direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C2×C29⋊D4, C58⋊2D4, C23⋊D29, C22⋊2D58, D58⋊3C22, C58.10C23, Dic29⋊2C22, C29⋊3(C2×D4), (C2×C58)⋊3C22, (C22×C58)⋊2C2, (C2×Dic29)⋊4C2, (C22×D29)⋊3C2, C2.10(C22×D29), SmallGroup(464,44)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C2×C29⋊D4
G = < a,b,c,d | a2=b29=c4=d2=1, ab=ba, ac=ca, ad=da, cbc-1=dbd=b-1, dcd=c-1 >
Subgroups: 602 in 54 conjugacy classes, 27 normal (11 characteristic)
C1, C2, C2, C2, C4, C22, C22, C22, C2×C4, D4, C23, C23, C2×D4, C29, D29, C58, C58, C58, Dic29, D58, D58, C2×C58, C2×C58, C2×C58, C2×Dic29, C29⋊D4, C22×D29, C22×C58, C2×C29⋊D4
Quotients: C1, C2, C22, D4, C23, C2×D4, D29, D58, C29⋊D4, C22×D29, C2×C29⋊D4
►On 232 points
Generators in S232
(1 146)(2 147)(3 148)(4 149)(5 150)(6 151)(7 152)(8 153)(9 154)(10 155)(11 156)(12 157)(13 158)(14 159)(15 160)(16 161)(17 162)(18 163)(19 164)(20 165)(21 166)(22 167)(23 168)(24 169)(25 170)(26 171)(27 172)(28 173)(29 174)(30 117)(31 118)(32 119)(33 120)(34 121)(35 122)(36 123)(37 124)(38 125)(39 126)(40 127)(41 128)(42 129)(43 130)(44 131)(45 132)(46 133)(47 134)(48 135)(49 136)(50 137)(51 138)(52 139)(53 140)(54 141)(55 142)(56 143)(57 144)(58 145)(59 204)(60 205)(61 206)(62 207)(63 208)(64 209)(65 210)(66 211)(67 212)(68 213)(69 214)(70 215)(71 216)(72 217)(73 218)(74 219)(75 220)(76 221)(77 222)(78 223)(79 224)(80 225)(81 226)(82 227)(83 228)(84 229)(85 230)(86 231)(87 232)(88 175)(89 176)(90 177)(91 178)(92 179)(93 180)(94 181)(95 182)(96 183)(97 184)(98 185)(99 186)(100 187)(101 188)(102 189)(103 190)(104 191)(105 192)(106 193)(107 194)(108 195)(109 196)(110 197)(111 198)(112 199)(113 200)(114 201)(115 202)(116 203)
(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)
(1 59 30 88)(2 87 31 116)(3 86 32 115)(4 85 33 114)(5 84 34 113)(6 83 35 112)(7 82 36 111)(8 81 37 110)(9 80 38 109)(10 79 39 108)(11 78 40 107)(12 77 41 106)(13 76 42 105)(14 75 43 104)(15 74 44 103)(16 73 45 102)(17 72 46 101)(18 71 47 100)(19 70 48 99)(20 69 49 98)(21 68 50 97)(22 67 51 96)(23 66 52 95)(24 65 53 94)(25 64 54 93)(26 63 55 92)(27 62 56 91)(28 61 57 90)(29 60 58 89)(117 175 146 204)(118 203 147 232)(119 202 148 231)(120 201 149 230)(121 200 150 229)(122 199 151 228)(123 198 152 227)(124 197 153 226)(125 196 154 225)(126 195 155 224)(127 194 156 223)(128 193 157 222)(129 192 158 221)(130 191 159 220)(131 190 160 219)(132 189 161 218)(133 188 162 217)(134 187 163 216)(135 186 164 215)(136 185 165 214)(137 184 166 213)(138 183 167 212)(139 182 168 211)(140 181 169 210)(141 180 170 209)(142 179 171 208)(143 178 172 207)(144 177 173 206)(145 176 174 205)
(2 29)(3 28)(4 27)(5 26)(6 25)(7 24)(8 23)(9 22)(10 21)(11 20)(12 19)(13 18)(14 17)(15 16)(31 58)(32 57)(33 56)(34 55)(35 54)(36 53)(37 52)(38 51)(39 50)(40 49)(41 48)(42 47)(43 46)(44 45)(59 88)(60 116)(61 115)(62 114)(63 113)(64 112)(65 111)(66 110)(67 109)(68 108)(69 107)(70 106)(71 105)(72 104)(73 103)(74 102)(75 101)(76 100)(77 99)(78 98)(79 97)(80 96)(81 95)(82 94)(83 93)(84 92)(85 91)(86 90)(87 89)(118 145)(119 144)(120 143)(121 142)(122 141)(123 140)(124 139)(125 138)(126 137)(127 136)(128 135)(129 134)(130 133)(131 132)(147 174)(148 173)(149 172)(150 171)(151 170)(152 169)(153 168)(154 167)(155 166)(156 165)(157 164)(158 163)(159 162)(160 161)(175 204)(176 232)(177 231)(178 230)(179 229)(180 228)(181 227)(182 226)(183 225)(184 224)(185 223)(186 222)(187 221)(188 220)(189 219)(190 218)(191 217)(192 216)(193 215)(194 214)(195 213)(196 212)(197 211)(198 210)(199 209)(200 208)(201 207)(202 206)(203 205)
G:=sub<Sym(232)| (1,146)(2,147)(3,148)(4,149)(5,150)(6,151)(7,152)(8,153)(9,154)(10,155)(11,156)(12,157)(13,158)(14,159)(15,160)(16,161)(17,162)(18,163)(19,164)(20,165)(21,166)(22,167)(23,168)(24,169)(25,170)(26,171)(27,172)(28,173)(29,174)(30,117)(31,118)(32,119)(33,120)(34,121)(35,122)(36,123)(37,124)(38,125)(39,126)(40,127)(41,128)(42,129)(43,130)(44,131)(45,132)(46,133)(47,134)(48,135)(49,136)(50,137)(51,138)(52,139)(53,140)(54,141)(55,142)(56,143)(57,144)(58,145)(59,204)(60,205)(61,206)(62,207)(63,208)(64,209)(65,210)(66,211)(67,212)(68,213)(69,214)(70,215)(71,216)(72,217)(73,218)(74,219)(75,220)(76,221)(77,222)(78,223)(79,224)(80,225)(81,226)(82,227)(83,228)(84,229)(85,230)(86,231)(87,232)(88,175)(89,176)(90,177)(91,178)(92,179)(93,180)(94,181)(95,182)(96,183)(97,184)(98,185)(99,186)(100,187)(101,188)(102,189)(103,190)(104,191)(105,192)(106,193)(107,194)(108,195)(109,196)(110,197)(111,198)(112,199)(113,200)(114,201)(115,202)(116,203), (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), (1,59,30,88)(2,87,31,116)(3,86,32,115)(4,85,33,114)(5,84,34,113)(6,83,35,112)(7,82,36,111)(8,81,37,110)(9,80,38,109)(10,79,39,108)(11,78,40,107)(12,77,41,106)(13,76,42,105)(14,75,43,104)(15,74,44,103)(16,73,45,102)(17,72,46,101)(18,71,47,100)(19,70,48,99)(20,69,49,98)(21,68,50,97)(22,67,51,96)(23,66,52,95)(24,65,53,94)(25,64,54,93)(26,63,55,92)(27,62,56,91)(28,61,57,90)(29,60,58,89)(117,175,146,204)(118,203,147,232)(119,202,148,231)(120,201,149,230)(121,200,150,229)(122,199,151,228)(123,198,152,227)(124,197,153,226)(125,196,154,225)(126,195,155,224)(127,194,156,223)(128,193,157,222)(129,192,158,221)(130,191,159,220)(131,190,160,219)(132,189,161,218)(133,188,162,217)(134,187,163,216)(135,186,164,215)(136,185,165,214)(137,184,166,213)(138,183,167,212)(139,182,168,211)(140,181,169,210)(141,180,170,209)(142,179,171,208)(143,178,172,207)(144,177,173,206)(145,176,174,205), (2,29)(3,28)(4,27)(5,26)(6,25)(7,24)(8,23)(9,22)(10,21)(11,20)(12,19)(13,18)(14,17)(15,16)(31,58)(32,57)(33,56)(34,55)(35,54)(36,53)(37,52)(38,51)(39,50)(40,49)(41,48)(42,47)(43,46)(44,45)(59,88)(60,116)(61,115)(62,114)(63,113)(64,112)(65,111)(66,110)(67,109)(68,108)(69,107)(70,106)(71,105)(72,104)(73,103)(74,102)(75,101)(76,100)(77,99)(78,98)(79,97)(80,96)(81,95)(82,94)(83,93)(84,92)(85,91)(86,90)(87,89)(118,145)(119,144)(120,143)(121,142)(122,141)(123,140)(124,139)(125,138)(126,137)(127,136)(128,135)(129,134)(130,133)(131,132)(147,174)(148,173)(149,172)(150,171)(151,170)(152,169)(153,168)(154,167)(155,166)(156,165)(157,164)(158,163)(159,162)(160,161)(175,204)(176,232)(177,231)(178,230)(179,229)(180,228)(181,227)(182,226)(183,225)(184,224)(185,223)(186,222)(187,221)(188,220)(189,219)(190,218)(191,217)(192,216)(193,215)(194,214)(195,213)(196,212)(197,211)(198,210)(199,209)(200,208)(201,207)(202,206)(203,205)>;
G:=Group( (1,146)(2,147)(3,148)(4,149)(5,150)(6,151)(7,152)(8,153)(9,154)(10,155)(11,156)(12,157)(13,158)(14,159)(15,160)(16,161)(17,162)(18,163)(19,164)(20,165)(21,166)(22,167)(23,168)(24,169)(25,170)(26,171)(27,172)(28,173)(29,174)(30,117)(31,118)(32,119)(33,120)(34,121)(35,122)(36,123)(37,124)(38,125)(39,126)(40,127)(41,128)(42,129)(43,130)(44,131)(45,132)(46,133)(47,134)(48,135)(49,136)(50,137)(51,138)(52,139)(53,140)(54,141)(55,142)(56,143)(57,144)(58,145)(59,204)(60,205)(61,206)(62,207)(63,208)(64,209)(65,210)(66,211)(67,212)(68,213)(69,214)(70,215)(71,216)(72,217)(73,218)(74,219)(75,220)(76,221)(77,222)(78,223)(79,224)(80,225)(81,226)(82,227)(83,228)(84,229)(85,230)(86,231)(87,232)(88,175)(89,176)(90,177)(91,178)(92,179)(93,180)(94,181)(95,182)(96,183)(97,184)(98,185)(99,186)(100,187)(101,188)(102,189)(103,190)(104,191)(105,192)(106,193)(107,194)(108,195)(109,196)(110,197)(111,198)(112,199)(113,200)(114,201)(115,202)(116,203), (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), (1,59,30,88)(2,87,31,116)(3,86,32,115)(4,85,33,114)(5,84,34,113)(6,83,35,112)(7,82,36,111)(8,81,37,110)(9,80,38,109)(10,79,39,108)(11,78,40,107)(12,77,41,106)(13,76,42,105)(14,75,43,104)(15,74,44,103)(16,73,45,102)(17,72,46,101)(18,71,47,100)(19,70,48,99)(20,69,49,98)(21,68,50,97)(22,67,51,96)(23,66,52,95)(24,65,53,94)(25,64,54,93)(26,63,55,92)(27,62,56,91)(28,61,57,90)(29,60,58,89)(117,175,146,204)(118,203,147,232)(119,202,148,231)(120,201,149,230)(121,200,150,229)(122,199,151,228)(123,198,152,227)(124,197,153,226)(125,196,154,225)(126,195,155,224)(127,194,156,223)(128,193,157,222)(129,192,158,221)(130,191,159,220)(131,190,160,219)(132,189,161,218)(133,188,162,217)(134,187,163,216)(135,186,164,215)(136,185,165,214)(137,184,166,213)(138,183,167,212)(139,182,168,211)(140,181,169,210)(141,180,170,209)(142,179,171,208)(143,178,172,207)(144,177,173,206)(145,176,174,205), (2,29)(3,28)(4,27)(5,26)(6,25)(7,24)(8,23)(9,22)(10,21)(11,20)(12,19)(13,18)(14,17)(15,16)(31,58)(32,57)(33,56)(34,55)(35,54)(36,53)(37,52)(38,51)(39,50)(40,49)(41,48)(42,47)(43,46)(44,45)(59,88)(60,116)(61,115)(62,114)(63,113)(64,112)(65,111)(66,110)(67,109)(68,108)(69,107)(70,106)(71,105)(72,104)(73,103)(74,102)(75,101)(76,100)(77,99)(78,98)(79,97)(80,96)(81,95)(82,94)(83,93)(84,92)(85,91)(86,90)(87,89)(118,145)(119,144)(120,143)(121,142)(122,141)(123,140)(124,139)(125,138)(126,137)(127,136)(128,135)(129,134)(130,133)(131,132)(147,174)(148,173)(149,172)(150,171)(151,170)(152,169)(153,168)(154,167)(155,166)(156,165)(157,164)(158,163)(159,162)(160,161)(175,204)(176,232)(177,231)(178,230)(179,229)(180,228)(181,227)(182,226)(183,225)(184,224)(185,223)(186,222)(187,221)(188,220)(189,219)(190,218)(191,217)(192,216)(193,215)(194,214)(195,213)(196,212)(197,211)(198,210)(199,209)(200,208)(201,207)(202,206)(203,205) );
G=PermutationGroup([[(1,146),(2,147),(3,148),(4,149),(5,150),(6,151),(7,152),(8,153),(9,154),(10,155),(11,156),(12,157),(13,158),(14,159),(15,160),(16,161),(17,162),(18,163),(19,164),(20,165),(21,166),(22,167),(23,168),(24,169),(25,170),(26,171),(27,172),(28,173),(29,174),(30,117),(31,118),(32,119),(33,120),(34,121),(35,122),(36,123),(37,124),(38,125),(39,126),(40,127),(41,128),(42,129),(43,130),(44,131),(45,132),(46,133),(47,134),(48,135),(49,136),(50,137),(51,138),(52,139),(53,140),(54,141),(55,142),(56,143),(57,144),(58,145),(59,204),(60,205),(61,206),(62,207),(63,208),(64,209),(65,210),(66,211),(67,212),(68,213),(69,214),(70,215),(71,216),(72,217),(73,218),(74,219),(75,220),(76,221),(77,222),(78,223),(79,224),(80,225),(81,226),(82,227),(83,228),(84,229),(85,230),(86,231),(87,232),(88,175),(89,176),(90,177),(91,178),(92,179),(93,180),(94,181),(95,182),(96,183),(97,184),(98,185),(99,186),(100,187),(101,188),(102,189),(103,190),(104,191),(105,192),(106,193),(107,194),(108,195),(109,196),(110,197),(111,198),(112,199),(113,200),(114,201),(115,202),(116,203)], [(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)], [(1,59,30,88),(2,87,31,116),(3,86,32,115),(4,85,33,114),(5,84,34,113),(6,83,35,112),(7,82,36,111),(8,81,37,110),(9,80,38,109),(10,79,39,108),(11,78,40,107),(12,77,41,106),(13,76,42,105),(14,75,43,104),(15,74,44,103),(16,73,45,102),(17,72,46,101),(18,71,47,100),(19,70,48,99),(20,69,49,98),(21,68,50,97),(22,67,51,96),(23,66,52,95),(24,65,53,94),(25,64,54,93),(26,63,55,92),(27,62,56,91),(28,61,57,90),(29,60,58,89),(117,175,146,204),(118,203,147,232),(119,202,148,231),(120,201,149,230),(121,200,150,229),(122,199,151,228),(123,198,152,227),(124,197,153,226),(125,196,154,225),(126,195,155,224),(127,194,156,223),(128,193,157,222),(129,192,158,221),(130,191,159,220),(131,190,160,219),(132,189,161,218),(133,188,162,217),(134,187,163,216),(135,186,164,215),(136,185,165,214),(137,184,166,213),(138,183,167,212),(139,182,168,211),(140,181,169,210),(141,180,170,209),(142,179,171,208),(143,178,172,207),(144,177,173,206),(145,176,174,205)], [(2,29),(3,28),(4,27),(5,26),(6,25),(7,24),(8,23),(9,22),(10,21),(11,20),(12,19),(13,18),(14,17),(15,16),(31,58),(32,57),(33,56),(34,55),(35,54),(36,53),(37,52),(38,51),(39,50),(40,49),(41,48),(42,47),(43,46),(44,45),(59,88),(60,116),(61,115),(62,114),(63,113),(64,112),(65,111),(66,110),(67,109),(68,108),(69,107),(70,106),(71,105),(72,104),(73,103),(74,102),(75,101),(76,100),(77,99),(78,98),(79,97),(80,96),(81,95),(82,94),(83,93),(84,92),(85,91),(86,90),(87,89),(118,145),(119,144),(120,143),(121,142),(122,141),(123,140),(124,139),(125,138),(126,137),(127,136),(128,135),(129,134),(130,133),(131,132),(147,174),(148,173),(149,172),(150,171),(151,170),(152,169),(153,168),(154,167),(155,166),(156,165),(157,164),(158,163),(159,162),(160,161),(175,204),(176,232),(177,231),(178,230),(179,229),(180,228),(181,227),(182,226),(183,225),(184,224),(185,223),(186,222),(187,221),(188,220),(189,219),(190,218),(191,217),(192,216),(193,215),(194,214),(195,213),(196,212),(197,211),(198,210),(199,209),(200,208),(201,207),(202,206),(203,205)]])
122 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 4A | 4B | 29A | ··· | 29N | 58A | ··· | 58CT |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 29 | ··· | 29 | 58 | ··· | 58 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 58 | 58 | 58 | 58 | 2 | ··· | 2 | 2 | ··· | 2 |
122 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | + | + | + | |
| image | C1 | C2 | C2 | C2 | C2 | D4 | D29 | D58 | C29⋊D4 |
| kernel | C2×C29⋊D4 | C2×Dic29 | C29⋊D4 | C22×D29 | C22×C58 | C58 | C23 | C22 | C2 |
| # reps | 1 | 1 | 4 | 1 | 1 | 2 | 14 | 42 | 56 |
Matrix representation of C2×C29⋊D4 ►in GL4(𝔽233) generated by
| 232 | 0 | 0 | 0 |
| 0 | 232 | 0 | 0 |
| 0 | 0 | 232 | 0 |
| 0 | 0 | 0 | 232 |
| 122 | 232 | 0 | 0 |
| 1 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 |
| 122 | 232 | 0 | 0 |
| 0 | 0 | 232 | 120 |
| 0 | 0 | 66 | 1 |
| 1 | 0 | 0 | 0 |
| 122 | 232 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 167 | 232 |
G:=sub<GL(4,GF(233))| [232,0,0,0,0,232,0,0,0,0,232,0,0,0,0,232],[122,1,0,0,232,0,0,0,0,0,1,0,0,0,0,1],[1,122,0,0,0,232,0,0,0,0,232,66,0,0,120,1],[1,122,0,0,0,232,0,0,0,0,1,167,0,0,0,232] >;
C2×C29⋊D4 in GAP, Magma, Sage, TeX
C_2\times C_{29}\rtimes D_4 % in TeX
G:=Group("C2xC29:D4"); // GroupNames label
G:=SmallGroup(464,44);
// by ID
G=gap.SmallGroup(464,44);
# by ID
G:=PCGroup([5,-2,-2,-2,-2,-29,182,11204]);
// Polycyclic
G:=Group<a,b,c,d|a^2=b^29=c^4=d^2=1,a*b=b*a,a*c=c*a,a*d=d*a,c*b*c^-1=d*b*d=b^-1,d*c*d=c^-1>;
// generators/relations