163,250,187,29,56),(5,18,102,90,155,173,209,158,251,182,30,51),(6,13,103,85,156,180,210,165,252,189,31,58),(7,20,104,92,145,175,211,160,241,184,32,53),(8,15,105,87,146,170,212,167,242,191,33,60),(9,22,106,94,147,177,213,162,243,186,34,55),(10,17,107,89,148,172,214,157,244,181,35,50),(11,24,108,96,149,179,215,164,245,188,36,57),(12,19,97,91,150,174,216,159,246,183,25,52),(37,229,130,228,280,267,137,83,63,253,109,199),(38,236,131,223,281,274,138,78,64,260,110,194),(39,231,132,218,282,269,139,73,65,255,111,201),(40,238,121,225,283,276,140,80,66,262,112,196),(41,233,122,220,284,271,141,75,67,257,113,203),(42,240,123,227,285,266,142,82,68,264,114,198),(43,235,124,222,286,273,143,77,69,259,115,193),(44,230,125,217,287,268,144,84,70,254,116,200),(45,237,126,224,288,275,133,79,71,261,117,195),(46,232,127,219,277,270,134,74,72,256,118,202),(47,239,128,226,278,265,135,81,61,263,119,197),(48,234,129,221,279,272,136,76,62,258,120,204)], [(1,126,205,71),(2,131,206,64),(3,124,207,69),(4,129,208,62),(5,122,209,67),(6,127,210,72),(7,132,211,65),(8,125,212,70),(9,130,213,63),(10,123,214,68),(11,128,215,61),(12,121,216,66),(13,232,165,74),(14,237,166,79),(15,230,167,84),(16,235,168,77),(17,240,157,82),(18,233,158,75),(19,238,159,80),(20,231,160,73),(21,236,161,78),(22,229,162,83),(23,234,163,76),(24,239,164,81),(25,283,150,112),(26,288,151,117),(27,281,152,110),(28,286,153,115),(29,279,154,120),(30,284,155,113),(31,277,156,118),(32,282,145,111),(33,287,146,116),(34,280,147,109),(35,285,148,114),(36,278,149,119),(37,243,137,106),(38,248,138,99),(39,241,139,104),(40,246,140,97),(41,251,141,102),(42,244,142,107),(43,249,143,100),(44,242,144,105),(45,247,133,98),(46,252,134,103),(47,245,135,108),(48,250,136,101),(49,222,171,259),(50,227,172,264),(51,220,173,257),(52,225,174,262),(53,218,175,255),(54,223,176,260),(55,228,177,253),(56,221,178,258),(57,226,179,263),(58,219,180,256),(59,224,169,261),(60,217,170,254),(85,202,189,270),(86,195,190,275),(87,200,191,268),(88,193,192,273),(89,198,181,266),(90,203,182,271),(91,196,183,276),(92,201,184,269),(93,194,185,274),(94,199,186,267),(95,204,187,272),(96,197,188,265)]])
54 conjugacy classes
| class | 1 | 2A | 2B | 2C | 3A | 3B | 3C | 3D | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 6A | ··· | 6L | 12A | ··· | 12X |
| order | 1 | 2 | 2 | 2 | 3 | 3 | 3 | 3 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 6 | ··· | 6 | 12 | ··· | 12 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 18 | 18 | 18 | 18 | 36 | 36 | 2 | ··· | 2 | 4 | ··· | 4 |
54 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | - | - | + | - | + | - |
| image | C1 | C2 | C2 | C2 | C2 | C2 | S3 | D4 | Q8 | Q8 | D6 | Dic6 | S3×D4 | S3×Q8 |
| kernel | C12⋊2Dic6 | C4×C3⋊Dic3 | C6.Dic6 | C12⋊Dic3 | C32×C4⋊C4 | C2×C32⋊4Q8 | C3×C4⋊C4 | C3⋊Dic3 | C3⋊Dic3 | C3×C12 | C2×C12 | C12 | C6 | C6 |
| # reps | 1 | 1 | 2 | 1 | 1 | 2 | 4 | 2 | 2 | 2 | 12 | 16 | 4 | 4 |
Matrix representation of C12⋊2Dic6 ►in GL6(𝔽13)
| 10 | 0 | 0 | 0 | 0 | 0 |
| 2 | 4 | 0 | 0 | 0 | 0 |
| 0 | 0 | 3 | 9 | 0 | 0 |
| 0 | 0 | 9 | 10 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 0 |
| 0 | 0 | 0 | 0 | 0 | 12 |
| 6 | 0 | 0 | 0 | 0 | 0 |
| 7 | 11 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 12 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 7 | 7 |
| 0 | 0 | 0 | 0 | 0 | 2 |
| 8 | 2 | 0 | 0 | 0 | 0 |
| 0 | 5 | 0 | 0 | 0 | 0 |
| 0 | 0 | 10 | 4 | 0 | 0 |
| 0 | 0 | 4 | 3 | 0 | 0 |
| 0 | 0 | 0 | 0 | 7 | 10 |
| 0 | 0 | 0 | 0 | 8 | 6 |
G:=sub<GL(6,GF(13))| [10,2,0,0,0,0,0,4,0,0,0,0,0,0,3,9,0,0,0,0,9,10,0,0,0,0,0,0,12,0,0,0,0,0,0,12],[6,7,0,0,0,0,0,11,0,0,0,0,0,0,0,12,0,0,0,0,1,0,0,0,0,0,0,0,7,0,0,0,0,0,7,2],[8,0,0,0,0,0,2,5,0,0,0,0,0,0,10,4,0,0,0,0,4,3,0,0,0,0,0,0,7,8,0,0,0,0,10,6] >;
C12⋊2Dic6 in GAP, Magma, Sage, TeX
C_{12}\rtimes_2{\rm Dic}_6 % in TeX
G:=Group("C12:2Dic6"); // GroupNames label
G:=SmallGroup(288,745);
// by ID
G=gap.SmallGroup(288,745);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-3,56,120,254,219,58,2693,9414]);
// Polycyclic
G:=Group<a,b,c|a^12=b^12=1,c^2=b^6,b*a*b^-1=a^7,c*a*c^-1=a^5,c*b*c^-1=b^-1>;
// generators/relations