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G = C28⋊(C4○D4)  order 448 = 26·7

2nd semidirect product of C28 and C4○D4 acting via C4○D4/C22=C22

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C28⋊Q8⋊18C2, C28⋊9(C4○D4), C4⋊D4⋊25D7, C4⋊3(D4⋊2D7), C28⋊D4⋊14C2, C28⋊7D4⋊31C2, C22.1(D4×D7), C4⋊C4.175D14, (D4×Dic7)⋊14C2, (C2×Dic7)⋊13D4, Dic7.5(C2×D4), D28⋊C4⋊19C2, Dic7⋊2(C4○D4), Dic7⋊D4⋊7C2, Dic7⋊4D4⋊5C2, (C2×D4).150D14, (C2×C28).34C23, C22⋊C4.45D14, C14.59(C22×D4), (C2×C14).140C24, D14⋊C4.57C22, (C22×C4).366D14, Dic7.D4⋊16C2, (C2×D28).141C22, (D4×C14).114C22, Dic7⋊C4.12C22, C4⋊Dic7.203C22, (C22×C14).11C23, C7⋊3(C22.26C24), (C22×D7).59C23, C23.178(C22×D7), C22.161(C23×D7), C23.D7.18C22, (C22×C28).235C22, (C4×Dic7).254C22, (C2×Dic7).223C23, (C2×Dic14).150C22, (C22×Dic7).221C22, C2.32(C2×D4×D7), (C2×C4×Dic7)⋊7C2, (C7×C4⋊D4)⋊5C2, C2.33(D7×C4○D4), (C2×C14).3(C2×D4), (C2×D4⋊2D7)⋊8C2, C14.79(C2×C4○D4), (C2×C4×D7).79C22, C2.30(C2×D4⋊2D7), (C2×C4).34(C22×D7), (C7×C4⋊C4).136C22, (C2×C7⋊D4).23C22, (C7×C22⋊C4).5C22, SmallGroup(448,1049)

Series: Derived ►Chief ►Lower central ►Upper central

Derived series
C1 — C2×C14 — C28⋊(C4○D4)
Chief series
C1 — C7 — C14 — C2×C14 — C2×Dic7 — C22×Dic7 — C2×D4⋊2D7 — C28⋊(C4○D4)
Lower central
C7 — C2×C14 — C28⋊(C4○D4)

Subgroups: 1420 in 310 conjugacy classes, 109 normal (43 characteristic)
C1, C2 [×3], C2 [×6], C4 [×2], C4 [×12], C22, C22 [×2], C22 [×14], C7, C2×C4 [×2], C2×C4 [×2], C2×C4 [×22], D4 [×20], Q8 [×4], C23, C23 [×2], C23 [×2], D7 [×2], C14 [×3], C14 [×4], C42 [×4], C22⋊C4 [×2], C22⋊C4 [×6], C4⋊C4, C4⋊C4 [×3], C22×C4, C22×C4 [×6], C2×D4, C2×D4 [×2], C2×D4 [×7], C2×Q8 [×2], C4○D4 [×8], Dic7 [×6], Dic7 [×3], C28 [×2], C28 [×3], D14 [×6], C2×C14, C2×C14 [×2], C2×C14 [×8], C2×C42, C4×D4 [×4], C4⋊D4, C4⋊D4 [×3], C4.4D4 [×2], C4⋊1D4, C4⋊Q8, C2×C4○D4 [×2], Dic14 [×4], C4×D7 [×4], D28 [×2], C2×Dic7 [×4], C2×Dic7 [×6], C2×Dic7 [×6], C7⋊D4 [×12], C2×C28 [×2], C2×C28 [×2], C2×C28 [×2], C7×D4 [×6], C22×D7 [×2], C22×C14, C22×C14 [×2], C22.26C24, C4×Dic7 [×4], Dic7⋊C4 [×2], C4⋊Dic7, D14⋊C4 [×4], C23.D7 [×2], C7×C22⋊C4 [×2], C7×C4⋊C4, C2×Dic14 [×2], C2×C4×D7 [×2], C2×D28, D4⋊2D7 [×8], C22×Dic7 [×2], C22×Dic7 [×2], C2×C7⋊D4 [×6], C22×C28, D4×C14, D4×C14 [×2], Dic7⋊4D4 [×2], Dic7.D4 [×2], C28⋊Q8, D28⋊C4, C2×C4×Dic7, C28⋊7D4, D4×Dic7, Dic7⋊D4 [×2], C28⋊D4, C7×C4⋊D4, C2×D4⋊2D7 [×2], C28⋊(C4○D4)

Quotients:
C1, C2 [×15], C22 [×35], D4 [×4], C23 [×15], D7, C2×D4 [×6], C4○D4 [×4], C24, D14 [×7], C22×D4, C2×C4○D4 [×2], C22×D7 [×7], C22.26C24, D4×D7 [×2], D4⋊2D7 [×2], C23×D7, C2×D4×D7, C2×D4⋊2D7, D7×C4○D4, C28⋊(C4○D4)

Generators and relations
 G = < a,b,c,d | a28=b4=d2=1, c2=b2, bab-1=a13, cac-1=a15, ad=da, bc=cb, bd=db, dcd=b2c >

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

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

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

Matrix representation ►G ⊆ GL6(𝔽29)

2800000
0280000
0017000
0001200
0000187
000040
,
1200000
0120000
0012000
0001200
00002519
0000164
,
010000
2800000
0002800
001000
0000280
0000028
,
2800000
010000
001000
0002800
000010
000001

G:=sub<GL(6,GF(29))| [28,0,0,0,0,0,0,28,0,0,0,0,0,0,17,0,0,0,0,0,0,12,0,0,0,0,0,0,18,4,0,0,0,0,7,0],[12,0,0,0,0,0,0,12,0,0,0,0,0,0,12,0,0,0,0,0,0,12,0,0,0,0,0,0,25,16,0,0,0,0,19,4],[0,28,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,28,0,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[28,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,1] >;
 

70 conjugacy classes

class 1 2A2B2C2D2E2F2G2H2I4A4B4C4D4E4F4G4H4I4J4K···4P4Q4R7A7B7C14A···14I14J···14O14P···14U28A···28L28M···28R
order122222222244444444444···44477714···1414···1414···1428···2828···28
size111122442828222244777714···1428282222···24···48···84···48···8

70 irreducible representations

dim11111111111122222222444
type++++++++++++++++++-+
imageC1C2C2C2C2C2C2C2C2C2C2C2D4D7C4○D4C4○D4D14D14D14D14D4⋊2D7D4×D7D7×C4○D4
kernelC28⋊(C4○D4)Dic7⋊4D4Dic7.D4C28⋊Q8D28⋊C4C2×C4×Dic7C28⋊7D4D4×Dic7Dic7⋊D4C28⋊D4C7×C4⋊D4C2×D4⋊2D7C2×Dic7C4⋊D4Dic7C28C22⋊C4C4⋊C4C22×C4C2×D4C4C22C2
# reps12211111211243446339666

In GAP, Magma, Sage, TeX 

C_{28}\rtimes (C_4\circ D_4)
 
% in TeX
 
G:=Group("C28:(C4oD4)");
 
// GroupNames label
 
G:=SmallGroup(448,1049);
 
// by ID
 
G=gap.SmallGroup(448,1049);
 
# by ID
 
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,224,387,570,185,18822]);
 
// Polycyclic
 
G:=Group<a,b,c,d|a^28=b^4=d^2=1,c^2=b^2,b*a*b^-1=a^13,c*a*c^-1=a^15,a*d=d*a,b*c=c*b,b*d=d*b,d*c*d=b^2*c>;
 
// generators/relations
 

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