metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: D14.4SD16, C4.Q8⋊7D7, D14⋊C8⋊30C2, C4⋊C4.37D14, (C2×C8).138D14, C4⋊D28.4C2, C2.D56⋊31C2, C14.D8⋊14C2, C2.23(D7×SD16), C4.73(C4○D28), C28.28(C4○D4), C4.Dic14⋊17C2, (C2×Dic7).41D4, C14.39(C2×SD16), (C22×D7).83D4, C22.215(D4×D7), C2.21(D56⋊C2), C14.69(C8⋊C22), (C2×C28).279C23, (C2×C56).285C22, C4.25(Q8⋊2D7), (C2×D28).73C22, C7⋊3(C23.46D4), C4⋊Dic7.111C22, C2.12(D14.5D4), C14.42(C22.D4), (D7×C4⋊C4)⋊6C2, (C7×C4.Q8)⋊16C2, (C2×C7⋊C8).57C22, (C2×C4×D7).32C22, (C2×C14).284(C2×D4), (C7×C4⋊C4).72C22, (C2×C4).382(C22×D7), SmallGroup(448,397)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for D14.4SD16
G = < a,b,c,d | a14=b2=c8=1, d2=a7, bab=a-1, ac=ca, ad=da, cbc-1=dbd-1=a7b, dcd-1=c3 >
Subgroups: 748 in 114 conjugacy classes, 39 normal (37 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C8, C2×C4, C2×C4, D4, C23, D7, C14, C22⋊C4, C4⋊C4, C4⋊C4, C2×C8, C2×C8, C22×C4, C2×D4, Dic7, C28, C28, D14, D14, C2×C14, C22⋊C8, D4⋊C4, C4.Q8, C4.Q8, C2×C4⋊C4, C4⋊D4, C7⋊C8, C56, C4×D7, D28, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C22×D7, C22×D7, C23.46D4, C2×C7⋊C8, Dic7⋊C4, C4⋊Dic7, D14⋊C4, C7×C4⋊C4, C2×C56, C2×C4×D7, C2×C4×D7, C2×D28, C2×D28, C4.Dic14, C14.D8, D14⋊C8, C2.D56, C7×C4.Q8, D7×C4⋊C4, C4⋊D28, D14.4SD16
Quotients: C1, C2, C22, D4, C23, D7, SD16, C2×D4, C4○D4, D14, C22.D4, C2×SD16, C8⋊C22, C22×D7, C23.46D4, C4○D28, D4×D7, Q8⋊2D7, D14.5D4, D7×SD16, D56⋊C2, D14.4SD16
►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 14)(2 13)(3 12)(4 11)(5 10)(6 9)(7 8)(15 16)(17 28)(18 27)(19 26)(20 25)(21 24)(22 23)(29 41)(30 40)(31 39)(32 38)(33 37)(34 36)(43 51)(44 50)(45 49)(46 48)(52 56)(53 55)(57 58)(59 70)(60 69)(61 68)(62 67)(63 66)(64 65)(71 78)(72 77)(73 76)(74 75)(79 84)(80 83)(81 82)(85 89)(86 88)(90 98)(91 97)(92 96)(93 95)(99 101)(102 112)(103 111)(104 110)(105 109)(106 108)(113 118)(114 117)(115 116)(119 126)(120 125)(121 124)(122 123)(127 137)(128 136)(129 135)(130 134)(131 133)(138 140)(141 142)(143 154)(144 153)(145 152)(146 151)(147 150)(148 149)(155 161)(156 160)(157 159)(162 168)(163 167)(164 166)(169 182)(170 181)(171 180)(172 179)(173 178)(174 177)(175 176)(183 191)(184 190)(185 189)(186 188)(192 196)(193 195)(198 210)(199 209)(200 208)(201 207)(202 206)(203 205)(211 222)(212 221)(213 220)(214 219)(215 218)(216 217)(223 224)
(1 191 176 201 82 136 149 162)(2 192 177 202 83 137 150 163)(3 193 178 203 84 138 151 164)(4 194 179 204 71 139 152 165)(5 195 180 205 72 140 153 166)(6 196 181 206 73 127 154 167)(7 183 182 207 74 128 141 168)(8 184 169 208 75 129 142 155)(9 185 170 209 76 130 143 156)(10 186 171 210 77 131 144 157)(11 187 172 197 78 132 145 158)(12 188 173 198 79 133 146 159)(13 189 174 199 80 134 147 160)(14 190 175 200 81 135 148 161)(15 43 115 31 216 110 57 97)(16 44 116 32 217 111 58 98)(17 45 117 33 218 112 59 85)(18 46 118 34 219 99 60 86)(19 47 119 35 220 100 61 87)(20 48 120 36 221 101 62 88)(21 49 121 37 222 102 63 89)(22 50 122 38 223 103 64 90)(23 51 123 39 224 104 65 91)(24 52 124 40 211 105 66 92)(25 53 125 41 212 106 67 93)(26 54 126 42 213 107 68 94)(27 55 113 29 214 108 69 95)(28 56 114 30 215 109 70 96)
(1 39 8 32)(2 40 9 33)(3 41 10 34)(4 42 11 35)(5 29 12 36)(6 30 13 37)(7 31 14 38)(15 161 22 168)(16 162 23 155)(17 163 24 156)(18 164 25 157)(19 165 26 158)(20 166 27 159)(21 167 28 160)(43 175 50 182)(44 176 51 169)(45 177 52 170)(46 178 53 171)(47 179 54 172)(48 180 55 173)(49 181 56 174)(57 190 64 183)(58 191 65 184)(59 192 66 185)(60 193 67 186)(61 194 68 187)(62 195 69 188)(63 196 70 189)(71 94 78 87)(72 95 79 88)(73 96 80 89)(74 97 81 90)(75 98 82 91)(76 85 83 92)(77 86 84 93)(99 151 106 144)(100 152 107 145)(101 153 108 146)(102 154 109 147)(103 141 110 148)(104 142 111 149)(105 143 112 150)(113 133 120 140)(114 134 121 127)(115 135 122 128)(116 136 123 129)(117 137 124 130)(118 138 125 131)(119 139 126 132)(197 220 204 213)(198 221 205 214)(199 222 206 215)(200 223 207 216)(201 224 208 217)(202 211 209 218)(203 212 210 219)
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), (1,14)(2,13)(3,12)(4,11)(5,10)(6,9)(7,8)(15,16)(17,28)(18,27)(19,26)(20,25)(21,24)(22,23)(29,41)(30,40)(31,39)(32,38)(33,37)(34,36)(43,51)(44,50)(45,49)(46,48)(52,56)(53,55)(57,58)(59,70)(60,69)(61,68)(62,67)(63,66)(64,65)(71,78)(72,77)(73,76)(74,75)(79,84)(80,83)(81,82)(85,89)(86,88)(90,98)(91,97)(92,96)(93,95)(99,101)(102,112)(103,111)(104,110)(105,109)(106,108)(113,118)(114,117)(115,116)(119,126)(120,125)(121,124)(122,123)(127,137)(128,136)(129,135)(130,134)(131,133)(138,140)(141,142)(143,154)(144,153)(145,152)(146,151)(147,150)(148,149)(155,161)(156,160)(157,159)(162,168)(163,167)(164,166)(169,182)(170,181)(171,180)(172,179)(173,178)(174,177)(175,176)(183,191)(184,190)(185,189)(186,188)(192,196)(193,195)(198,210)(199,209)(200,208)(201,207)(202,206)(203,205)(211,222)(212,221)(213,220)(214,219)(215,218)(216,217)(223,224), (1,191,176,201,82,136,149,162)(2,192,177,202,83,137,150,163)(3,193,178,203,84,138,151,164)(4,194,179,204,71,139,152,165)(5,195,180,205,72,140,153,166)(6,196,181,206,73,127,154,167)(7,183,182,207,74,128,141,168)(8,184,169,208,75,129,142,155)(9,185,170,209,76,130,143,156)(10,186,171,210,77,131,144,157)(11,187,172,197,78,132,145,158)(12,188,173,198,79,133,146,159)(13,189,174,199,80,134,147,160)(14,190,175,200,81,135,148,161)(15,43,115,31,216,110,57,97)(16,44,116,32,217,111,58,98)(17,45,117,33,218,112,59,85)(18,46,118,34,219,99,60,86)(19,47,119,35,220,100,61,87)(20,48,120,36,221,101,62,88)(21,49,121,37,222,102,63,89)(22,50,122,38,223,103,64,90)(23,51,123,39,224,104,65,91)(24,52,124,40,211,105,66,92)(25,53,125,41,212,106,67,93)(26,54,126,42,213,107,68,94)(27,55,113,29,214,108,69,95)(28,56,114,30,215,109,70,96), (1,39,8,32)(2,40,9,33)(3,41,10,34)(4,42,11,35)(5,29,12,36)(6,30,13,37)(7,31,14,38)(15,161,22,168)(16,162,23,155)(17,163,24,156)(18,164,25,157)(19,165,26,158)(20,166,27,159)(21,167,28,160)(43,175,50,182)(44,176,51,169)(45,177,52,170)(46,178,53,171)(47,179,54,172)(48,180,55,173)(49,181,56,174)(57,190,64,183)(58,191,65,184)(59,192,66,185)(60,193,67,186)(61,194,68,187)(62,195,69,188)(63,196,70,189)(71,94,78,87)(72,95,79,88)(73,96,80,89)(74,97,81,90)(75,98,82,91)(76,85,83,92)(77,86,84,93)(99,151,106,144)(100,152,107,145)(101,153,108,146)(102,154,109,147)(103,141,110,148)(104,142,111,149)(105,143,112,150)(113,133,120,140)(114,134,121,127)(115,135,122,128)(116,136,123,129)(117,137,124,130)(118,138,125,131)(119,139,126,132)(197,220,204,213)(198,221,205,214)(199,222,206,215)(200,223,207,216)(201,224,208,217)(202,211,209,218)(203,212,210,219)>;
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), (1,14)(2,13)(3,12)(4,11)(5,10)(6,9)(7,8)(15,16)(17,28)(18,27)(19,26)(20,25)(21,24)(22,23)(29,41)(30,40)(31,39)(32,38)(33,37)(34,36)(43,51)(44,50)(45,49)(46,48)(52,56)(53,55)(57,58)(59,70)(60,69)(61,68)(62,67)(63,66)(64,65)(71,78)(72,77)(73,76)(74,75)(79,84)(80,83)(81,82)(85,89)(86,88)(90,98)(91,97)(92,96)(93,95)(99,101)(102,112)(103,111)(104,110)(105,109)(106,108)(113,118)(114,117)(115,116)(119,126)(120,125)(121,124)(122,123)(127,137)(128,136)(129,135)(130,134)(131,133)(138,140)(141,142)(143,154)(144,153)(145,152)(146,151)(147,150)(148,149)(155,161)(156,160)(157,159)(162,168)(163,167)(164,166)(169,182)(170,181)(171,180)(172,179)(173,178)(174,177)(175,176)(183,191)(184,190)(185,189)(186,188)(192,196)(193,195)(198,210)(199,209)(200,208)(201,207)(202,206)(203,205)(211,222)(212,221)(213,220)(214,219)(215,218)(216,217)(223,224), (1,191,176,201,82,136,149,162)(2,192,177,202,83,137,150,163)(3,193,178,203,84,138,151,164)(4,194,179,204,71,139,152,165)(5,195,180,205,72,140,153,166)(6,196,181,206,73,127,154,167)(7,183,182,207,74,128,141,168)(8,184,169,208,75,129,142,155)(9,185,170,209,76,130,143,156)(10,186,171,210,77,131,144,157)(11,187,172,197,78,132,145,158)(12,188,173,198,79,133,146,159)(13,189,174,199,80,134,147,160)(14,190,175,200,81,135,148,161)(15,43,115,31,216,110,57,97)(16,44,116,32,217,111,58,98)(17,45,117,33,218,112,59,85)(18,46,118,34,219,99,60,86)(19,47,119,35,220,100,61,87)(20,48,120,36,221,101,62,88)(21,49,121,37,222,102,63,89)(22,50,122,38,223,103,64,90)(23,51,123,39,224,104,65,91)(24,52,124,40,211,105,66,92)(25,53,125,41,212,106,67,93)(26,54,126,42,213,107,68,94)(27,55,113,29,214,108,69,95)(28,56,114,30,215,109,70,96), (1,39,8,32)(2,40,9,33)(3,41,10,34)(4,42,11,35)(5,29,12,36)(6,30,13,37)(7,31,14,38)(15,161,22,168)(16,162,23,155)(17,163,24,156)(18,164,25,157)(19,165,26,158)(20,166,27,159)(21,167,28,160)(43,175,50,182)(44,176,51,169)(45,177,52,170)(46,178,53,171)(47,179,54,172)(48,180,55,173)(49,181,56,174)(57,190,64,183)(58,191,65,184)(59,192,66,185)(60,193,67,186)(61,194,68,187)(62,195,69,188)(63,196,70,189)(71,94,78,87)(72,95,79,88)(73,96,80,89)(74,97,81,90)(75,98,82,91)(76,85,83,92)(77,86,84,93)(99,151,106,144)(100,152,107,145)(101,153,108,146)(102,154,109,147)(103,141,110,148)(104,142,111,149)(105,143,112,150)(113,133,120,140)(114,134,121,127)(115,135,122,128)(116,136,123,129)(117,137,124,130)(118,138,125,131)(119,139,126,132)(197,220,204,213)(198,221,205,214)(199,222,206,215)(200,223,207,216)(201,224,208,217)(202,211,209,218)(203,212,210,219) );
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)], [(1,14),(2,13),(3,12),(4,11),(5,10),(6,9),(7,8),(15,16),(17,28),(18,27),(19,26),(20,25),(21,24),(22,23),(29,41),(30,40),(31,39),(32,38),(33,37),(34,36),(43,51),(44,50),(45,49),(46,48),(52,56),(53,55),(57,58),(59,70),(60,69),(61,68),(62,67),(63,66),(64,65),(71,78),(72,77),(73,76),(74,75),(79,84),(80,83),(81,82),(85,89),(86,88),(90,98),(91,97),(92,96),(93,95),(99,101),(102,112),(103,111),(104,110),(105,109),(106,108),(113,118),(114,117),(115,116),(119,126),(120,125),(121,124),(122,123),(127,137),(128,136),(129,135),(130,134),(131,133),(138,140),(141,142),(143,154),(144,153),(145,152),(146,151),(147,150),(148,149),(155,161),(156,160),(157,159),(162,168),(163,167),(164,166),(169,182),(170,181),(171,180),(172,179),(173,178),(174,177),(175,176),(183,191),(184,190),(185,189),(186,188),(192,196),(193,195),(198,210),(199,209),(200,208),(201,207),(202,206),(203,205),(211,222),(212,221),(213,220),(214,219),(215,218),(216,217),(223,224)], [(1,191,176,201,82,136,149,162),(2,192,177,202,83,137,150,163),(3,193,178,203,84,138,151,164),(4,194,179,204,71,139,152,165),(5,195,180,205,72,140,153,166),(6,196,181,206,73,127,154,167),(7,183,182,207,74,128,141,168),(8,184,169,208,75,129,142,155),(9,185,170,209,76,130,143,156),(10,186,171,210,77,131,144,157),(11,187,172,197,78,132,145,158),(12,188,173,198,79,133,146,159),(13,189,174,199,80,134,147,160),(14,190,175,200,81,135,148,161),(15,43,115,31,216,110,57,97),(16,44,116,32,217,111,58,98),(17,45,117,33,218,112,59,85),(18,46,118,34,219,99,60,86),(19,47,119,35,220,100,61,87),(20,48,120,36,221,101,62,88),(21,49,121,37,222,102,63,89),(22,50,122,38,223,103,64,90),(23,51,123,39,224,104,65,91),(24,52,124,40,211,105,66,92),(25,53,125,41,212,106,67,93),(26,54,126,42,213,107,68,94),(27,55,113,29,214,108,69,95),(28,56,114,30,215,109,70,96)], [(1,39,8,32),(2,40,9,33),(3,41,10,34),(4,42,11,35),(5,29,12,36),(6,30,13,37),(7,31,14,38),(15,161,22,168),(16,162,23,155),(17,163,24,156),(18,164,25,157),(19,165,26,158),(20,166,27,159),(21,167,28,160),(43,175,50,182),(44,176,51,169),(45,177,52,170),(46,178,53,171),(47,179,54,172),(48,180,55,173),(49,181,56,174),(57,190,64,183),(58,191,65,184),(59,192,66,185),(60,193,67,186),(61,194,68,187),(62,195,69,188),(63,196,70,189),(71,94,78,87),(72,95,79,88),(73,96,80,89),(74,97,81,90),(75,98,82,91),(76,85,83,92),(77,86,84,93),(99,151,106,144),(100,152,107,145),(101,153,108,146),(102,154,109,147),(103,141,110,148),(104,142,111,149),(105,143,112,150),(113,133,120,140),(114,134,121,127),(115,135,122,128),(116,136,123,129),(117,137,124,130),(118,138,125,131),(119,139,126,132),(197,220,204,213),(198,221,205,214),(199,222,206,215),(200,223,207,216),(201,224,208,217),(202,211,209,218),(203,212,210,219)]])
61 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 7A | 7B | 7C | 8A | 8B | 8C | 8D | 14A | ··· | 14I | 28A | ··· | 28F | 28G | ··· | 28R | 56A | ··· | 56L |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 8 | 8 | 8 | 8 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 | 56 | ··· | 56 |
| size | 1 | 1 | 1 | 1 | 14 | 14 | 56 | 2 | 2 | 4 | 4 | 8 | 28 | 28 | 28 | 2 | 2 | 2 | 4 | 4 | 28 | 28 | 2 | ··· | 2 | 4 | ··· | 4 | 8 | ··· | 8 | 4 | ··· | 4 |
61 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | ||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | D4 | D7 | C4○D4 | SD16 | D14 | D14 | C4○D28 | C8⋊C22 | Q8⋊2D7 | D4×D7 | D7×SD16 | D56⋊C2 |
| kernel | D14.4SD16 | C4.Dic14 | C14.D8 | D14⋊C8 | C2.D56 | C7×C4.Q8 | D7×C4⋊C4 | C4⋊D28 | C2×Dic7 | C22×D7 | C4.Q8 | C28 | D14 | C4⋊C4 | C2×C8 | C4 | C14 | C4 | C22 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 3 | 4 | 4 | 6 | 3 | 12 | 1 | 3 | 3 | 6 | 6 |
Matrix representation of D14.4SD16 ►in GL4(𝔽113) generated by
| 10 | 10 | 0 | 0 |
| 103 | 24 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 0 | 112 | 0 | 0 |
| 112 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 29 | 7 | 0 | 0 |
| 106 | 84 | 0 | 0 |
| 0 | 0 | 87 | 60 |
| 0 | 0 | 81 | 0 |
| 17 | 8 | 0 | 0 |
| 105 | 96 | 0 | 0 |
| 0 | 0 | 58 | 14 |
| 0 | 0 | 10 | 55 |
G:=sub<GL(4,GF(113))| [10,103,0,0,10,24,0,0,0,0,1,0,0,0,0,1],[0,112,0,0,112,0,0,0,0,0,1,0,0,0,0,1],[29,106,0,0,7,84,0,0,0,0,87,81,0,0,60,0],[17,105,0,0,8,96,0,0,0,0,58,10,0,0,14,55] >;
D14.4SD16 in GAP, Magma, Sage, TeX
D_{14}._4{\rm SD}_{16} % in TeX
G:=Group("D14.4SD16"); // GroupNames label
G:=SmallGroup(448,397);
// by ID
G=gap.SmallGroup(448,397);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,64,926,219,100,851,102,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^14=b^2=c^8=1,d^2=a^7,b*a*b=a^-1,a*c=c*a,a*d=d*a,c*b*c^-1=d*b*d^-1=a^7*b,d*c*d^-1=c^3>;
// generators/relations