Copied to
clipboard

G = (C2×C10).D12order 480 = 25·3·5

8th non-split extension by C2×C10 of D12 acting via D12/C6=C22

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: (C2×C10).8D12, (C2×C30).74D4, C23.D56S3, D6⋊Dic527C2, C10.68(C2×D12), C30.223(C2×D4), C23.50(S3×D5), C30.Q832C2, (C2×Dic5).58D6, (C22×C6).28D10, (C22×C10).42D6, C30.141(C4○D4), C6.80(D42D5), (C2×C30).185C23, (C2×Dic3).57D10, (C22×S3).26D10, C55(C23.21D6), C10.80(D42S3), (C22×Dic15)⋊13C2, C1520(C22.D4), C32(C23.18D10), C22.11(C5⋊D12), (C22×C30).47C22, C2.25(C30.C23), (C6×Dic5).108C22, (C2×Dic15).224C22, (C10×Dic3).107C22, (C2×C3⋊D4).4D5, C6.22(C2×C5⋊D4), (C10×C3⋊D4).4C2, C2.23(C2×C5⋊D12), (C3×C23.D5)⋊6C2, C22.225(C2×S3×D5), (C2×C6).18(C5⋊D4), (S3×C2×C10).46C22, (C2×C6).197(C22×D5), (C2×C10).197(C22×S3), SmallGroup(480,619)

Series: Derived Chief Lower central Upper central

C1C2×C30 — (C2×C10).D12
C1C5C15C30C2×C30C6×Dic5C30.Q8 — (C2×C10).D12
C15C2×C30 — (C2×C10).D12
C1C22C23

Generators and relations for (C2×C10).D12
 G = < a,b,c,d | a2=b10=c12=1, d2=b5, ab=ba, cac-1=ab5, ad=da, cbc-1=dbd-1=b-1, dcd-1=c-1 >

Subgroups: 684 in 156 conjugacy classes, 52 normal (26 characteristic)
C1, C2, C2 [×2], C2 [×3], C3, C4 [×5], C22, C22 [×2], C22 [×5], C5, S3, C6, C6 [×2], C6 [×2], C2×C4 [×7], D4 [×2], C23, C23, C10, C10 [×2], C10 [×3], Dic3 [×3], C12 [×2], D6 [×3], C2×C6, C2×C6 [×2], C2×C6 [×2], C15, C22⋊C4 [×3], C4⋊C4 [×2], C22×C4, C2×D4, Dic5 [×4], C20, C2×C10, C2×C10 [×2], C2×C10 [×5], C2×Dic3, C2×Dic3 [×4], C3⋊D4 [×2], C2×C12 [×2], C22×S3, C22×C6, C5×S3, C30, C30 [×2], C30 [×2], C22.D4, C2×Dic5 [×2], C2×Dic5 [×4], C2×C20, C5×D4 [×2], C22×C10, C22×C10, C4⋊Dic3 [×2], D6⋊C4 [×2], C3×C22⋊C4, C22×Dic3, C2×C3⋊D4, C5×Dic3, C3×Dic5 [×2], Dic15 [×2], S3×C10 [×3], C2×C30, C2×C30 [×2], C2×C30 [×2], C10.D4 [×2], C23.D5, C23.D5 [×2], C22×Dic5, D4×C10, C23.21D6, C6×Dic5 [×2], C10×Dic3, C5×C3⋊D4 [×2], C2×Dic15 [×2], C2×Dic15 [×2], S3×C2×C10, C22×C30, C23.18D10, D6⋊Dic5 [×2], C30.Q8 [×2], C3×C23.D5, C10×C3⋊D4, C22×Dic15, (C2×C10).D12
Quotients: C1, C2 [×7], C22 [×7], S3, D4 [×2], C23, D5, D6 [×3], C2×D4, C4○D4 [×2], D10 [×3], D12 [×2], C22×S3, C22.D4, C5⋊D4 [×2], C22×D5, C2×D12, D42S3 [×2], S3×D5, D42D5 [×2], C2×C5⋊D4, C23.21D6, C5⋊D12 [×2], C2×S3×D5, C23.18D10, C30.C23 [×2], C2×C5⋊D12, (C2×C10).D12

Smallest permutation representation of (C2×C10).D12
On 240 points
Generators in S240
(2 159)(4 161)(6 163)(8 165)(10 167)(12 157)(14 82)(16 84)(18 74)(20 76)(22 78)(24 80)(26 113)(28 115)(30 117)(32 119)(34 109)(36 111)(38 151)(40 153)(42 155)(44 145)(46 147)(48 149)(50 189)(52 191)(54 181)(56 183)(58 185)(60 187)(61 176)(63 178)(65 180)(67 170)(69 172)(71 174)(85 208)(87 210)(89 212)(91 214)(93 216)(95 206)(98 234)(100 236)(102 238)(104 240)(106 230)(108 232)(121 144)(123 134)(125 136)(127 138)(129 140)(131 142)(194 218)(196 220)(198 222)(200 224)(202 226)(204 228)
(1 68 31 45 197 158 171 118 146 221)(2 222 147 119 172 159 198 46 32 69)(3 70 33 47 199 160 173 120 148 223)(4 224 149 109 174 161 200 48 34 71)(5 72 35 37 201 162 175 110 150 225)(6 226 151 111 176 163 202 38 36 61)(7 62 25 39 203 164 177 112 152 227)(8 228 153 113 178 165 204 40 26 63)(9 64 27 41 193 166 179 114 154 217)(10 218 155 115 180 167 194 42 28 65)(11 66 29 43 195 168 169 116 156 219)(12 220 145 117 170 157 196 44 30 67)(13 207 97 182 126 81 96 233 55 137)(14 138 56 234 85 82 127 183 98 208)(15 209 99 184 128 83 86 235 57 139)(16 140 58 236 87 84 129 185 100 210)(17 211 101 186 130 73 88 237 59 141)(18 142 60 238 89 74 131 187 102 212)(19 213 103 188 132 75 90 239 49 143)(20 144 50 240 91 76 121 189 104 214)(21 215 105 190 122 77 92 229 51 133)(22 134 52 230 93 78 123 191 106 216)(23 205 107 192 124 79 94 231 53 135)(24 136 54 232 95 80 125 181 108 206)
(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)
(1 59 158 186)(2 58 159 185)(3 57 160 184)(4 56 161 183)(5 55 162 182)(6 54 163 181)(7 53 164 192)(8 52 165 191)(9 51 166 190)(10 50 167 189)(11 49 168 188)(12 60 157 187)(13 37 81 150)(14 48 82 149)(15 47 83 148)(16 46 84 147)(17 45 73 146)(18 44 74 145)(19 43 75 156)(20 42 76 155)(21 41 77 154)(22 40 78 153)(23 39 79 152)(24 38 80 151)(25 94 112 205)(26 93 113 216)(27 92 114 215)(28 91 115 214)(29 90 116 213)(30 89 117 212)(31 88 118 211)(32 87 119 210)(33 86 120 209)(34 85 109 208)(35 96 110 207)(36 95 111 206)(61 232 176 108)(62 231 177 107)(63 230 178 106)(64 229 179 105)(65 240 180 104)(66 239 169 103)(67 238 170 102)(68 237 171 101)(69 236 172 100)(70 235 173 99)(71 234 174 98)(72 233 175 97)(121 218 144 194)(122 217 133 193)(123 228 134 204)(124 227 135 203)(125 226 136 202)(126 225 137 201)(127 224 138 200)(128 223 139 199)(129 222 140 198)(130 221 141 197)(131 220 142 196)(132 219 143 195)

G:=sub<Sym(240)| (2,159)(4,161)(6,163)(8,165)(10,167)(12,157)(14,82)(16,84)(18,74)(20,76)(22,78)(24,80)(26,113)(28,115)(30,117)(32,119)(34,109)(36,111)(38,151)(40,153)(42,155)(44,145)(46,147)(48,149)(50,189)(52,191)(54,181)(56,183)(58,185)(60,187)(61,176)(63,178)(65,180)(67,170)(69,172)(71,174)(85,208)(87,210)(89,212)(91,214)(93,216)(95,206)(98,234)(100,236)(102,238)(104,240)(106,230)(108,232)(121,144)(123,134)(125,136)(127,138)(129,140)(131,142)(194,218)(196,220)(198,222)(200,224)(202,226)(204,228), (1,68,31,45,197,158,171,118,146,221)(2,222,147,119,172,159,198,46,32,69)(3,70,33,47,199,160,173,120,148,223)(4,224,149,109,174,161,200,48,34,71)(5,72,35,37,201,162,175,110,150,225)(6,226,151,111,176,163,202,38,36,61)(7,62,25,39,203,164,177,112,152,227)(8,228,153,113,178,165,204,40,26,63)(9,64,27,41,193,166,179,114,154,217)(10,218,155,115,180,167,194,42,28,65)(11,66,29,43,195,168,169,116,156,219)(12,220,145,117,170,157,196,44,30,67)(13,207,97,182,126,81,96,233,55,137)(14,138,56,234,85,82,127,183,98,208)(15,209,99,184,128,83,86,235,57,139)(16,140,58,236,87,84,129,185,100,210)(17,211,101,186,130,73,88,237,59,141)(18,142,60,238,89,74,131,187,102,212)(19,213,103,188,132,75,90,239,49,143)(20,144,50,240,91,76,121,189,104,214)(21,215,105,190,122,77,92,229,51,133)(22,134,52,230,93,78,123,191,106,216)(23,205,107,192,124,79,94,231,53,135)(24,136,54,232,95,80,125,181,108,206), (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), (1,59,158,186)(2,58,159,185)(3,57,160,184)(4,56,161,183)(5,55,162,182)(6,54,163,181)(7,53,164,192)(8,52,165,191)(9,51,166,190)(10,50,167,189)(11,49,168,188)(12,60,157,187)(13,37,81,150)(14,48,82,149)(15,47,83,148)(16,46,84,147)(17,45,73,146)(18,44,74,145)(19,43,75,156)(20,42,76,155)(21,41,77,154)(22,40,78,153)(23,39,79,152)(24,38,80,151)(25,94,112,205)(26,93,113,216)(27,92,114,215)(28,91,115,214)(29,90,116,213)(30,89,117,212)(31,88,118,211)(32,87,119,210)(33,86,120,209)(34,85,109,208)(35,96,110,207)(36,95,111,206)(61,232,176,108)(62,231,177,107)(63,230,178,106)(64,229,179,105)(65,240,180,104)(66,239,169,103)(67,238,170,102)(68,237,171,101)(69,236,172,100)(70,235,173,99)(71,234,174,98)(72,233,175,97)(121,218,144,194)(122,217,133,193)(123,228,134,204)(124,227,135,203)(125,226,136,202)(126,225,137,201)(127,224,138,200)(128,223,139,199)(129,222,140,198)(130,221,141,197)(131,220,142,196)(132,219,143,195)>;

G:=Group( (2,159)(4,161)(6,163)(8,165)(10,167)(12,157)(14,82)(16,84)(18,74)(20,76)(22,78)(24,80)(26,113)(28,115)(30,117)(32,119)(34,109)(36,111)(38,151)(40,153)(42,155)(44,145)(46,147)(48,149)(50,189)(52,191)(54,181)(56,183)(58,185)(60,187)(61,176)(63,178)(65,180)(67,170)(69,172)(71,174)(85,208)(87,210)(89,212)(91,214)(93,216)(95,206)(98,234)(100,236)(102,238)(104,240)(106,230)(108,232)(121,144)(123,134)(125,136)(127,138)(129,140)(131,142)(194,218)(196,220)(198,222)(200,224)(202,226)(204,228), (1,68,31,45,197,158,171,118,146,221)(2,222,147,119,172,159,198,46,32,69)(3,70,33,47,199,160,173,120,148,223)(4,224,149,109,174,161,200,48,34,71)(5,72,35,37,201,162,175,110,150,225)(6,226,151,111,176,163,202,38,36,61)(7,62,25,39,203,164,177,112,152,227)(8,228,153,113,178,165,204,40,26,63)(9,64,27,41,193,166,179,114,154,217)(10,218,155,115,180,167,194,42,28,65)(11,66,29,43,195,168,169,116,156,219)(12,220,145,117,170,157,196,44,30,67)(13,207,97,182,126,81,96,233,55,137)(14,138,56,234,85,82,127,183,98,208)(15,209,99,184,128,83,86,235,57,139)(16,140,58,236,87,84,129,185,100,210)(17,211,101,186,130,73,88,237,59,141)(18,142,60,238,89,74,131,187,102,212)(19,213,103,188,132,75,90,239,49,143)(20,144,50,240,91,76,121,189,104,214)(21,215,105,190,122,77,92,229,51,133)(22,134,52,230,93,78,123,191,106,216)(23,205,107,192,124,79,94,231,53,135)(24,136,54,232,95,80,125,181,108,206), (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), (1,59,158,186)(2,58,159,185)(3,57,160,184)(4,56,161,183)(5,55,162,182)(6,54,163,181)(7,53,164,192)(8,52,165,191)(9,51,166,190)(10,50,167,189)(11,49,168,188)(12,60,157,187)(13,37,81,150)(14,48,82,149)(15,47,83,148)(16,46,84,147)(17,45,73,146)(18,44,74,145)(19,43,75,156)(20,42,76,155)(21,41,77,154)(22,40,78,153)(23,39,79,152)(24,38,80,151)(25,94,112,205)(26,93,113,216)(27,92,114,215)(28,91,115,214)(29,90,116,213)(30,89,117,212)(31,88,118,211)(32,87,119,210)(33,86,120,209)(34,85,109,208)(35,96,110,207)(36,95,111,206)(61,232,176,108)(62,231,177,107)(63,230,178,106)(64,229,179,105)(65,240,180,104)(66,239,169,103)(67,238,170,102)(68,237,171,101)(69,236,172,100)(70,235,173,99)(71,234,174,98)(72,233,175,97)(121,218,144,194)(122,217,133,193)(123,228,134,204)(124,227,135,203)(125,226,136,202)(126,225,137,201)(127,224,138,200)(128,223,139,199)(129,222,140,198)(130,221,141,197)(131,220,142,196)(132,219,143,195) );

G=PermutationGroup([(2,159),(4,161),(6,163),(8,165),(10,167),(12,157),(14,82),(16,84),(18,74),(20,76),(22,78),(24,80),(26,113),(28,115),(30,117),(32,119),(34,109),(36,111),(38,151),(40,153),(42,155),(44,145),(46,147),(48,149),(50,189),(52,191),(54,181),(56,183),(58,185),(60,187),(61,176),(63,178),(65,180),(67,170),(69,172),(71,174),(85,208),(87,210),(89,212),(91,214),(93,216),(95,206),(98,234),(100,236),(102,238),(104,240),(106,230),(108,232),(121,144),(123,134),(125,136),(127,138),(129,140),(131,142),(194,218),(196,220),(198,222),(200,224),(202,226),(204,228)], [(1,68,31,45,197,158,171,118,146,221),(2,222,147,119,172,159,198,46,32,69),(3,70,33,47,199,160,173,120,148,223),(4,224,149,109,174,161,200,48,34,71),(5,72,35,37,201,162,175,110,150,225),(6,226,151,111,176,163,202,38,36,61),(7,62,25,39,203,164,177,112,152,227),(8,228,153,113,178,165,204,40,26,63),(9,64,27,41,193,166,179,114,154,217),(10,218,155,115,180,167,194,42,28,65),(11,66,29,43,195,168,169,116,156,219),(12,220,145,117,170,157,196,44,30,67),(13,207,97,182,126,81,96,233,55,137),(14,138,56,234,85,82,127,183,98,208),(15,209,99,184,128,83,86,235,57,139),(16,140,58,236,87,84,129,185,100,210),(17,211,101,186,130,73,88,237,59,141),(18,142,60,238,89,74,131,187,102,212),(19,213,103,188,132,75,90,239,49,143),(20,144,50,240,91,76,121,189,104,214),(21,215,105,190,122,77,92,229,51,133),(22,134,52,230,93,78,123,191,106,216),(23,205,107,192,124,79,94,231,53,135),(24,136,54,232,95,80,125,181,108,206)], [(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)], [(1,59,158,186),(2,58,159,185),(3,57,160,184),(4,56,161,183),(5,55,162,182),(6,54,163,181),(7,53,164,192),(8,52,165,191),(9,51,166,190),(10,50,167,189),(11,49,168,188),(12,60,157,187),(13,37,81,150),(14,48,82,149),(15,47,83,148),(16,46,84,147),(17,45,73,146),(18,44,74,145),(19,43,75,156),(20,42,76,155),(21,41,77,154),(22,40,78,153),(23,39,79,152),(24,38,80,151),(25,94,112,205),(26,93,113,216),(27,92,114,215),(28,91,115,214),(29,90,116,213),(30,89,117,212),(31,88,118,211),(32,87,119,210),(33,86,120,209),(34,85,109,208),(35,96,110,207),(36,95,111,206),(61,232,176,108),(62,231,177,107),(63,230,178,106),(64,229,179,105),(65,240,180,104),(66,239,169,103),(67,238,170,102),(68,237,171,101),(69,236,172,100),(70,235,173,99),(71,234,174,98),(72,233,175,97),(121,218,144,194),(122,217,133,193),(123,228,134,204),(124,227,135,203),(125,226,136,202),(126,225,137,201),(127,224,138,200),(128,223,139,199),(129,222,140,198),(130,221,141,197),(131,220,142,196),(132,219,143,195)])

60 conjugacy classes

class 1 2A2B2C2D2E2F 3 4A4B4C4D4E4F4G5A5B6A6B6C6D6E10A···10F10G10H10I10J10K10L10M10N12A12B12C12D15A15B20A20B20C20D30A···30N
order122222234444444556666610···1010101010101010101212121215152020202030···30
size1111221221220203030303022222442···24444121212122020202044121212124···4

60 irreducible representations

dim11111122222222222444444
type+++++++++++++++-+-++-
imageC1C2C2C2C2C2S3D4D5D6D6C4○D4D10D10D10D12C5⋊D4D42S3S3×D5D42D5C5⋊D12C2×S3×D5C30.C23
kernel(C2×C10).D12D6⋊Dic5C30.Q8C3×C23.D5C10×C3⋊D4C22×Dic15C23.D5C2×C30C2×C3⋊D4C2×Dic5C22×C10C30C2×Dic3C22×S3C22×C6C2×C10C2×C6C10C23C6C22C22C2
# reps12211112221422248224428

Matrix representation of (C2×C10).D12 in GL6(𝔽61)

100000
010000
001000
00206000
000010
000001
,
100000
010000
0060000
0006000
0000044
00001843
,
60460000
4920000
0011500
00375000
00003116
00003930
,
35120000
20260000
0050000
0005000
000010
00001960

G:=sub<GL(6,GF(61))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,20,0,0,0,0,0,60,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,60,0,0,0,0,0,0,60,0,0,0,0,0,0,0,18,0,0,0,0,44,43],[60,49,0,0,0,0,46,2,0,0,0,0,0,0,11,37,0,0,0,0,5,50,0,0,0,0,0,0,31,39,0,0,0,0,16,30],[35,20,0,0,0,0,12,26,0,0,0,0,0,0,50,0,0,0,0,0,0,50,0,0,0,0,0,0,1,19,0,0,0,0,0,60] >;

(C2×C10).D12 in GAP, Magma, Sage, TeX

(C_2\times C_{10}).D_{12}
% in TeX

G:=Group("(C2xC10).D12");
// GroupNames label

G:=SmallGroup(480,619);
// by ID

G=gap.SmallGroup(480,619);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,56,141,120,422,219,1356,18822]);
// Polycyclic

G:=Group<a,b,c,d|a^2=b^10=c^12=1,d^2=b^5,a*b=b*a,c*a*c^-1=a*b^5,a*d=d*a,c*b*c^-1=d*b*d^-1=b^-1,d*c*d^-1=c^-1>;
// generators/relations

׿
×
𝔽