direct product, metabelian, supersoluble, monomial, A-group, 2-hyperelementary
Aliases: C22×D59, C59⋊C23, C118⋊C22, (C2×C118)⋊3C2, SmallGroup(472,11)
Series: Derived ►Chief ►Lower central ►Upper central
| C59 — C22×D59 |
Generators and relations for C22×D59
G = < a,b,c,d | a2=b2=c59=d2=1, ab=ba, ac=ca, ad=da, bc=cb, bd=db, dcd=c-1 >
Smallest permutation representation of C22×D59
►On 236 points
Generators in S236
(1 226)(2 227)(3 228)(4 229)(5 230)(6 231)(7 232)(8 233)(9 234)(10 235)(11 236)(12 178)(13 179)(14 180)(15 181)(16 182)(17 183)(18 184)(19 185)(20 186)(21 187)(22 188)(23 189)(24 190)(25 191)(26 192)(27 193)(28 194)(29 195)(30 196)(31 197)(32 198)(33 199)(34 200)(35 201)(36 202)(37 203)(38 204)(39 205)(40 206)(41 207)(42 208)(43 209)(44 210)(45 211)(46 212)(47 213)(48 214)(49 215)(50 216)(51 217)(52 218)(53 219)(54 220)(55 221)(56 222)(57 223)(58 224)(59 225)(60 122)(61 123)(62 124)(63 125)(64 126)(65 127)(66 128)(67 129)(68 130)(69 131)(70 132)(71 133)(72 134)(73 135)(74 136)(75 137)(76 138)(77 139)(78 140)(79 141)(80 142)(81 143)(82 144)(83 145)(84 146)(85 147)(86 148)(87 149)(88 150)(89 151)(90 152)(91 153)(92 154)(93 155)(94 156)(95 157)(96 158)(97 159)(98 160)(99 161)(100 162)(101 163)(102 164)(103 165)(104 166)(105 167)(106 168)(107 169)(108 170)(109 171)(110 172)(111 173)(112 174)(113 175)(114 176)(115 177)(116 119)(117 120)(118 121)
(1 87)(2 88)(3 89)(4 90)(5 91)(6 92)(7 93)(8 94)(9 95)(10 96)(11 97)(12 98)(13 99)(14 100)(15 101)(16 102)(17 103)(18 104)(19 105)(20 106)(21 107)(22 108)(23 109)(24 110)(25 111)(26 112)(27 113)(28 114)(29 115)(30 116)(31 117)(32 118)(33 60)(34 61)(35 62)(36 63)(37 64)(38 65)(39 66)(40 67)(41 68)(42 69)(43 70)(44 71)(45 72)(46 73)(47 74)(48 75)(49 76)(50 77)(51 78)(52 79)(53 80)(54 81)(55 82)(56 83)(57 84)(58 85)(59 86)(119 196)(120 197)(121 198)(122 199)(123 200)(124 201)(125 202)(126 203)(127 204)(128 205)(129 206)(130 207)(131 208)(132 209)(133 210)(134 211)(135 212)(136 213)(137 214)(138 215)(139 216)(140 217)(141 218)(142 219)(143 220)(144 221)(145 222)(146 223)(147 224)(148 225)(149 226)(150 227)(151 228)(152 229)(153 230)(154 231)(155 232)(156 233)(157 234)(158 235)(159 236)(160 178)(161 179)(162 180)(163 181)(164 182)(165 183)(166 184)(167 185)(168 186)(169 187)(170 188)(171 189)(172 190)(173 191)(174 192)(175 193)(176 194)(177 195)
(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)
(1 148)(2 147)(3 146)(4 145)(5 144)(6 143)(7 142)(8 141)(9 140)(10 139)(11 138)(12 137)(13 136)(14 135)(15 134)(16 133)(17 132)(18 131)(19 130)(20 129)(21 128)(22 127)(23 126)(24 125)(25 124)(26 123)(27 122)(28 121)(29 120)(30 119)(31 177)(32 176)(33 175)(34 174)(35 173)(36 172)(37 171)(38 170)(39 169)(40 168)(41 167)(42 166)(43 165)(44 164)(45 163)(46 162)(47 161)(48 160)(49 159)(50 158)(51 157)(52 156)(53 155)(54 154)(55 153)(56 152)(57 151)(58 150)(59 149)(60 193)(61 192)(62 191)(63 190)(64 189)(65 188)(66 187)(67 186)(68 185)(69 184)(70 183)(71 182)(72 181)(73 180)(74 179)(75 178)(76 236)(77 235)(78 234)(79 233)(80 232)(81 231)(82 230)(83 229)(84 228)(85 227)(86 226)(87 225)(88 224)(89 223)(90 222)(91 221)(92 220)(93 219)(94 218)(95 217)(96 216)(97 215)(98 214)(99 213)(100 212)(101 211)(102 210)(103 209)(104 208)(105 207)(106 206)(107 205)(108 204)(109 203)(110 202)(111 201)(112 200)(113 199)(114 198)(115 197)(116 196)(117 195)(118 194)
G:=sub<Sym(236)| (1,226)(2,227)(3,228)(4,229)(5,230)(6,231)(7,232)(8,233)(9,234)(10,235)(11,236)(12,178)(13,179)(14,180)(15,181)(16,182)(17,183)(18,184)(19,185)(20,186)(21,187)(22,188)(23,189)(24,190)(25,191)(26,192)(27,193)(28,194)(29,195)(30,196)(31,197)(32,198)(33,199)(34,200)(35,201)(36,202)(37,203)(38,204)(39,205)(40,206)(41,207)(42,208)(43,209)(44,210)(45,211)(46,212)(47,213)(48,214)(49,215)(50,216)(51,217)(52,218)(53,219)(54,220)(55,221)(56,222)(57,223)(58,224)(59,225)(60,122)(61,123)(62,124)(63,125)(64,126)(65,127)(66,128)(67,129)(68,130)(69,131)(70,132)(71,133)(72,134)(73,135)(74,136)(75,137)(76,138)(77,139)(78,140)(79,141)(80,142)(81,143)(82,144)(83,145)(84,146)(85,147)(86,148)(87,149)(88,150)(89,151)(90,152)(91,153)(92,154)(93,155)(94,156)(95,157)(96,158)(97,159)(98,160)(99,161)(100,162)(101,163)(102,164)(103,165)(104,166)(105,167)(106,168)(107,169)(108,170)(109,171)(110,172)(111,173)(112,174)(113,175)(114,176)(115,177)(116,119)(117,120)(118,121), (1,87)(2,88)(3,89)(4,90)(5,91)(6,92)(7,93)(8,94)(9,95)(10,96)(11,97)(12,98)(13,99)(14,100)(15,101)(16,102)(17,103)(18,104)(19,105)(20,106)(21,107)(22,108)(23,109)(24,110)(25,111)(26,112)(27,113)(28,114)(29,115)(30,116)(31,117)(32,118)(33,60)(34,61)(35,62)(36,63)(37,64)(38,65)(39,66)(40,67)(41,68)(42,69)(43,70)(44,71)(45,72)(46,73)(47,74)(48,75)(49,76)(50,77)(51,78)(52,79)(53,80)(54,81)(55,82)(56,83)(57,84)(58,85)(59,86)(119,196)(120,197)(121,198)(122,199)(123,200)(124,201)(125,202)(126,203)(127,204)(128,205)(129,206)(130,207)(131,208)(132,209)(133,210)(134,211)(135,212)(136,213)(137,214)(138,215)(139,216)(140,217)(141,218)(142,219)(143,220)(144,221)(145,222)(146,223)(147,224)(148,225)(149,226)(150,227)(151,228)(152,229)(153,230)(154,231)(155,232)(156,233)(157,234)(158,235)(159,236)(160,178)(161,179)(162,180)(163,181)(164,182)(165,183)(166,184)(167,185)(168,186)(169,187)(170,188)(171,189)(172,190)(173,191)(174,192)(175,193)(176,194)(177,195), (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), (1,148)(2,147)(3,146)(4,145)(5,144)(6,143)(7,142)(8,141)(9,140)(10,139)(11,138)(12,137)(13,136)(14,135)(15,134)(16,133)(17,132)(18,131)(19,130)(20,129)(21,128)(22,127)(23,126)(24,125)(25,124)(26,123)(27,122)(28,121)(29,120)(30,119)(31,177)(32,176)(33,175)(34,174)(35,173)(36,172)(37,171)(38,170)(39,169)(40,168)(41,167)(42,166)(43,165)(44,164)(45,163)(46,162)(47,161)(48,160)(49,159)(50,158)(51,157)(52,156)(53,155)(54,154)(55,153)(56,152)(57,151)(58,150)(59,149)(60,193)(61,192)(62,191)(63,190)(64,189)(65,188)(66,187)(67,186)(68,185)(69,184)(70,183)(71,182)(72,181)(73,180)(74,179)(75,178)(76,236)(77,235)(78,234)(79,233)(80,232)(81,231)(82,230)(83,229)(84,228)(85,227)(86,226)(87,225)(88,224)(89,223)(90,222)(91,221)(92,220)(93,219)(94,218)(95,217)(96,216)(97,215)(98,214)(99,213)(100,212)(101,211)(102,210)(103,209)(104,208)(105,207)(106,206)(107,205)(108,204)(109,203)(110,202)(111,201)(112,200)(113,199)(114,198)(115,197)(116,196)(117,195)(118,194)>;
G:=Group( (1,226)(2,227)(3,228)(4,229)(5,230)(6,231)(7,232)(8,233)(9,234)(10,235)(11,236)(12,178)(13,179)(14,180)(15,181)(16,182)(17,183)(18,184)(19,185)(20,186)(21,187)(22,188)(23,189)(24,190)(25,191)(26,192)(27,193)(28,194)(29,195)(30,196)(31,197)(32,198)(33,199)(34,200)(35,201)(36,202)(37,203)(38,204)(39,205)(40,206)(41,207)(42,208)(43,209)(44,210)(45,211)(46,212)(47,213)(48,214)(49,215)(50,216)(51,217)(52,218)(53,219)(54,220)(55,221)(56,222)(57,223)(58,224)(59,225)(60,122)(61,123)(62,124)(63,125)(64,126)(65,127)(66,128)(67,129)(68,130)(69,131)(70,132)(71,133)(72,134)(73,135)(74,136)(75,137)(76,138)(77,139)(78,140)(79,141)(80,142)(81,143)(82,144)(83,145)(84,146)(85,147)(86,148)(87,149)(88,150)(89,151)(90,152)(91,153)(92,154)(93,155)(94,156)(95,157)(96,158)(97,159)(98,160)(99,161)(100,162)(101,163)(102,164)(103,165)(104,166)(105,167)(106,168)(107,169)(108,170)(109,171)(110,172)(111,173)(112,174)(113,175)(114,176)(115,177)(116,119)(117,120)(118,121), (1,87)(2,88)(3,89)(4,90)(5,91)(6,92)(7,93)(8,94)(9,95)(10,96)(11,97)(12,98)(13,99)(14,100)(15,101)(16,102)(17,103)(18,104)(19,105)(20,106)(21,107)(22,108)(23,109)(24,110)(25,111)(26,112)(27,113)(28,114)(29,115)(30,116)(31,117)(32,118)(33,60)(34,61)(35,62)(36,63)(37,64)(38,65)(39,66)(40,67)(41,68)(42,69)(43,70)(44,71)(45,72)(46,73)(47,74)(48,75)(49,76)(50,77)(51,78)(52,79)(53,80)(54,81)(55,82)(56,83)(57,84)(58,85)(59,86)(119,196)(120,197)(121,198)(122,199)(123,200)(124,201)(125,202)(126,203)(127,204)(128,205)(129,206)(130,207)(131,208)(132,209)(133,210)(134,211)(135,212)(136,213)(137,214)(138,215)(139,216)(140,217)(141,218)(142,219)(143,220)(144,221)(145,222)(146,223)(147,224)(148,225)(149,226)(150,227)(151,228)(152,229)(153,230)(154,231)(155,232)(156,233)(157,234)(158,235)(159,236)(160,178)(161,179)(162,180)(163,181)(164,182)(165,183)(166,184)(167,185)(168,186)(169,187)(170,188)(171,189)(172,190)(173,191)(174,192)(175,193)(176,194)(177,195), (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), (1,148)(2,147)(3,146)(4,145)(5,144)(6,143)(7,142)(8,141)(9,140)(10,139)(11,138)(12,137)(13,136)(14,135)(15,134)(16,133)(17,132)(18,131)(19,130)(20,129)(21,128)(22,127)(23,126)(24,125)(25,124)(26,123)(27,122)(28,121)(29,120)(30,119)(31,177)(32,176)(33,175)(34,174)(35,173)(36,172)(37,171)(38,170)(39,169)(40,168)(41,167)(42,166)(43,165)(44,164)(45,163)(46,162)(47,161)(48,160)(49,159)(50,158)(51,157)(52,156)(53,155)(54,154)(55,153)(56,152)(57,151)(58,150)(59,149)(60,193)(61,192)(62,191)(63,190)(64,189)(65,188)(66,187)(67,186)(68,185)(69,184)(70,183)(71,182)(72,181)(73,180)(74,179)(75,178)(76,236)(77,235)(78,234)(79,233)(80,232)(81,231)(82,230)(83,229)(84,228)(85,227)(86,226)(87,225)(88,224)(89,223)(90,222)(91,221)(92,220)(93,219)(94,218)(95,217)(96,216)(97,215)(98,214)(99,213)(100,212)(101,211)(102,210)(103,209)(104,208)(105,207)(106,206)(107,205)(108,204)(109,203)(110,202)(111,201)(112,200)(113,199)(114,198)(115,197)(116,196)(117,195)(118,194) );
G=PermutationGroup([[(1,226),(2,227),(3,228),(4,229),(5,230),(6,231),(7,232),(8,233),(9,234),(10,235),(11,236),(12,178),(13,179),(14,180),(15,181),(16,182),(17,183),(18,184),(19,185),(20,186),(21,187),(22,188),(23,189),(24,190),(25,191),(26,192),(27,193),(28,194),(29,195),(30,196),(31,197),(32,198),(33,199),(34,200),(35,201),(36,202),(37,203),(38,204),(39,205),(40,206),(41,207),(42,208),(43,209),(44,210),(45,211),(46,212),(47,213),(48,214),(49,215),(50,216),(51,217),(52,218),(53,219),(54,220),(55,221),(56,222),(57,223),(58,224),(59,225),(60,122),(61,123),(62,124),(63,125),(64,126),(65,127),(66,128),(67,129),(68,130),(69,131),(70,132),(71,133),(72,134),(73,135),(74,136),(75,137),(76,138),(77,139),(78,140),(79,141),(80,142),(81,143),(82,144),(83,145),(84,146),(85,147),(86,148),(87,149),(88,150),(89,151),(90,152),(91,153),(92,154),(93,155),(94,156),(95,157),(96,158),(97,159),(98,160),(99,161),(100,162),(101,163),(102,164),(103,165),(104,166),(105,167),(106,168),(107,169),(108,170),(109,171),(110,172),(111,173),(112,174),(113,175),(114,176),(115,177),(116,119),(117,120),(118,121)], [(1,87),(2,88),(3,89),(4,90),(5,91),(6,92),(7,93),(8,94),(9,95),(10,96),(11,97),(12,98),(13,99),(14,100),(15,101),(16,102),(17,103),(18,104),(19,105),(20,106),(21,107),(22,108),(23,109),(24,110),(25,111),(26,112),(27,113),(28,114),(29,115),(30,116),(31,117),(32,118),(33,60),(34,61),(35,62),(36,63),(37,64),(38,65),(39,66),(40,67),(41,68),(42,69),(43,70),(44,71),(45,72),(46,73),(47,74),(48,75),(49,76),(50,77),(51,78),(52,79),(53,80),(54,81),(55,82),(56,83),(57,84),(58,85),(59,86),(119,196),(120,197),(121,198),(122,199),(123,200),(124,201),(125,202),(126,203),(127,204),(128,205),(129,206),(130,207),(131,208),(132,209),(133,210),(134,211),(135,212),(136,213),(137,214),(138,215),(139,216),(140,217),(141,218),(142,219),(143,220),(144,221),(145,222),(146,223),(147,224),(148,225),(149,226),(150,227),(151,228),(152,229),(153,230),(154,231),(155,232),(156,233),(157,234),(158,235),(159,236),(160,178),(161,179),(162,180),(163,181),(164,182),(165,183),(166,184),(167,185),(168,186),(169,187),(170,188),(171,189),(172,190),(173,191),(174,192),(175,193),(176,194),(177,195)], [(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)], [(1,148),(2,147),(3,146),(4,145),(5,144),(6,143),(7,142),(8,141),(9,140),(10,139),(11,138),(12,137),(13,136),(14,135),(15,134),(16,133),(17,132),(18,131),(19,130),(20,129),(21,128),(22,127),(23,126),(24,125),(25,124),(26,123),(27,122),(28,121),(29,120),(30,119),(31,177),(32,176),(33,175),(34,174),(35,173),(36,172),(37,171),(38,170),(39,169),(40,168),(41,167),(42,166),(43,165),(44,164),(45,163),(46,162),(47,161),(48,160),(49,159),(50,158),(51,157),(52,156),(53,155),(54,154),(55,153),(56,152),(57,151),(58,150),(59,149),(60,193),(61,192),(62,191),(63,190),(64,189),(65,188),(66,187),(67,186),(68,185),(69,184),(70,183),(71,182),(72,181),(73,180),(74,179),(75,178),(76,236),(77,235),(78,234),(79,233),(80,232),(81,231),(82,230),(83,229),(84,228),(85,227),(86,226),(87,225),(88,224),(89,223),(90,222),(91,221),(92,220),(93,219),(94,218),(95,217),(96,216),(97,215),(98,214),(99,213),(100,212),(101,211),(102,210),(103,209),(104,208),(105,207),(106,206),(107,205),(108,204),(109,203),(110,202),(111,201),(112,200),(113,199),(114,198),(115,197),(116,196),(117,195),(118,194)]])
124 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 59A | ··· | 59AC | 118A | ··· | 118CI |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 59 | ··· | 59 | 118 | ··· | 118 |
| size | 1 | 1 | 1 | 1 | 59 | 59 | 59 | 59 | 2 | ··· | 2 | 2 | ··· | 2 |
124 irreducible representations
| dim | 1 | 1 | 1 | 2 | 2 |
| type | + | + | + | + | + |
| image | C1 | C2 | C2 | D59 | D118 |
| kernel | C22×D59 | D118 | C2×C118 | C22 | C2 |
| # reps | 1 | 6 | 1 | 29 | 87 |
Matrix representation of C22×D59 ►in GL4(𝔽709) generated by
| 708 | 0 | 0 | 0 |
| 0 | 708 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 708 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 31 | 1 |
| 0 | 0 | 591 | 568 |
| 708 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 568 | 708 |
| 0 | 0 | 28 | 141 |
G:=sub<GL(4,GF(709))| [708,0,0,0,0,708,0,0,0,0,1,0,0,0,0,1],[708,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1],[1,0,0,0,0,1,0,0,0,0,31,591,0,0,1,568],[708,0,0,0,0,1,0,0,0,0,568,28,0,0,708,141] >;
C22×D59 in GAP, Magma, Sage, TeX
C_2^2\times D_{59} % in TeX
G:=Group("C2^2xD59"); // GroupNames label
G:=SmallGroup(472,11);
// by ID
G=gap.SmallGroup(472,11);
# by ID
G:=PCGroup([4,-2,-2,-2,-59,7427]);
// Polycyclic
G:=Group<a,b,c,d|a^2=b^2=c^59=d^2=1,a*b=b*a,a*c=c*a,a*d=d*a,b*c=c*b,b*d=d*b,d*c*d=c^-1>;
// generators/relations
Export