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## G = D4×Dic14order 448 = 26·7

### Direct product of D4 and Dic14

Series: Derived Chief Lower central Upper central

 Derived series C1 — C2×C14 — D4×Dic14
 Chief series C1 — C7 — C14 — C2×C14 — C2×Dic7 — C22×Dic7 — D4×Dic7 — D4×Dic14
 Lower central C7 — C2×C14 — D4×Dic14
 Upper central C1 — C22 — C4×D4

Generators and relations for D4×Dic14
G = < a,b,c,d | a4=b2=c28=1, d2=c14, bab=a-1, ac=ca, ad=da, bc=cb, bd=db, dcd-1=c-1 >

Subgroups: 1140 in 280 conjugacy classes, 123 normal (29 characteristic)
C1, C2, C2, C4, C4, C22, C22, C22, C7, C2×C4, C2×C4, C2×C4, D4, Q8, C23, C14, C14, C42, C42, C22⋊C4, C22⋊C4, C4⋊C4, C4⋊C4, C22×C4, C22×C4, C2×D4, C2×Q8, Dic7, Dic7, C28, C28, C2×C14, C2×C14, C2×C14, C4×D4, C4×D4, C4×Q8, C22⋊Q8, C4⋊Q8, C22×Q8, Dic14, Dic14, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C2×C28, C7×D4, C22×C14, D4×Q8, C4×Dic7, Dic7⋊C4, C4⋊Dic7, C4⋊Dic7, C23.D7, C4×C28, C7×C22⋊C4, C7×C4⋊C4, C2×Dic14, C2×Dic14, C2×Dic14, C22×Dic7, C22×C28, D4×C14, C4×Dic14, C282Q8, C22⋊Dic14, C28⋊Q8, C28.48D4, D4×Dic7, D4×C28, C22×Dic14, D4×Dic14
Quotients: C1, C2, C22, D4, Q8, C23, D7, C2×D4, C2×Q8, C24, D14, C22×D4, C22×Q8, 2- 1+4, Dic14, C22×D7, D4×Q8, C2×Dic14, D4×D7, C23×D7, C22×Dic14, C2×D4×D7, D4.10D14, D4×Dic14

Smallest permutation representation of D4×Dic14
On 224 points
Generators in S224
(1 113 79 175)(2 114 80 176)(3 115 81 177)(4 116 82 178)(5 117 83 179)(6 118 84 180)(7 119 57 181)(8 120 58 182)(9 121 59 183)(10 122 60 184)(11 123 61 185)(12 124 62 186)(13 125 63 187)(14 126 64 188)(15 127 65 189)(16 128 66 190)(17 129 67 191)(18 130 68 192)(19 131 69 193)(20 132 70 194)(21 133 71 195)(22 134 72 196)(23 135 73 169)(24 136 74 170)(25 137 75 171)(26 138 76 172)(27 139 77 173)(28 140 78 174)(29 147 213 110)(30 148 214 111)(31 149 215 112)(32 150 216 85)(33 151 217 86)(34 152 218 87)(35 153 219 88)(36 154 220 89)(37 155 221 90)(38 156 222 91)(39 157 223 92)(40 158 224 93)(41 159 197 94)(42 160 198 95)(43 161 199 96)(44 162 200 97)(45 163 201 98)(46 164 202 99)(47 165 203 100)(48 166 204 101)(49 167 205 102)(50 168 206 103)(51 141 207 104)(52 142 208 105)(53 143 209 106)(54 144 210 107)(55 145 211 108)(56 146 212 109)
(1 15)(2 16)(3 17)(4 18)(5 19)(6 20)(7 21)(8 22)(9 23)(10 24)(11 25)(12 26)(13 27)(14 28)(29 199)(30 200)(31 201)(32 202)(33 203)(34 204)(35 205)(36 206)(37 207)(38 208)(39 209)(40 210)(41 211)(42 212)(43 213)(44 214)(45 215)(46 216)(47 217)(48 218)(49 219)(50 220)(51 221)(52 222)(53 223)(54 224)(55 197)(56 198)(57 71)(58 72)(59 73)(60 74)(61 75)(62 76)(63 77)(64 78)(65 79)(66 80)(67 81)(68 82)(69 83)(70 84)(85 99)(86 100)(87 101)(88 102)(89 103)(90 104)(91 105)(92 106)(93 107)(94 108)(95 109)(96 110)(97 111)(98 112)(113 189)(114 190)(115 191)(116 192)(117 193)(118 194)(119 195)(120 196)(121 169)(122 170)(123 171)(124 172)(125 173)(126 174)(127 175)(128 176)(129 177)(130 178)(131 179)(132 180)(133 181)(134 182)(135 183)(136 184)(137 185)(138 186)(139 187)(140 188)(141 155)(142 156)(143 157)(144 158)(145 159)(146 160)(147 161)(148 162)(149 163)(150 164)(151 165)(152 166)(153 167)(154 168)
(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 86 15 100)(2 85 16 99)(3 112 17 98)(4 111 18 97)(5 110 19 96)(6 109 20 95)(7 108 21 94)(8 107 22 93)(9 106 23 92)(10 105 24 91)(11 104 25 90)(12 103 26 89)(13 102 27 88)(14 101 28 87)(29 131 43 117)(30 130 44 116)(31 129 45 115)(32 128 46 114)(33 127 47 113)(34 126 48 140)(35 125 49 139)(36 124 50 138)(37 123 51 137)(38 122 52 136)(39 121 53 135)(40 120 54 134)(41 119 55 133)(42 118 56 132)(57 145 71 159)(58 144 72 158)(59 143 73 157)(60 142 74 156)(61 141 75 155)(62 168 76 154)(63 167 77 153)(64 166 78 152)(65 165 79 151)(66 164 80 150)(67 163 81 149)(68 162 82 148)(69 161 83 147)(70 160 84 146)(169 223 183 209)(170 222 184 208)(171 221 185 207)(172 220 186 206)(173 219 187 205)(174 218 188 204)(175 217 189 203)(176 216 190 202)(177 215 191 201)(178 214 192 200)(179 213 193 199)(180 212 194 198)(181 211 195 197)(182 210 196 224)

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

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

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

85 conjugacy classes

 class 1 2A 2B 2C 2D 2E 2F 2G 4A 4B 4C 4D 4E 4F 4G 4H 4I 4J 4K 4L ··· 4Q 7A 7B 7C 14A ··· 14I 14J ··· 14U 28A ··· 28L 28M ··· 28AJ order 1 2 2 2 2 2 2 2 4 4 4 4 4 4 4 4 4 4 4 4 ··· 4 7 7 7 14 ··· 14 14 ··· 14 28 ··· 28 28 ··· 28 size 1 1 1 1 2 2 2 2 2 2 2 2 4 4 4 14 14 14 14 28 ··· 28 2 2 2 2 ··· 2 4 ··· 4 2 ··· 2 4 ··· 4

85 irreducible representations

 dim 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 4 4 4 type + + + + + + + + + + - + + + + + + - - + - image C1 C2 C2 C2 C2 C2 C2 C2 C2 D4 Q8 D7 D14 D14 D14 D14 D14 Dic14 2- 1+4 D4×D7 D4.10D14 kernel D4×Dic14 C4×Dic14 C28⋊2Q8 C22⋊Dic14 C28⋊Q8 C28.48D4 D4×Dic7 D4×C28 C22×Dic14 Dic14 C7×D4 C4×D4 C42 C22⋊C4 C4⋊C4 C22×C4 C2×D4 D4 C14 C4 C2 # reps 1 1 1 4 2 2 2 1 2 4 4 3 3 6 3 6 3 24 1 6 6

Matrix representation of D4×Dic14 in GL4(𝔽29) generated by

 28 0 0 0 0 28 0 0 0 0 3 2 0 0 24 26
,
 28 0 0 0 0 28 0 0 0 0 1 0 0 0 26 28
,
 7 8 0 0 17 3 0 0 0 0 28 0 0 0 0 28
,
 19 12 0 0 23 10 0 0 0 0 28 0 0 0 0 28
G:=sub<GL(4,GF(29))| [28,0,0,0,0,28,0,0,0,0,3,24,0,0,2,26],[28,0,0,0,0,28,0,0,0,0,1,26,0,0,0,28],[7,17,0,0,8,3,0,0,0,0,28,0,0,0,0,28],[19,23,0,0,12,10,0,0,0,0,28,0,0,0,0,28] >;

D4×Dic14 in GAP, Magma, Sage, TeX

D_4\times {\rm Dic}_{14}
% in TeX

G:=Group("D4xDic14");
// GroupNames label

G:=SmallGroup(448,990);
// by ID

G=gap.SmallGroup(448,990);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,112,387,675,80,18822]);
// Polycyclic

G:=Group<a,b,c,d|a^4=b^2=c^28=1,d^2=c^14,b*a*b=a^-1,a*c=c*a,a*d=d*a,b*c=c*b,b*d=d*b,d*c*d^-1=c^-1>;
// generators/relations

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