metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.7Dic7, C42.270D14, C28.26M4(2), C28⋊C8⋊5C2, (C4×C28).12C4, (C2×C42).12D7, (C22×C28).24C4, C7⋊4(C42.6C4), C4.8(C4.Dic7), C28.249(C4○D4), C4.133(C4○D28), (C4×C28).331C22, (C2×C28).844C23, (C22×C4).393D14, C42.D7⋊20C2, (C2×C14).26M4(2), C14.39(C2×M4(2)), (C22×C4).11Dic7, C23.27(C2×Dic7), C28.55D4.15C2, C14.40(C42⋊C2), C22.6(C4.Dic7), (C22×C28).554C22, C22.35(C22×Dic7), C2.5(C23.21D14), (C2×C4×C28).20C2, (C2×C28).277(C2×C4), C2.7(C2×C4.Dic7), (C2×C7⋊C8).199C22, (C2×C4).59(C2×Dic7), (C2×C4).786(C22×D7), (C2×C14).173(C22×C4), (C22×C14).132(C2×C4), SmallGroup(448,460)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.7Dic7
G = < a,b,c,d | a4=b4=1, c14=a2, d2=a2c7, ab=ba, ac=ca, dad-1=a-1b2, bc=cb, dbd-1=a2b, dcd-1=c13 >
Subgroups: 260 in 110 conjugacy classes, 63 normal (41 characteristic)
C1, C2, C2, C4, C4, C22, C22, C22, C7, C8, C2×C4, C2×C4, C23, C14, C14, C42, C2×C8, C22×C4, C28, C28, C2×C14, C2×C14, C2×C14, C8⋊C4, C22⋊C8, C4⋊C8, C2×C42, C7⋊C8, C2×C28, C2×C28, C22×C14, C42.6C4, C2×C7⋊C8, C4×C28, C22×C28, C42.D7, C28⋊C8, C28.55D4, C2×C4×C28, C42.7Dic7
Quotients: C1, C2, C4, C22, C2×C4, C23, D7, M4(2), C22×C4, C4○D4, Dic7, D14, C42⋊C2, C2×M4(2), C2×Dic7, C22×D7, C42.6C4, C4.Dic7, C4○D28, C22×Dic7, C2×C4.Dic7, C23.21D14, C42.7Dic7
►On 224 points
Generators in S224
(1 8 15 22)(2 9 16 23)(3 10 17 24)(4 11 18 25)(5 12 19 26)(6 13 20 27)(7 14 21 28)(29 69 43 83)(30 70 44 84)(31 71 45 57)(32 72 46 58)(33 73 47 59)(34 74 48 60)(35 75 49 61)(36 76 50 62)(37 77 51 63)(38 78 52 64)(39 79 53 65)(40 80 54 66)(41 81 55 67)(42 82 56 68)(85 173 99 187)(86 174 100 188)(87 175 101 189)(88 176 102 190)(89 177 103 191)(90 178 104 192)(91 179 105 193)(92 180 106 194)(93 181 107 195)(94 182 108 196)(95 183 109 169)(96 184 110 170)(97 185 111 171)(98 186 112 172)(113 120 127 134)(114 121 128 135)(115 122 129 136)(116 123 130 137)(117 124 131 138)(118 125 132 139)(119 126 133 140)(141 148 155 162)(142 149 156 163)(143 150 157 164)(144 151 158 165)(145 152 159 166)(146 153 160 167)(147 154 161 168)(197 204 211 218)(198 205 212 219)(199 206 213 220)(200 207 214 221)(201 208 215 222)(202 209 216 223)(203 210 217 224)
(1 124 152 207)(2 125 153 208)(3 126 154 209)(4 127 155 210)(5 128 156 211)(6 129 157 212)(7 130 158 213)(8 131 159 214)(9 132 160 215)(10 133 161 216)(11 134 162 217)(12 135 163 218)(13 136 164 219)(14 137 165 220)(15 138 166 221)(16 139 167 222)(17 140 168 223)(18 113 141 224)(19 114 142 197)(20 115 143 198)(21 116 144 199)(22 117 145 200)(23 118 146 201)(24 119 147 202)(25 120 148 203)(26 121 149 204)(27 122 150 205)(28 123 151 206)(29 178 76 111)(30 179 77 112)(31 180 78 85)(32 181 79 86)(33 182 80 87)(34 183 81 88)(35 184 82 89)(36 185 83 90)(37 186 84 91)(38 187 57 92)(39 188 58 93)(40 189 59 94)(41 190 60 95)(42 191 61 96)(43 192 62 97)(44 193 63 98)(45 194 64 99)(46 195 65 100)(47 196 66 101)(48 169 67 102)(49 170 68 103)(50 171 69 104)(51 172 70 105)(52 173 71 106)(53 174 72 107)(54 175 73 108)(55 176 74 109)(56 177 75 110)
(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)
(1 101 22 94 15 87 8 108)(2 86 23 107 16 100 9 93)(3 99 24 92 17 85 10 106)(4 112 25 105 18 98 11 91)(5 97 26 90 19 111 12 104)(6 110 27 103 20 96 13 89)(7 95 28 88 21 109 14 102)(29 121 50 114 43 135 36 128)(30 134 51 127 44 120 37 113)(31 119 52 140 45 133 38 126)(32 132 53 125 46 118 39 139)(33 117 54 138 47 131 40 124)(34 130 55 123 48 116 41 137)(35 115 56 136 49 129 42 122)(57 209 78 202 71 223 64 216)(58 222 79 215 72 208 65 201)(59 207 80 200 73 221 66 214)(60 220 81 213 74 206 67 199)(61 205 82 198 75 219 68 212)(62 218 83 211 76 204 69 197)(63 203 84 224 77 217 70 210)(141 193 162 186 155 179 148 172)(142 178 163 171 156 192 149 185)(143 191 164 184 157 177 150 170)(144 176 165 169 158 190 151 183)(145 189 166 182 159 175 152 196)(146 174 167 195 160 188 153 181)(147 187 168 180 161 173 154 194)
G:=sub<Sym(224)| (1,8,15,22)(2,9,16,23)(3,10,17,24)(4,11,18,25)(5,12,19,26)(6,13,20,27)(7,14,21,28)(29,69,43,83)(30,70,44,84)(31,71,45,57)(32,72,46,58)(33,73,47,59)(34,74,48,60)(35,75,49,61)(36,76,50,62)(37,77,51,63)(38,78,52,64)(39,79,53,65)(40,80,54,66)(41,81,55,67)(42,82,56,68)(85,173,99,187)(86,174,100,188)(87,175,101,189)(88,176,102,190)(89,177,103,191)(90,178,104,192)(91,179,105,193)(92,180,106,194)(93,181,107,195)(94,182,108,196)(95,183,109,169)(96,184,110,170)(97,185,111,171)(98,186,112,172)(113,120,127,134)(114,121,128,135)(115,122,129,136)(116,123,130,137)(117,124,131,138)(118,125,132,139)(119,126,133,140)(141,148,155,162)(142,149,156,163)(143,150,157,164)(144,151,158,165)(145,152,159,166)(146,153,160,167)(147,154,161,168)(197,204,211,218)(198,205,212,219)(199,206,213,220)(200,207,214,221)(201,208,215,222)(202,209,216,223)(203,210,217,224), (1,124,152,207)(2,125,153,208)(3,126,154,209)(4,127,155,210)(5,128,156,211)(6,129,157,212)(7,130,158,213)(8,131,159,214)(9,132,160,215)(10,133,161,216)(11,134,162,217)(12,135,163,218)(13,136,164,219)(14,137,165,220)(15,138,166,221)(16,139,167,222)(17,140,168,223)(18,113,141,224)(19,114,142,197)(20,115,143,198)(21,116,144,199)(22,117,145,200)(23,118,146,201)(24,119,147,202)(25,120,148,203)(26,121,149,204)(27,122,150,205)(28,123,151,206)(29,178,76,111)(30,179,77,112)(31,180,78,85)(32,181,79,86)(33,182,80,87)(34,183,81,88)(35,184,82,89)(36,185,83,90)(37,186,84,91)(38,187,57,92)(39,188,58,93)(40,189,59,94)(41,190,60,95)(42,191,61,96)(43,192,62,97)(44,193,63,98)(45,194,64,99)(46,195,65,100)(47,196,66,101)(48,169,67,102)(49,170,68,103)(50,171,69,104)(51,172,70,105)(52,173,71,106)(53,174,72,107)(54,175,73,108)(55,176,74,109)(56,177,75,110), (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), (1,101,22,94,15,87,8,108)(2,86,23,107,16,100,9,93)(3,99,24,92,17,85,10,106)(4,112,25,105,18,98,11,91)(5,97,26,90,19,111,12,104)(6,110,27,103,20,96,13,89)(7,95,28,88,21,109,14,102)(29,121,50,114,43,135,36,128)(30,134,51,127,44,120,37,113)(31,119,52,140,45,133,38,126)(32,132,53,125,46,118,39,139)(33,117,54,138,47,131,40,124)(34,130,55,123,48,116,41,137)(35,115,56,136,49,129,42,122)(57,209,78,202,71,223,64,216)(58,222,79,215,72,208,65,201)(59,207,80,200,73,221,66,214)(60,220,81,213,74,206,67,199)(61,205,82,198,75,219,68,212)(62,218,83,211,76,204,69,197)(63,203,84,224,77,217,70,210)(141,193,162,186,155,179,148,172)(142,178,163,171,156,192,149,185)(143,191,164,184,157,177,150,170)(144,176,165,169,158,190,151,183)(145,189,166,182,159,175,152,196)(146,174,167,195,160,188,153,181)(147,187,168,180,161,173,154,194)>;
G:=Group( (1,8,15,22)(2,9,16,23)(3,10,17,24)(4,11,18,25)(5,12,19,26)(6,13,20,27)(7,14,21,28)(29,69,43,83)(30,70,44,84)(31,71,45,57)(32,72,46,58)(33,73,47,59)(34,74,48,60)(35,75,49,61)(36,76,50,62)(37,77,51,63)(38,78,52,64)(39,79,53,65)(40,80,54,66)(41,81,55,67)(42,82,56,68)(85,173,99,187)(86,174,100,188)(87,175,101,189)(88,176,102,190)(89,177,103,191)(90,178,104,192)(91,179,105,193)(92,180,106,194)(93,181,107,195)(94,182,108,196)(95,183,109,169)(96,184,110,170)(97,185,111,171)(98,186,112,172)(113,120,127,134)(114,121,128,135)(115,122,129,136)(116,123,130,137)(117,124,131,138)(118,125,132,139)(119,126,133,140)(141,148,155,162)(142,149,156,163)(143,150,157,164)(144,151,158,165)(145,152,159,166)(146,153,160,167)(147,154,161,168)(197,204,211,218)(198,205,212,219)(199,206,213,220)(200,207,214,221)(201,208,215,222)(202,209,216,223)(203,210,217,224), (1,124,152,207)(2,125,153,208)(3,126,154,209)(4,127,155,210)(5,128,156,211)(6,129,157,212)(7,130,158,213)(8,131,159,214)(9,132,160,215)(10,133,161,216)(11,134,162,217)(12,135,163,218)(13,136,164,219)(14,137,165,220)(15,138,166,221)(16,139,167,222)(17,140,168,223)(18,113,141,224)(19,114,142,197)(20,115,143,198)(21,116,144,199)(22,117,145,200)(23,118,146,201)(24,119,147,202)(25,120,148,203)(26,121,149,204)(27,122,150,205)(28,123,151,206)(29,178,76,111)(30,179,77,112)(31,180,78,85)(32,181,79,86)(33,182,80,87)(34,183,81,88)(35,184,82,89)(36,185,83,90)(37,186,84,91)(38,187,57,92)(39,188,58,93)(40,189,59,94)(41,190,60,95)(42,191,61,96)(43,192,62,97)(44,193,63,98)(45,194,64,99)(46,195,65,100)(47,196,66,101)(48,169,67,102)(49,170,68,103)(50,171,69,104)(51,172,70,105)(52,173,71,106)(53,174,72,107)(54,175,73,108)(55,176,74,109)(56,177,75,110), (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), (1,101,22,94,15,87,8,108)(2,86,23,107,16,100,9,93)(3,99,24,92,17,85,10,106)(4,112,25,105,18,98,11,91)(5,97,26,90,19,111,12,104)(6,110,27,103,20,96,13,89)(7,95,28,88,21,109,14,102)(29,121,50,114,43,135,36,128)(30,134,51,127,44,120,37,113)(31,119,52,140,45,133,38,126)(32,132,53,125,46,118,39,139)(33,117,54,138,47,131,40,124)(34,130,55,123,48,116,41,137)(35,115,56,136,49,129,42,122)(57,209,78,202,71,223,64,216)(58,222,79,215,72,208,65,201)(59,207,80,200,73,221,66,214)(60,220,81,213,74,206,67,199)(61,205,82,198,75,219,68,212)(62,218,83,211,76,204,69,197)(63,203,84,224,77,217,70,210)(141,193,162,186,155,179,148,172)(142,178,163,171,156,192,149,185)(143,191,164,184,157,177,150,170)(144,176,165,169,158,190,151,183)(145,189,166,182,159,175,152,196)(146,174,167,195,160,188,153,181)(147,187,168,180,161,173,154,194) );
G=PermutationGroup([[(1,8,15,22),(2,9,16,23),(3,10,17,24),(4,11,18,25),(5,12,19,26),(6,13,20,27),(7,14,21,28),(29,69,43,83),(30,70,44,84),(31,71,45,57),(32,72,46,58),(33,73,47,59),(34,74,48,60),(35,75,49,61),(36,76,50,62),(37,77,51,63),(38,78,52,64),(39,79,53,65),(40,80,54,66),(41,81,55,67),(42,82,56,68),(85,173,99,187),(86,174,100,188),(87,175,101,189),(88,176,102,190),(89,177,103,191),(90,178,104,192),(91,179,105,193),(92,180,106,194),(93,181,107,195),(94,182,108,196),(95,183,109,169),(96,184,110,170),(97,185,111,171),(98,186,112,172),(113,120,127,134),(114,121,128,135),(115,122,129,136),(116,123,130,137),(117,124,131,138),(118,125,132,139),(119,126,133,140),(141,148,155,162),(142,149,156,163),(143,150,157,164),(144,151,158,165),(145,152,159,166),(146,153,160,167),(147,154,161,168),(197,204,211,218),(198,205,212,219),(199,206,213,220),(200,207,214,221),(201,208,215,222),(202,209,216,223),(203,210,217,224)], [(1,124,152,207),(2,125,153,208),(3,126,154,209),(4,127,155,210),(5,128,156,211),(6,129,157,212),(7,130,158,213),(8,131,159,214),(9,132,160,215),(10,133,161,216),(11,134,162,217),(12,135,163,218),(13,136,164,219),(14,137,165,220),(15,138,166,221),(16,139,167,222),(17,140,168,223),(18,113,141,224),(19,114,142,197),(20,115,143,198),(21,116,144,199),(22,117,145,200),(23,118,146,201),(24,119,147,202),(25,120,148,203),(26,121,149,204),(27,122,150,205),(28,123,151,206),(29,178,76,111),(30,179,77,112),(31,180,78,85),(32,181,79,86),(33,182,80,87),(34,183,81,88),(35,184,82,89),(36,185,83,90),(37,186,84,91),(38,187,57,92),(39,188,58,93),(40,189,59,94),(41,190,60,95),(42,191,61,96),(43,192,62,97),(44,193,63,98),(45,194,64,99),(46,195,65,100),(47,196,66,101),(48,169,67,102),(49,170,68,103),(50,171,69,104),(51,172,70,105),(52,173,71,106),(53,174,72,107),(54,175,73,108),(55,176,74,109),(56,177,75,110)], [(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)], [(1,101,22,94,15,87,8,108),(2,86,23,107,16,100,9,93),(3,99,24,92,17,85,10,106),(4,112,25,105,18,98,11,91),(5,97,26,90,19,111,12,104),(6,110,27,103,20,96,13,89),(7,95,28,88,21,109,14,102),(29,121,50,114,43,135,36,128),(30,134,51,127,44,120,37,113),(31,119,52,140,45,133,38,126),(32,132,53,125,46,118,39,139),(33,117,54,138,47,131,40,124),(34,130,55,123,48,116,41,137),(35,115,56,136,49,129,42,122),(57,209,78,202,71,223,64,216),(58,222,79,215,72,208,65,201),(59,207,80,200,73,221,66,214),(60,220,81,213,74,206,67,199),(61,205,82,198,75,219,68,212),(62,218,83,211,76,204,69,197),(63,203,84,224,77,217,70,210),(141,193,162,186,155,179,148,172),(142,178,163,171,156,192,149,185),(143,191,164,184,157,177,150,170),(144,176,165,169,158,190,151,183),(145,189,166,182,159,175,152,196),(146,174,167,195,160,188,153,181),(147,187,168,180,161,173,154,194)]])
124 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | 4B | 4C | 4D | 4E | ··· | 4N | 7A | 7B | 7C | 8A | ··· | 8H | 14A | ··· | 14U | 28A | ··· | 28BT |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 7 | 7 | 7 | 8 | ··· | 8 | 14 | ··· | 14 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 1 | 1 | 1 | 1 | 2 | ··· | 2 | 2 | 2 | 2 | 28 | ··· | 28 | 2 | ··· | 2 | 2 | ··· | 2 |
124 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | + | - | + | - | + | ||||||||
| image | C1 | C2 | C2 | C2 | C2 | C4 | C4 | D7 | M4(2) | C4○D4 | M4(2) | Dic7 | D14 | Dic7 | D14 | C4.Dic7 | C4○D28 | C4.Dic7 |
| kernel | C42.7Dic7 | C42.D7 | C28⋊C8 | C28.55D4 | C2×C4×C28 | C4×C28 | C22×C28 | C2×C42 | C28 | C28 | C2×C14 | C42 | C42 | C22×C4 | C22×C4 | C4 | C4 | C22 |
| # reps | 1 | 2 | 2 | 2 | 1 | 4 | 4 | 3 | 4 | 4 | 4 | 6 | 6 | 6 | 3 | 24 | 24 | 24 |
Matrix representation of C42.7Dic7 ►in GL4(𝔽113) generated by
| 98 | 0 | 0 | 0 |
| 0 | 98 | 0 | 0 |
| 0 | 0 | 15 | 0 |
| 0 | 0 | 0 | 98 |
| 96 | 67 | 0 | 0 |
| 80 | 17 | 0 | 0 |
| 0 | 0 | 112 | 0 |
| 0 | 0 | 0 | 1 |
| 92 | 15 | 0 | 0 |
| 82 | 76 | 0 | 0 |
| 0 | 0 | 98 | 0 |
| 0 | 0 | 0 | 98 |
| 106 | 8 | 0 | 0 |
| 24 | 7 | 0 | 0 |
| 0 | 0 | 0 | 1 |
| 0 | 0 | 98 | 0 |
G:=sub<GL(4,GF(113))| [98,0,0,0,0,98,0,0,0,0,15,0,0,0,0,98],[96,80,0,0,67,17,0,0,0,0,112,0,0,0,0,1],[92,82,0,0,15,76,0,0,0,0,98,0,0,0,0,98],[106,24,0,0,8,7,0,0,0,0,0,98,0,0,1,0] >;
C42.7Dic7 in GAP, Magma, Sage, TeX
C_4^2._7{\rm Dic}_7 % in TeX
G:=Group("C4^2.7Dic7"); // GroupNames label
G:=SmallGroup(448,460);
// by ID
G=gap.SmallGroup(448,460);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,56,253,758,100,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=1,c^14=a^2,d^2=a^2*c^7,a*b=b*a,a*c=c*a,d*a*d^-1=a^-1*b^2,b*c=c*b,d*b*d^-1=a^2*b,d*c*d^-1=c^13>;
// generators/relations