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## G = C4.Dic7⋊C4order 448 = 26·7

### 7th semidirect product of C4.Dic7 and C4 acting via C4/C2=C2

Series: Derived Chief Lower central Upper central

 Derived series C1 — C28 — C4.Dic7⋊C4
 Chief series C1 — C7 — C14 — C2×C14 — C2×C28 — C2×C7⋊C8 — C2×C4.Dic7 — C4.Dic7⋊C4
 Lower central C7 — C14 — C28 — C4.Dic7⋊C4
 Upper central C1 — C22 — C22×C4 — C2×C4⋊C4

Generators and relations for C4.Dic7⋊C4
G = < a,b,c,d | a4=d4=1, b14=a2, c2=a2b7, ab=ba, cac-1=dad-1=a-1, cbc-1=b13, dbd-1=a2b, dcd-1=b7c >

Subgroups: 388 in 118 conjugacy classes, 63 normal (29 characteristic)
C1, C2, C2, C4, C4, C4, C22, C22, C22, C7, C8, C2×C4, C2×C4, C2×C4, C23, C14, C14, C42, C22⋊C4, C4⋊C4, C4⋊C4, C2×C8, M4(2), C22×C4, C22×C4, Dic7, C28, C28, C28, C2×C14, C2×C14, C2×C14, C4.Q8, C2.D8, C2×C4⋊C4, C42⋊C2, C2×M4(2), C7⋊C8, C2×Dic7, C2×C28, C2×C28, C2×C28, C22×C14, M4(2)⋊C4, C2×C7⋊C8, C4.Dic7, C4×Dic7, C4⋊Dic7, C23.D7, C7×C4⋊C4, C7×C4⋊C4, C22×C28, C22×C28, C28.Q8, C4.Dic14, C2×C4.Dic7, C23.21D14, C14×C4⋊C4, C4.Dic7⋊C4
Quotients: C1, C2, C4, C22, C2×C4, D4, Q8, C23, D7, C4⋊C4, C22×C4, C2×D4, C2×Q8, D14, C2×C4⋊C4, C8⋊C22, C8.C22, Dic14, C4×D7, C7⋊D4, C22×D7, M4(2)⋊C4, Dic7⋊C4, C2×Dic14, C2×C4×D7, C2×C7⋊D4, C2×Dic7⋊C4, D4.D14, C28.C23, C4.Dic7⋊C4

Smallest permutation representation of C4.Dic7⋊C4
On 224 points
Generators in S224
(1 22 15 8)(2 23 16 9)(3 24 17 10)(4 25 18 11)(5 26 19 12)(6 27 20 13)(7 28 21 14)(29 50 43 36)(30 51 44 37)(31 52 45 38)(32 53 46 39)(33 54 47 40)(34 55 48 41)(35 56 49 42)(57 78 71 64)(58 79 72 65)(59 80 73 66)(60 81 74 67)(61 82 75 68)(62 83 76 69)(63 84 77 70)(85 106 99 92)(86 107 100 93)(87 108 101 94)(88 109 102 95)(89 110 103 96)(90 111 104 97)(91 112 105 98)(113 120 127 134)(114 121 128 135)(115 122 129 136)(116 123 130 137)(117 124 131 138)(118 125 132 139)(119 126 133 140)(141 148 155 162)(142 149 156 163)(143 150 157 164)(144 151 158 165)(145 152 159 166)(146 153 160 167)(147 154 161 168)(169 176 183 190)(170 177 184 191)(171 178 185 192)(172 179 186 193)(173 180 187 194)(174 181 188 195)(175 182 189 196)(197 204 211 218)(198 205 212 219)(199 206 213 220)(200 207 214 221)(201 208 215 222)(202 209 216 223)(203 210 217 224)
(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)
(1 124 22 117 15 138 8 131)(2 137 23 130 16 123 9 116)(3 122 24 115 17 136 10 129)(4 135 25 128 18 121 11 114)(5 120 26 113 19 134 12 127)(6 133 27 126 20 119 13 140)(7 118 28 139 21 132 14 125)(29 147 50 168 43 161 36 154)(30 160 51 153 44 146 37 167)(31 145 52 166 45 159 38 152)(32 158 53 151 46 144 39 165)(33 143 54 164 47 157 40 150)(34 156 55 149 48 142 41 163)(35 141 56 162 49 155 42 148)(57 179 78 172 71 193 64 186)(58 192 79 185 72 178 65 171)(59 177 80 170 73 191 66 184)(60 190 81 183 74 176 67 169)(61 175 82 196 75 189 68 182)(62 188 83 181 76 174 69 195)(63 173 84 194 77 187 70 180)(85 197 106 218 99 211 92 204)(86 210 107 203 100 224 93 217)(87 223 108 216 101 209 94 202)(88 208 109 201 102 222 95 215)(89 221 110 214 103 207 96 200)(90 206 111 199 104 220 97 213)(91 219 112 212 105 205 98 198)
(1 106 43 78)(2 93 44 65)(3 108 45 80)(4 95 46 67)(5 110 47 82)(6 97 48 69)(7 112 49 84)(8 99 50 71)(9 86 51 58)(10 101 52 73)(11 88 53 60)(12 103 54 75)(13 90 55 62)(14 105 56 77)(15 92 29 64)(16 107 30 79)(17 94 31 66)(18 109 32 81)(19 96 33 68)(20 111 34 83)(21 98 35 70)(22 85 36 57)(23 100 37 72)(24 87 38 59)(25 102 39 74)(26 89 40 61)(27 104 41 76)(28 91 42 63)(113 200 150 182)(114 215 151 169)(115 202 152 184)(116 217 153 171)(117 204 154 186)(118 219 155 173)(119 206 156 188)(120 221 157 175)(121 208 158 190)(122 223 159 177)(123 210 160 192)(124 197 161 179)(125 212 162 194)(126 199 163 181)(127 214 164 196)(128 201 165 183)(129 216 166 170)(130 203 167 185)(131 218 168 172)(132 205 141 187)(133 220 142 174)(134 207 143 189)(135 222 144 176)(136 209 145 191)(137 224 146 178)(138 211 147 193)(139 198 148 180)(140 213 149 195)

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

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

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

82 conjugacy classes

 class 1 2A 2B 2C 2D 2E 4A 4B 4C 4D 4E 4F 4G 4H 4I 4J 4K 4L 7A 7B 7C 8A 8B 8C 8D 14A ··· 14U 28A ··· 28AJ order 1 2 2 2 2 2 4 4 4 4 4 4 4 4 4 4 4 4 7 7 7 8 8 8 8 14 ··· 14 28 ··· 28 size 1 1 1 1 2 2 2 2 2 2 4 4 4 4 28 28 28 28 2 2 2 28 28 28 28 2 ··· 2 4 ··· 4

82 irreducible representations

 dim 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 4 4 4 4 type + + + + + + + - + + + + - + - image C1 C2 C2 C2 C2 C2 C4 D4 Q8 D4 D7 D14 D14 Dic14 C4×D7 C7⋊D4 C7⋊D4 C8⋊C22 C8.C22 D4.D14 C28.C23 kernel C4.Dic7⋊C4 C28.Q8 C4.Dic14 C2×C4.Dic7 C23.21D14 C14×C4⋊C4 C4.Dic7 C2×C28 C2×C28 C22×C14 C2×C4⋊C4 C4⋊C4 C22×C4 C2×C4 C2×C4 C2×C4 C23 C14 C14 C2 C2 # reps 1 2 2 1 1 1 8 1 2 1 3 6 3 12 12 6 6 1 1 6 6

Matrix representation of C4.Dic7⋊C4 in GL6(𝔽113)

 1 0 0 0 0 0 0 1 0 0 0 0 0 0 112 23 0 0 0 0 108 1 0 0 0 0 79 55 0 112 0 0 98 64 1 0
,
 112 0 0 0 0 0 0 112 0 0 0 0 0 0 85 79 0 0 0 0 86 28 0 0 0 0 26 59 0 109 0 0 67 35 4 0
,
 21 90 0 0 0 0 88 92 0 0 0 0 0 0 50 89 111 0 0 0 6 112 108 108 0 0 105 22 10 60 0 0 0 17 79 54
,
 60 106 0 0 0 0 14 53 0 0 0 0 0 0 105 7 0 0 0 0 104 8 0 0 0 0 58 96 74 47 0 0 86 9 47 39

G:=sub<GL(6,GF(113))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,112,108,79,98,0,0,23,1,55,64,0,0,0,0,0,1,0,0,0,0,112,0],[112,0,0,0,0,0,0,112,0,0,0,0,0,0,85,86,26,67,0,0,79,28,59,35,0,0,0,0,0,4,0,0,0,0,109,0],[21,88,0,0,0,0,90,92,0,0,0,0,0,0,50,6,105,0,0,0,89,112,22,17,0,0,111,108,10,79,0,0,0,108,60,54],[60,14,0,0,0,0,106,53,0,0,0,0,0,0,105,104,58,86,0,0,7,8,96,9,0,0,0,0,74,47,0,0,0,0,47,39] >;

C4.Dic7⋊C4 in GAP, Magma, Sage, TeX

C_4.{\rm Dic}_7\rtimes C_4
% in TeX

G:=Group("C4.Dic7:C4");
// GroupNames label

G:=SmallGroup(448,498);
// by ID

G=gap.SmallGroup(448,498);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,112,477,422,58,438,102,18822]);
// Polycyclic

G:=Group<a,b,c,d|a^4=d^4=1,b^14=a^2,c^2=a^2*b^7,a*b=b*a,c*a*c^-1=d*a*d^-1=a^-1,c*b*c^-1=b^13,d*b*d^-1=a^2*b,d*c*d^-1=b^7*c>;
// generators/relations

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