direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C2×D56⋊7C2, D56⋊23C22, C56.62C23, C28.56C24, C23.29D28, D28.21C23, Dic28⋊20C22, Dic14.20C23, (C2×C8)⋊34D14, (C22×C8)⋊8D7, (C2×D56)⋊27C2, C14⋊1(C4○D8), C4.46(C2×D28), (C22×C56)⋊12C2, (C2×C56)⋊45C22, (C2×C28).404D4, C28.291(C2×D4), (C2×C4).101D28, C4.53(C23×D7), C8.51(C22×D7), (C2×Dic28)⋊27C2, C4○D28⋊16C22, C56⋊C2⋊22C22, C22.71(C2×D28), C14.23(C22×D4), C2.25(C22×D28), (C2×C28).797C23, (C22×C14).146D4, (C22×C4).444D14, (C2×D28).229C22, (C22×C28).545C22, (C2×Dic14).257C22, C7⋊1(C2×C4○D8), (C2×C4○D28)⋊13C2, (C2×C56⋊C2)⋊33C2, (C2×C14).179(C2×D4), (C2×C4).737(C22×D7), SmallGroup(448,1194)
Series: Derived ►Chief ►Lower central ►Upper central
Subgroups: 1380 in 266 conjugacy classes, 111 normal (27 characteristic)
C1, C2, C2 [×2], C2 [×6], C4 [×2], C4 [×2], C4 [×4], C22, C22 [×2], C22 [×10], C7, C8 [×4], C2×C4 [×2], C2×C4 [×4], C2×C4 [×10], D4 [×14], Q8 [×6], C23, C23 [×2], D7 [×4], C14, C14 [×2], C14 [×2], C2×C8 [×2], C2×C8 [×4], D8 [×4], SD16 [×8], Q16 [×4], C22×C4, C22×C4 [×2], C2×D4 [×4], C2×Q8 [×2], C4○D4 [×12], Dic7 [×4], C28 [×2], C28 [×2], D14 [×8], C2×C14, C2×C14 [×2], C2×C14 [×2], C22×C8, C2×D8, C2×SD16 [×2], C2×Q16, C4○D8 [×8], C2×C4○D4 [×2], C56 [×4], Dic14 [×4], Dic14 [×2], C4×D7 [×8], D28 [×4], D28 [×2], C2×Dic7 [×2], C7⋊D4 [×8], C2×C28 [×2], C2×C28 [×4], C22×D7 [×2], C22×C14, C2×C4○D8, C56⋊C2 [×8], D56 [×4], Dic28 [×4], C2×C56 [×2], C2×C56 [×4], C2×Dic14 [×2], C2×C4×D7 [×2], C2×D28 [×2], C4○D28 [×8], C4○D28 [×4], C2×C7⋊D4 [×2], C22×C28, C2×C56⋊C2 [×2], C2×D56, D56⋊7C2 [×8], C2×Dic28, C22×C56, C2×C4○D28 [×2], C2×D56⋊7C2
Quotients:
C1, C2 [×15], C22 [×35], D4 [×4], C23 [×15], D7, C2×D4 [×6], C24, D14 [×7], C4○D8 [×2], C22×D4, D28 [×4], C22×D7 [×7], C2×C4○D8, C2×D28 [×6], C23×D7, D56⋊7C2 [×2], C22×D28, C2×D56⋊7C2
Generators and relations
G = < a,b,c,d | a2=b56=c2=d2=1, ab=ba, ac=ca, ad=da, cbc=b-1, bd=db, dcd=b28c >
►On 224 points
Generators in S224
(1 108)(2 109)(3 110)(4 111)(5 112)(6 57)(7 58)(8 59)(9 60)(10 61)(11 62)(12 63)(13 64)(14 65)(15 66)(16 67)(17 68)(18 69)(19 70)(20 71)(21 72)(22 73)(23 74)(24 75)(25 76)(26 77)(27 78)(28 79)(29 80)(30 81)(31 82)(32 83)(33 84)(34 85)(35 86)(36 87)(37 88)(38 89)(39 90)(40 91)(41 92)(42 93)(43 94)(44 95)(45 96)(46 97)(47 98)(48 99)(49 100)(50 101)(51 102)(52 103)(53 104)(54 105)(55 106)(56 107)(113 218)(114 219)(115 220)(116 221)(117 222)(118 223)(119 224)(120 169)(121 170)(122 171)(123 172)(124 173)(125 174)(126 175)(127 176)(128 177)(129 178)(130 179)(131 180)(132 181)(133 182)(134 183)(135 184)(136 185)(137 186)(138 187)(139 188)(140 189)(141 190)(142 191)(143 192)(144 193)(145 194)(146 195)(147 196)(148 197)(149 198)(150 199)(151 200)(152 201)(153 202)(154 203)(155 204)(156 205)(157 206)(158 207)(159 208)(160 209)(161 210)(162 211)(163 212)(164 213)(165 214)(166 215)(167 216)(168 217)
(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)
(1 161)(2 160)(3 159)(4 158)(5 157)(6 156)(7 155)(8 154)(9 153)(10 152)(11 151)(12 150)(13 149)(14 148)(15 147)(16 146)(17 145)(18 144)(19 143)(20 142)(21 141)(22 140)(23 139)(24 138)(25 137)(26 136)(27 135)(28 134)(29 133)(30 132)(31 131)(32 130)(33 129)(34 128)(35 127)(36 126)(37 125)(38 124)(39 123)(40 122)(41 121)(42 120)(43 119)(44 118)(45 117)(46 116)(47 115)(48 114)(49 113)(50 168)(51 167)(52 166)(53 165)(54 164)(55 163)(56 162)(57 205)(58 204)(59 203)(60 202)(61 201)(62 200)(63 199)(64 198)(65 197)(66 196)(67 195)(68 194)(69 193)(70 192)(71 191)(72 190)(73 189)(74 188)(75 187)(76 186)(77 185)(78 184)(79 183)(80 182)(81 181)(82 180)(83 179)(84 178)(85 177)(86 176)(87 175)(88 174)(89 173)(90 172)(91 171)(92 170)(93 169)(94 224)(95 223)(96 222)(97 221)(98 220)(99 219)(100 218)(101 217)(102 216)(103 215)(104 214)(105 213)(106 212)(107 211)(108 210)(109 209)(110 208)(111 207)(112 206)
(113 141)(114 142)(115 143)(116 144)(117 145)(118 146)(119 147)(120 148)(121 149)(122 150)(123 151)(124 152)(125 153)(126 154)(127 155)(128 156)(129 157)(130 158)(131 159)(132 160)(133 161)(134 162)(135 163)(136 164)(137 165)(138 166)(139 167)(140 168)(169 197)(170 198)(171 199)(172 200)(173 201)(174 202)(175 203)(176 204)(177 205)(178 206)(179 207)(180 208)(181 209)(182 210)(183 211)(184 212)(185 213)(186 214)(187 215)(188 216)(189 217)(190 218)(191 219)(192 220)(193 221)(194 222)(195 223)(196 224)
G:=sub<Sym(224)| (1,108)(2,109)(3,110)(4,111)(5,112)(6,57)(7,58)(8,59)(9,60)(10,61)(11,62)(12,63)(13,64)(14,65)(15,66)(16,67)(17,68)(18,69)(19,70)(20,71)(21,72)(22,73)(23,74)(24,75)(25,76)(26,77)(27,78)(28,79)(29,80)(30,81)(31,82)(32,83)(33,84)(34,85)(35,86)(36,87)(37,88)(38,89)(39,90)(40,91)(41,92)(42,93)(43,94)(44,95)(45,96)(46,97)(47,98)(48,99)(49,100)(50,101)(51,102)(52,103)(53,104)(54,105)(55,106)(56,107)(113,218)(114,219)(115,220)(116,221)(117,222)(118,223)(119,224)(120,169)(121,170)(122,171)(123,172)(124,173)(125,174)(126,175)(127,176)(128,177)(129,178)(130,179)(131,180)(132,181)(133,182)(134,183)(135,184)(136,185)(137,186)(138,187)(139,188)(140,189)(141,190)(142,191)(143,192)(144,193)(145,194)(146,195)(147,196)(148,197)(149,198)(150,199)(151,200)(152,201)(153,202)(154,203)(155,204)(156,205)(157,206)(158,207)(159,208)(160,209)(161,210)(162,211)(163,212)(164,213)(165,214)(166,215)(167,216)(168,217), (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), (1,161)(2,160)(3,159)(4,158)(5,157)(6,156)(7,155)(8,154)(9,153)(10,152)(11,151)(12,150)(13,149)(14,148)(15,147)(16,146)(17,145)(18,144)(19,143)(20,142)(21,141)(22,140)(23,139)(24,138)(25,137)(26,136)(27,135)(28,134)(29,133)(30,132)(31,131)(32,130)(33,129)(34,128)(35,127)(36,126)(37,125)(38,124)(39,123)(40,122)(41,121)(42,120)(43,119)(44,118)(45,117)(46,116)(47,115)(48,114)(49,113)(50,168)(51,167)(52,166)(53,165)(54,164)(55,163)(56,162)(57,205)(58,204)(59,203)(60,202)(61,201)(62,200)(63,199)(64,198)(65,197)(66,196)(67,195)(68,194)(69,193)(70,192)(71,191)(72,190)(73,189)(74,188)(75,187)(76,186)(77,185)(78,184)(79,183)(80,182)(81,181)(82,180)(83,179)(84,178)(85,177)(86,176)(87,175)(88,174)(89,173)(90,172)(91,171)(92,170)(93,169)(94,224)(95,223)(96,222)(97,221)(98,220)(99,219)(100,218)(101,217)(102,216)(103,215)(104,214)(105,213)(106,212)(107,211)(108,210)(109,209)(110,208)(111,207)(112,206), (113,141)(114,142)(115,143)(116,144)(117,145)(118,146)(119,147)(120,148)(121,149)(122,150)(123,151)(124,152)(125,153)(126,154)(127,155)(128,156)(129,157)(130,158)(131,159)(132,160)(133,161)(134,162)(135,163)(136,164)(137,165)(138,166)(139,167)(140,168)(169,197)(170,198)(171,199)(172,200)(173,201)(174,202)(175,203)(176,204)(177,205)(178,206)(179,207)(180,208)(181,209)(182,210)(183,211)(184,212)(185,213)(186,214)(187,215)(188,216)(189,217)(190,218)(191,219)(192,220)(193,221)(194,222)(195,223)(196,224)>;
G:=Group( (1,108)(2,109)(3,110)(4,111)(5,112)(6,57)(7,58)(8,59)(9,60)(10,61)(11,62)(12,63)(13,64)(14,65)(15,66)(16,67)(17,68)(18,69)(19,70)(20,71)(21,72)(22,73)(23,74)(24,75)(25,76)(26,77)(27,78)(28,79)(29,80)(30,81)(31,82)(32,83)(33,84)(34,85)(35,86)(36,87)(37,88)(38,89)(39,90)(40,91)(41,92)(42,93)(43,94)(44,95)(45,96)(46,97)(47,98)(48,99)(49,100)(50,101)(51,102)(52,103)(53,104)(54,105)(55,106)(56,107)(113,218)(114,219)(115,220)(116,221)(117,222)(118,223)(119,224)(120,169)(121,170)(122,171)(123,172)(124,173)(125,174)(126,175)(127,176)(128,177)(129,178)(130,179)(131,180)(132,181)(133,182)(134,183)(135,184)(136,185)(137,186)(138,187)(139,188)(140,189)(141,190)(142,191)(143,192)(144,193)(145,194)(146,195)(147,196)(148,197)(149,198)(150,199)(151,200)(152,201)(153,202)(154,203)(155,204)(156,205)(157,206)(158,207)(159,208)(160,209)(161,210)(162,211)(163,212)(164,213)(165,214)(166,215)(167,216)(168,217), (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), (1,161)(2,160)(3,159)(4,158)(5,157)(6,156)(7,155)(8,154)(9,153)(10,152)(11,151)(12,150)(13,149)(14,148)(15,147)(16,146)(17,145)(18,144)(19,143)(20,142)(21,141)(22,140)(23,139)(24,138)(25,137)(26,136)(27,135)(28,134)(29,133)(30,132)(31,131)(32,130)(33,129)(34,128)(35,127)(36,126)(37,125)(38,124)(39,123)(40,122)(41,121)(42,120)(43,119)(44,118)(45,117)(46,116)(47,115)(48,114)(49,113)(50,168)(51,167)(52,166)(53,165)(54,164)(55,163)(56,162)(57,205)(58,204)(59,203)(60,202)(61,201)(62,200)(63,199)(64,198)(65,197)(66,196)(67,195)(68,194)(69,193)(70,192)(71,191)(72,190)(73,189)(74,188)(75,187)(76,186)(77,185)(78,184)(79,183)(80,182)(81,181)(82,180)(83,179)(84,178)(85,177)(86,176)(87,175)(88,174)(89,173)(90,172)(91,171)(92,170)(93,169)(94,224)(95,223)(96,222)(97,221)(98,220)(99,219)(100,218)(101,217)(102,216)(103,215)(104,214)(105,213)(106,212)(107,211)(108,210)(109,209)(110,208)(111,207)(112,206), (113,141)(114,142)(115,143)(116,144)(117,145)(118,146)(119,147)(120,148)(121,149)(122,150)(123,151)(124,152)(125,153)(126,154)(127,155)(128,156)(129,157)(130,158)(131,159)(132,160)(133,161)(134,162)(135,163)(136,164)(137,165)(138,166)(139,167)(140,168)(169,197)(170,198)(171,199)(172,200)(173,201)(174,202)(175,203)(176,204)(177,205)(178,206)(179,207)(180,208)(181,209)(182,210)(183,211)(184,212)(185,213)(186,214)(187,215)(188,216)(189,217)(190,218)(191,219)(192,220)(193,221)(194,222)(195,223)(196,224) );
G=PermutationGroup([(1,108),(2,109),(3,110),(4,111),(5,112),(6,57),(7,58),(8,59),(9,60),(10,61),(11,62),(12,63),(13,64),(14,65),(15,66),(16,67),(17,68),(18,69),(19,70),(20,71),(21,72),(22,73),(23,74),(24,75),(25,76),(26,77),(27,78),(28,79),(29,80),(30,81),(31,82),(32,83),(33,84),(34,85),(35,86),(36,87),(37,88),(38,89),(39,90),(40,91),(41,92),(42,93),(43,94),(44,95),(45,96),(46,97),(47,98),(48,99),(49,100),(50,101),(51,102),(52,103),(53,104),(54,105),(55,106),(56,107),(113,218),(114,219),(115,220),(116,221),(117,222),(118,223),(119,224),(120,169),(121,170),(122,171),(123,172),(124,173),(125,174),(126,175),(127,176),(128,177),(129,178),(130,179),(131,180),(132,181),(133,182),(134,183),(135,184),(136,185),(137,186),(138,187),(139,188),(140,189),(141,190),(142,191),(143,192),(144,193),(145,194),(146,195),(147,196),(148,197),(149,198),(150,199),(151,200),(152,201),(153,202),(154,203),(155,204),(156,205),(157,206),(158,207),(159,208),(160,209),(161,210),(162,211),(163,212),(164,213),(165,214),(166,215),(167,216),(168,217)], [(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)], [(1,161),(2,160),(3,159),(4,158),(5,157),(6,156),(7,155),(8,154),(9,153),(10,152),(11,151),(12,150),(13,149),(14,148),(15,147),(16,146),(17,145),(18,144),(19,143),(20,142),(21,141),(22,140),(23,139),(24,138),(25,137),(26,136),(27,135),(28,134),(29,133),(30,132),(31,131),(32,130),(33,129),(34,128),(35,127),(36,126),(37,125),(38,124),(39,123),(40,122),(41,121),(42,120),(43,119),(44,118),(45,117),(46,116),(47,115),(48,114),(49,113),(50,168),(51,167),(52,166),(53,165),(54,164),(55,163),(56,162),(57,205),(58,204),(59,203),(60,202),(61,201),(62,200),(63,199),(64,198),(65,197),(66,196),(67,195),(68,194),(69,193),(70,192),(71,191),(72,190),(73,189),(74,188),(75,187),(76,186),(77,185),(78,184),(79,183),(80,182),(81,181),(82,180),(83,179),(84,178),(85,177),(86,176),(87,175),(88,174),(89,173),(90,172),(91,171),(92,170),(93,169),(94,224),(95,223),(96,222),(97,221),(98,220),(99,219),(100,218),(101,217),(102,216),(103,215),(104,214),(105,213),(106,212),(107,211),(108,210),(109,209),(110,208),(111,207),(112,206)], [(113,141),(114,142),(115,143),(116,144),(117,145),(118,146),(119,147),(120,148),(121,149),(122,150),(123,151),(124,152),(125,153),(126,154),(127,155),(128,156),(129,157),(130,158),(131,159),(132,160),(133,161),(134,162),(135,163),(136,164),(137,165),(138,166),(139,167),(140,168),(169,197),(170,198),(171,199),(172,200),(173,201),(174,202),(175,203),(176,204),(177,205),(178,206),(179,207),(180,208),(181,209),(182,210),(183,211),(184,212),(185,213),(186,214),(187,215),(188,216),(189,217),(190,218),(191,219),(192,220),(193,221),(194,222),(195,223),(196,224)])
Matrix representation ►G ⊆ GL3(𝔽113) generated by
| 112 | 0 | 0 |
| 0 | 112 | 0 |
| 0 | 0 | 112 |
| 1 | 0 | 0 |
| 0 | 22 | 0 |
| 0 | 0 | 36 |
| 112 | 0 | 0 |
| 0 | 0 | 36 |
| 0 | 22 | 0 |
| 112 | 0 | 0 |
| 0 | 1 | 0 |
| 0 | 0 | 112 |
G:=sub<GL(3,GF(113))| [112,0,0,0,112,0,0,0,112],[1,0,0,0,22,0,0,0,36],[112,0,0,0,0,22,0,36,0],[112,0,0,0,1,0,0,0,112] >;
124 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 2H | 2I | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 7A | 7B | 7C | 8A | ··· | 8H | 14A | ··· | 14U | 28A | ··· | 28X | 56A | ··· | 56AV |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 8 | ··· | 8 | 14 | ··· | 14 | 28 | ··· | 28 | 56 | ··· | 56 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 28 | 28 | 28 | 28 | 1 | 1 | 1 | 1 | 2 | 2 | 28 | 28 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
124 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | D4 | D7 | D14 | D14 | C4○D8 | D28 | D28 | D56⋊7C2 |
| kernel | C2×D56⋊7C2 | C2×C56⋊C2 | C2×D56 | D56⋊7C2 | C2×Dic28 | C22×C56 | C2×C4○D28 | C2×C28 | C22×C14 | C22×C8 | C2×C8 | C22×C4 | C14 | C2×C4 | C23 | C2 |
| # reps | 1 | 2 | 1 | 8 | 1 | 1 | 2 | 3 | 1 | 3 | 18 | 3 | 8 | 18 | 6 | 48 |
In GAP, Magma, Sage, TeX
C_2\times D_{56}\rtimes_7C_2 % in TeX
G:=Group("C2xD56:7C2"); // GroupNames label
G:=SmallGroup(448,1194);
// by ID
G=gap.SmallGroup(448,1194);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,184,675,80,1684,102,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^2=b^56=c^2=d^2=1,a*b=b*a,a*c=c*a,a*d=d*a,c*b*c=b^-1,b*d=d*b,d*c*d=b^28*c>;
// generators/relations
×
⋊
ℤ
𝔽
○
≀