metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: D14.2Q16, C2.D8⋊4D7, C4⋊C4.49D14, (C2×C8).28D14, C2.14(D7×Q16), D14⋊C8.10C2, C14.24(C2×Q16), C4.81(C4○D28), C28.39(C4○D4), C14.Q16⋊19C2, C28.Q8⋊22C2, D14⋊2Q8.7C2, (C2×Dic7).49D4, (C22×D7).86D4, C22.230(D4×D7), C28.44D4⋊26C2, C2.22(D8⋊D7), C14.41(C8⋊C22), (C2×C56).242C22, (C2×C28).300C23, C4.29(Q8⋊2D7), C7⋊3(C23.48D4), C4⋊Dic7.125C22, C2.16(D14.5D4), (C2×Dic14).89C22, C14.46(C22.D4), (D7×C4⋊C4).9C2, (C7×C2.D8)⋊12C2, (C2×C7⋊C8).70C22, (C2×C4×D7).39C22, (C2×C14).305(C2×D4), (C7×C4⋊C4).93C22, (C2×C4).403(C22×D7), SmallGroup(448,418)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for D14.2Q16
G = < a,b,c,d | a14=b2=c8=1, d2=a7c4, bab=a-1, ac=ca, ad=da, cbc-1=a7b, bd=db, dcd-1=c-1 >
Subgroups: 556 in 104 conjugacy classes, 39 normal (37 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C8, C2×C4, C2×C4, Q8, C23, D7, C14, C22⋊C4, C4⋊C4, C4⋊C4, C2×C8, C2×C8, C22×C4, C2×Q8, Dic7, C28, C28, D14, D14, C2×C14, C22⋊C8, Q8⋊C4, C2.D8, C2.D8, C2×C4⋊C4, C22⋊Q8, C7⋊C8, C56, Dic14, C4×D7, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C22×D7, C23.48D4, C2×C7⋊C8, Dic7⋊C4, C4⋊Dic7, C4⋊Dic7, D14⋊C4, C7×C4⋊C4, C2×C56, C2×Dic14, C2×C4×D7, C2×C4×D7, C28.Q8, C14.Q16, C28.44D4, D14⋊C8, C7×C2.D8, D7×C4⋊C4, D14⋊2Q8, D14.2Q16
Quotients: C1, C2, C22, D4, C23, D7, Q16, C2×D4, C4○D4, D14, C22.D4, C2×Q16, C8⋊C22, C22×D7, C23.48D4, C4○D28, D4×D7, Q8⋊2D7, D14.5D4, D8⋊D7, D7×Q16, D14.2Q16
►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 23)(16 22)(17 21)(18 20)(24 28)(25 27)(29 42)(30 41)(31 40)(32 39)(33 38)(34 37)(35 36)(43 45)(46 56)(47 55)(48 54)(49 53)(50 52)(57 70)(58 69)(59 68)(60 67)(61 66)(62 65)(63 64)(71 84)(72 83)(73 82)(74 81)(75 80)(76 79)(77 78)(85 94)(86 93)(87 92)(88 91)(89 90)(95 98)(96 97)(99 109)(100 108)(101 107)(102 106)(103 105)(110 112)(113 116)(114 115)(117 126)(118 125)(119 124)(120 123)(121 122)(127 136)(128 135)(129 134)(130 133)(131 132)(137 140)(138 139)(141 143)(144 154)(145 153)(146 152)(147 151)(148 150)(155 167)(156 166)(157 165)(158 164)(159 163)(160 162)(169 170)(171 182)(172 181)(173 180)(174 179)(175 178)(176 177)(183 185)(186 196)(187 195)(188 194)(189 193)(190 192)(197 205)(198 204)(199 203)(200 202)(206 210)(207 209)(211 217)(212 216)(213 215)(218 224)(219 223)(220 222)
(1 101 29 153 177 55 115 205)(2 102 30 154 178 56 116 206)(3 103 31 141 179 43 117 207)(4 104 32 142 180 44 118 208)(5 105 33 143 181 45 119 209)(6 106 34 144 182 46 120 210)(7 107 35 145 169 47 121 197)(8 108 36 146 170 48 122 198)(9 109 37 147 171 49 123 199)(10 110 38 148 172 50 124 200)(11 111 39 149 173 51 125 201)(12 112 40 150 174 52 126 202)(13 99 41 151 175 53 113 203)(14 100 42 152 176 54 114 204)(15 89 187 77 224 63 157 131)(16 90 188 78 211 64 158 132)(17 91 189 79 212 65 159 133)(18 92 190 80 213 66 160 134)(19 93 191 81 214 67 161 135)(20 94 192 82 215 68 162 136)(21 95 193 83 216 69 163 137)(22 96 194 84 217 70 164 138)(23 97 195 71 218 57 165 139)(24 98 196 72 219 58 166 140)(25 85 183 73 220 59 167 127)(26 86 184 74 221 60 168 128)(27 87 185 75 222 61 155 129)(28 88 186 76 223 62 156 130)
(1 78 170 139)(2 79 171 140)(3 80 172 127)(4 81 173 128)(5 82 174 129)(6 83 175 130)(7 84 176 131)(8 71 177 132)(9 72 178 133)(10 73 179 134)(11 74 180 135)(12 75 181 136)(13 76 182 137)(14 77 169 138)(15 197 217 152)(16 198 218 153)(17 199 219 154)(18 200 220 141)(19 201 221 142)(20 202 222 143)(21 203 223 144)(22 204 224 145)(23 205 211 146)(24 206 212 147)(25 207 213 148)(26 208 214 149)(27 209 215 150)(28 210 216 151)(29 90 122 57)(30 91 123 58)(31 92 124 59)(32 93 125 60)(33 94 126 61)(34 95 113 62)(35 96 114 63)(36 97 115 64)(37 98 116 65)(38 85 117 66)(39 86 118 67)(40 87 119 68)(41 88 120 69)(42 89 121 70)(43 160 110 183)(44 161 111 184)(45 162 112 185)(46 163 99 186)(47 164 100 187)(48 165 101 188)(49 166 102 189)(50 167 103 190)(51 168 104 191)(52 155 105 192)(53 156 106 193)(54 157 107 194)(55 158 108 195)(56 159 109 196)
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)(15,23)(16,22)(17,21)(18,20)(24,28)(25,27)(29,42)(30,41)(31,40)(32,39)(33,38)(34,37)(35,36)(43,45)(46,56)(47,55)(48,54)(49,53)(50,52)(57,70)(58,69)(59,68)(60,67)(61,66)(62,65)(63,64)(71,84)(72,83)(73,82)(74,81)(75,80)(76,79)(77,78)(85,94)(86,93)(87,92)(88,91)(89,90)(95,98)(96,97)(99,109)(100,108)(101,107)(102,106)(103,105)(110,112)(113,116)(114,115)(117,126)(118,125)(119,124)(120,123)(121,122)(127,136)(128,135)(129,134)(130,133)(131,132)(137,140)(138,139)(141,143)(144,154)(145,153)(146,152)(147,151)(148,150)(155,167)(156,166)(157,165)(158,164)(159,163)(160,162)(169,170)(171,182)(172,181)(173,180)(174,179)(175,178)(176,177)(183,185)(186,196)(187,195)(188,194)(189,193)(190,192)(197,205)(198,204)(199,203)(200,202)(206,210)(207,209)(211,217)(212,216)(213,215)(218,224)(219,223)(220,222), (1,101,29,153,177,55,115,205)(2,102,30,154,178,56,116,206)(3,103,31,141,179,43,117,207)(4,104,32,142,180,44,118,208)(5,105,33,143,181,45,119,209)(6,106,34,144,182,46,120,210)(7,107,35,145,169,47,121,197)(8,108,36,146,170,48,122,198)(9,109,37,147,171,49,123,199)(10,110,38,148,172,50,124,200)(11,111,39,149,173,51,125,201)(12,112,40,150,174,52,126,202)(13,99,41,151,175,53,113,203)(14,100,42,152,176,54,114,204)(15,89,187,77,224,63,157,131)(16,90,188,78,211,64,158,132)(17,91,189,79,212,65,159,133)(18,92,190,80,213,66,160,134)(19,93,191,81,214,67,161,135)(20,94,192,82,215,68,162,136)(21,95,193,83,216,69,163,137)(22,96,194,84,217,70,164,138)(23,97,195,71,218,57,165,139)(24,98,196,72,219,58,166,140)(25,85,183,73,220,59,167,127)(26,86,184,74,221,60,168,128)(27,87,185,75,222,61,155,129)(28,88,186,76,223,62,156,130), (1,78,170,139)(2,79,171,140)(3,80,172,127)(4,81,173,128)(5,82,174,129)(6,83,175,130)(7,84,176,131)(8,71,177,132)(9,72,178,133)(10,73,179,134)(11,74,180,135)(12,75,181,136)(13,76,182,137)(14,77,169,138)(15,197,217,152)(16,198,218,153)(17,199,219,154)(18,200,220,141)(19,201,221,142)(20,202,222,143)(21,203,223,144)(22,204,224,145)(23,205,211,146)(24,206,212,147)(25,207,213,148)(26,208,214,149)(27,209,215,150)(28,210,216,151)(29,90,122,57)(30,91,123,58)(31,92,124,59)(32,93,125,60)(33,94,126,61)(34,95,113,62)(35,96,114,63)(36,97,115,64)(37,98,116,65)(38,85,117,66)(39,86,118,67)(40,87,119,68)(41,88,120,69)(42,89,121,70)(43,160,110,183)(44,161,111,184)(45,162,112,185)(46,163,99,186)(47,164,100,187)(48,165,101,188)(49,166,102,189)(50,167,103,190)(51,168,104,191)(52,155,105,192)(53,156,106,193)(54,157,107,194)(55,158,108,195)(56,159,109,196)>;
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)(15,23)(16,22)(17,21)(18,20)(24,28)(25,27)(29,42)(30,41)(31,40)(32,39)(33,38)(34,37)(35,36)(43,45)(46,56)(47,55)(48,54)(49,53)(50,52)(57,70)(58,69)(59,68)(60,67)(61,66)(62,65)(63,64)(71,84)(72,83)(73,82)(74,81)(75,80)(76,79)(77,78)(85,94)(86,93)(87,92)(88,91)(89,90)(95,98)(96,97)(99,109)(100,108)(101,107)(102,106)(103,105)(110,112)(113,116)(114,115)(117,126)(118,125)(119,124)(120,123)(121,122)(127,136)(128,135)(129,134)(130,133)(131,132)(137,140)(138,139)(141,143)(144,154)(145,153)(146,152)(147,151)(148,150)(155,167)(156,166)(157,165)(158,164)(159,163)(160,162)(169,170)(171,182)(172,181)(173,180)(174,179)(175,178)(176,177)(183,185)(186,196)(187,195)(188,194)(189,193)(190,192)(197,205)(198,204)(199,203)(200,202)(206,210)(207,209)(211,217)(212,216)(213,215)(218,224)(219,223)(220,222), (1,101,29,153,177,55,115,205)(2,102,30,154,178,56,116,206)(3,103,31,141,179,43,117,207)(4,104,32,142,180,44,118,208)(5,105,33,143,181,45,119,209)(6,106,34,144,182,46,120,210)(7,107,35,145,169,47,121,197)(8,108,36,146,170,48,122,198)(9,109,37,147,171,49,123,199)(10,110,38,148,172,50,124,200)(11,111,39,149,173,51,125,201)(12,112,40,150,174,52,126,202)(13,99,41,151,175,53,113,203)(14,100,42,152,176,54,114,204)(15,89,187,77,224,63,157,131)(16,90,188,78,211,64,158,132)(17,91,189,79,212,65,159,133)(18,92,190,80,213,66,160,134)(19,93,191,81,214,67,161,135)(20,94,192,82,215,68,162,136)(21,95,193,83,216,69,163,137)(22,96,194,84,217,70,164,138)(23,97,195,71,218,57,165,139)(24,98,196,72,219,58,166,140)(25,85,183,73,220,59,167,127)(26,86,184,74,221,60,168,128)(27,87,185,75,222,61,155,129)(28,88,186,76,223,62,156,130), (1,78,170,139)(2,79,171,140)(3,80,172,127)(4,81,173,128)(5,82,174,129)(6,83,175,130)(7,84,176,131)(8,71,177,132)(9,72,178,133)(10,73,179,134)(11,74,180,135)(12,75,181,136)(13,76,182,137)(14,77,169,138)(15,197,217,152)(16,198,218,153)(17,199,219,154)(18,200,220,141)(19,201,221,142)(20,202,222,143)(21,203,223,144)(22,204,224,145)(23,205,211,146)(24,206,212,147)(25,207,213,148)(26,208,214,149)(27,209,215,150)(28,210,216,151)(29,90,122,57)(30,91,123,58)(31,92,124,59)(32,93,125,60)(33,94,126,61)(34,95,113,62)(35,96,114,63)(36,97,115,64)(37,98,116,65)(38,85,117,66)(39,86,118,67)(40,87,119,68)(41,88,120,69)(42,89,121,70)(43,160,110,183)(44,161,111,184)(45,162,112,185)(46,163,99,186)(47,164,100,187)(48,165,101,188)(49,166,102,189)(50,167,103,190)(51,168,104,191)(52,155,105,192)(53,156,106,193)(54,157,107,194)(55,158,108,195)(56,159,109,196) );
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),(15,23),(16,22),(17,21),(18,20),(24,28),(25,27),(29,42),(30,41),(31,40),(32,39),(33,38),(34,37),(35,36),(43,45),(46,56),(47,55),(48,54),(49,53),(50,52),(57,70),(58,69),(59,68),(60,67),(61,66),(62,65),(63,64),(71,84),(72,83),(73,82),(74,81),(75,80),(76,79),(77,78),(85,94),(86,93),(87,92),(88,91),(89,90),(95,98),(96,97),(99,109),(100,108),(101,107),(102,106),(103,105),(110,112),(113,116),(114,115),(117,126),(118,125),(119,124),(120,123),(121,122),(127,136),(128,135),(129,134),(130,133),(131,132),(137,140),(138,139),(141,143),(144,154),(145,153),(146,152),(147,151),(148,150),(155,167),(156,166),(157,165),(158,164),(159,163),(160,162),(169,170),(171,182),(172,181),(173,180),(174,179),(175,178),(176,177),(183,185),(186,196),(187,195),(188,194),(189,193),(190,192),(197,205),(198,204),(199,203),(200,202),(206,210),(207,209),(211,217),(212,216),(213,215),(218,224),(219,223),(220,222)], [(1,101,29,153,177,55,115,205),(2,102,30,154,178,56,116,206),(3,103,31,141,179,43,117,207),(4,104,32,142,180,44,118,208),(5,105,33,143,181,45,119,209),(6,106,34,144,182,46,120,210),(7,107,35,145,169,47,121,197),(8,108,36,146,170,48,122,198),(9,109,37,147,171,49,123,199),(10,110,38,148,172,50,124,200),(11,111,39,149,173,51,125,201),(12,112,40,150,174,52,126,202),(13,99,41,151,175,53,113,203),(14,100,42,152,176,54,114,204),(15,89,187,77,224,63,157,131),(16,90,188,78,211,64,158,132),(17,91,189,79,212,65,159,133),(18,92,190,80,213,66,160,134),(19,93,191,81,214,67,161,135),(20,94,192,82,215,68,162,136),(21,95,193,83,216,69,163,137),(22,96,194,84,217,70,164,138),(23,97,195,71,218,57,165,139),(24,98,196,72,219,58,166,140),(25,85,183,73,220,59,167,127),(26,86,184,74,221,60,168,128),(27,87,185,75,222,61,155,129),(28,88,186,76,223,62,156,130)], [(1,78,170,139),(2,79,171,140),(3,80,172,127),(4,81,173,128),(5,82,174,129),(6,83,175,130),(7,84,176,131),(8,71,177,132),(9,72,178,133),(10,73,179,134),(11,74,180,135),(12,75,181,136),(13,76,182,137),(14,77,169,138),(15,197,217,152),(16,198,218,153),(17,199,219,154),(18,200,220,141),(19,201,221,142),(20,202,222,143),(21,203,223,144),(22,204,224,145),(23,205,211,146),(24,206,212,147),(25,207,213,148),(26,208,214,149),(27,209,215,150),(28,210,216,151),(29,90,122,57),(30,91,123,58),(31,92,124,59),(32,93,125,60),(33,94,126,61),(34,95,113,62),(35,96,114,63),(36,97,115,64),(37,98,116,65),(38,85,117,66),(39,86,118,67),(40,87,119,68),(41,88,120,69),(42,89,121,70),(43,160,110,183),(44,161,111,184),(45,162,112,185),(46,163,99,186),(47,164,100,187),(48,165,101,188),(49,166,102,189),(50,167,103,190),(51,168,104,191),(52,155,105,192),(53,156,106,193),(54,157,107,194),(55,158,108,195),(56,159,109,196)]])
61 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 7A | 7B | 7C | 8A | 8B | 8C | 8D | 14A | ··· | 14I | 28A | ··· | 28F | 28G | ··· | 28R | 56A | ··· | 56L |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 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 | 2 | 2 | 4 | 4 | 8 | 28 | 28 | 28 | 56 | 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 | Q16 | D14 | D14 | C4○D28 | C8⋊C22 | Q8⋊2D7 | D4×D7 | D8⋊D7 | D7×Q16 |
| kernel | D14.2Q16 | C28.Q8 | C14.Q16 | C28.44D4 | D14⋊C8 | C7×C2.D8 | D7×C4⋊C4 | D14⋊2Q8 | C2×Dic7 | C22×D7 | C2.D8 | 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 D14.2Q16 ►in GL4(𝔽113) generated by
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 80 | 80 |
| 0 | 0 | 33 | 9 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 80 | 80 |
| 0 | 0 | 9 | 33 |
| 0 | 4 | 0 | 0 |
| 28 | 62 | 0 | 0 |
| 0 | 0 | 79 | 108 |
| 0 | 0 | 5 | 34 |
| 49 | 98 | 0 | 0 |
| 17 | 64 | 0 | 0 |
| 0 | 0 | 98 | 0 |
| 0 | 0 | 0 | 98 |
G:=sub<GL(4,GF(113))| [1,0,0,0,0,1,0,0,0,0,80,33,0,0,80,9],[1,0,0,0,0,1,0,0,0,0,80,9,0,0,80,33],[0,28,0,0,4,62,0,0,0,0,79,5,0,0,108,34],[49,17,0,0,98,64,0,0,0,0,98,0,0,0,0,98] >;
D14.2Q16 in GAP, Magma, Sage, TeX
D_{14}._2Q_{16} % in TeX
G:=Group("D14.2Q16"); // GroupNames label
G:=SmallGroup(448,418);
// by ID
G=gap.SmallGroup(448,418);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,64,926,219,268,851,102,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^14=b^2=c^8=1,d^2=a^7*c^4,b*a*b=a^-1,a*c=c*a,a*d=d*a,c*b*c^-1=a^7*b,b*d=d*b,d*c*d^-1=c^-1>;
// generators/relations