metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: D14.2SD16, C4.Q8⋊6D7, C4⋊C4.36D14, D14⋊C8.13C2, (C2×C8).137D14, C2.22(D7×SD16), C4.72(C4○D28), C28.27(C4○D4), C14.Q16⋊15C2, D14⋊2Q8.4C2, C4.Dic14⋊16C2, (C2×Dic7).40D4, C14.38(C2×SD16), (C22×D7).82D4, C22.214(D4×D7), C28.44D4⋊31C2, (C2×C28).278C23, (C2×C56).284C22, C4.24(Q8⋊2D7), C7⋊3(C23.47D4), C2.23(SD16⋊D7), C14.42(C8.C22), C4⋊Dic7.110C22, C2.11(D14.5D4), (C2×Dic14).82C22, C14.41(C22.D4), (D7×C4⋊C4).6C2, (C7×C4.Q8)⋊15C2, (C2×C7⋊C8).56C22, (C2×C4×D7).31C22, (C2×C14).283(C2×D4), (C7×C4⋊C4).71C22, (C2×C4).381(C22×D7), SmallGroup(448,396)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for D14.2SD16
G = < a,b,c,d | a14=b2=c8=1, d2=a7, bab=a-1, ac=ca, ad=da, cbc-1=a7b, bd=db, dcd-1=c3 >
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, C4.Q8, C4.Q8, C2×C4⋊C4, C22⋊Q8, C7⋊C8, C56, Dic14, C4×D7, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C22×D7, C23.47D4, C2×C7⋊C8, Dic7⋊C4, C4⋊Dic7, C4⋊Dic7, D14⋊C4, C7×C4⋊C4, C2×C56, C2×Dic14, C2×C4×D7, C2×C4×D7, C4.Dic14, C14.Q16, C28.44D4, D14⋊C8, C7×C4.Q8, D7×C4⋊C4, D14⋊2Q8, D14.2SD16
Quotients: C1, C2, C22, D4, C23, D7, SD16, C2×D4, C4○D4, D14, C22.D4, C2×SD16, C8.C22, C22×D7, C23.47D4, C4○D28, D4×D7, Q8⋊2D7, D14.5D4, D7×SD16, SD16⋊D7, D14.2SD16
►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 19)(16 18)(20 28)(21 27)(22 26)(23 25)(29 42)(30 41)(31 40)(32 39)(33 38)(34 37)(35 36)(43 49)(44 48)(45 47)(50 56)(51 55)(52 54)(57 69)(58 68)(59 67)(60 66)(61 65)(62 64)(71 72)(73 84)(74 83)(75 82)(76 81)(77 80)(78 79)(85 88)(86 87)(89 98)(90 97)(91 96)(92 95)(93 94)(99 101)(102 112)(103 111)(104 110)(105 109)(106 108)(113 121)(114 120)(115 119)(116 118)(122 126)(123 125)(127 140)(128 139)(129 138)(130 137)(131 136)(132 135)(133 134)(141 143)(144 154)(145 153)(146 152)(147 151)(148 150)(155 166)(156 165)(157 164)(158 163)(159 162)(160 161)(167 168)(169 178)(170 177)(171 176)(172 175)(173 174)(179 182)(180 181)(183 191)(184 190)(185 189)(186 188)(192 196)(193 195)(197 202)(198 201)(199 200)(203 210)(204 209)(205 208)(206 207)(211 213)(214 224)(215 223)(216 222)(217 221)(218 220)
(1 114 36 28 87 43 168 223)(2 115 37 15 88 44 155 224)(3 116 38 16 89 45 156 211)(4 117 39 17 90 46 157 212)(5 118 40 18 91 47 158 213)(6 119 41 19 92 48 159 214)(7 120 42 20 93 49 160 215)(8 121 29 21 94 50 161 216)(9 122 30 22 95 51 162 217)(10 123 31 23 96 52 163 218)(11 124 32 24 97 53 164 219)(12 125 33 25 98 54 165 220)(13 126 34 26 85 55 166 221)(14 113 35 27 86 56 167 222)(57 138 143 83 195 178 101 197)(58 139 144 84 196 179 102 198)(59 140 145 71 183 180 103 199)(60 127 146 72 184 181 104 200)(61 128 147 73 185 182 105 201)(62 129 148 74 186 169 106 202)(63 130 149 75 187 170 107 203)(64 131 150 76 188 171 108 204)(65 132 151 77 189 172 109 205)(66 133 152 78 190 173 110 206)(67 134 153 79 191 174 111 207)(68 135 154 80 192 175 112 208)(69 136 141 81 193 176 99 209)(70 137 142 82 194 177 100 210)
(1 200 8 207)(2 201 9 208)(3 202 10 209)(4 203 11 210)(5 204 12 197)(6 205 13 198)(7 206 14 199)(15 61 22 68)(16 62 23 69)(17 63 24 70)(18 64 25 57)(19 65 26 58)(20 66 27 59)(21 67 28 60)(29 174 36 181)(30 175 37 182)(31 176 38 169)(32 177 39 170)(33 178 40 171)(34 179 41 172)(35 180 42 173)(43 104 50 111)(44 105 51 112)(45 106 52 99)(46 107 53 100)(47 108 54 101)(48 109 55 102)(49 110 56 103)(71 93 78 86)(72 94 79 87)(73 95 80 88)(74 96 81 89)(75 97 82 90)(76 98 83 91)(77 85 84 92)(113 145 120 152)(114 146 121 153)(115 147 122 154)(116 148 123 141)(117 149 124 142)(118 150 125 143)(119 151 126 144)(127 161 134 168)(128 162 135 155)(129 163 136 156)(130 164 137 157)(131 165 138 158)(132 166 139 159)(133 167 140 160)(183 215 190 222)(184 216 191 223)(185 217 192 224)(186 218 193 211)(187 219 194 212)(188 220 195 213)(189 221 196 214)
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)(15,19)(16,18)(20,28)(21,27)(22,26)(23,25)(29,42)(30,41)(31,40)(32,39)(33,38)(34,37)(35,36)(43,49)(44,48)(45,47)(50,56)(51,55)(52,54)(57,69)(58,68)(59,67)(60,66)(61,65)(62,64)(71,72)(73,84)(74,83)(75,82)(76,81)(77,80)(78,79)(85,88)(86,87)(89,98)(90,97)(91,96)(92,95)(93,94)(99,101)(102,112)(103,111)(104,110)(105,109)(106,108)(113,121)(114,120)(115,119)(116,118)(122,126)(123,125)(127,140)(128,139)(129,138)(130,137)(131,136)(132,135)(133,134)(141,143)(144,154)(145,153)(146,152)(147,151)(148,150)(155,166)(156,165)(157,164)(158,163)(159,162)(160,161)(167,168)(169,178)(170,177)(171,176)(172,175)(173,174)(179,182)(180,181)(183,191)(184,190)(185,189)(186,188)(192,196)(193,195)(197,202)(198,201)(199,200)(203,210)(204,209)(205,208)(206,207)(211,213)(214,224)(215,223)(216,222)(217,221)(218,220), (1,114,36,28,87,43,168,223)(2,115,37,15,88,44,155,224)(3,116,38,16,89,45,156,211)(4,117,39,17,90,46,157,212)(5,118,40,18,91,47,158,213)(6,119,41,19,92,48,159,214)(7,120,42,20,93,49,160,215)(8,121,29,21,94,50,161,216)(9,122,30,22,95,51,162,217)(10,123,31,23,96,52,163,218)(11,124,32,24,97,53,164,219)(12,125,33,25,98,54,165,220)(13,126,34,26,85,55,166,221)(14,113,35,27,86,56,167,222)(57,138,143,83,195,178,101,197)(58,139,144,84,196,179,102,198)(59,140,145,71,183,180,103,199)(60,127,146,72,184,181,104,200)(61,128,147,73,185,182,105,201)(62,129,148,74,186,169,106,202)(63,130,149,75,187,170,107,203)(64,131,150,76,188,171,108,204)(65,132,151,77,189,172,109,205)(66,133,152,78,190,173,110,206)(67,134,153,79,191,174,111,207)(68,135,154,80,192,175,112,208)(69,136,141,81,193,176,99,209)(70,137,142,82,194,177,100,210), (1,200,8,207)(2,201,9,208)(3,202,10,209)(4,203,11,210)(5,204,12,197)(6,205,13,198)(7,206,14,199)(15,61,22,68)(16,62,23,69)(17,63,24,70)(18,64,25,57)(19,65,26,58)(20,66,27,59)(21,67,28,60)(29,174,36,181)(30,175,37,182)(31,176,38,169)(32,177,39,170)(33,178,40,171)(34,179,41,172)(35,180,42,173)(43,104,50,111)(44,105,51,112)(45,106,52,99)(46,107,53,100)(47,108,54,101)(48,109,55,102)(49,110,56,103)(71,93,78,86)(72,94,79,87)(73,95,80,88)(74,96,81,89)(75,97,82,90)(76,98,83,91)(77,85,84,92)(113,145,120,152)(114,146,121,153)(115,147,122,154)(116,148,123,141)(117,149,124,142)(118,150,125,143)(119,151,126,144)(127,161,134,168)(128,162,135,155)(129,163,136,156)(130,164,137,157)(131,165,138,158)(132,166,139,159)(133,167,140,160)(183,215,190,222)(184,216,191,223)(185,217,192,224)(186,218,193,211)(187,219,194,212)(188,220,195,213)(189,221,196,214)>;
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)(15,19)(16,18)(20,28)(21,27)(22,26)(23,25)(29,42)(30,41)(31,40)(32,39)(33,38)(34,37)(35,36)(43,49)(44,48)(45,47)(50,56)(51,55)(52,54)(57,69)(58,68)(59,67)(60,66)(61,65)(62,64)(71,72)(73,84)(74,83)(75,82)(76,81)(77,80)(78,79)(85,88)(86,87)(89,98)(90,97)(91,96)(92,95)(93,94)(99,101)(102,112)(103,111)(104,110)(105,109)(106,108)(113,121)(114,120)(115,119)(116,118)(122,126)(123,125)(127,140)(128,139)(129,138)(130,137)(131,136)(132,135)(133,134)(141,143)(144,154)(145,153)(146,152)(147,151)(148,150)(155,166)(156,165)(157,164)(158,163)(159,162)(160,161)(167,168)(169,178)(170,177)(171,176)(172,175)(173,174)(179,182)(180,181)(183,191)(184,190)(185,189)(186,188)(192,196)(193,195)(197,202)(198,201)(199,200)(203,210)(204,209)(205,208)(206,207)(211,213)(214,224)(215,223)(216,222)(217,221)(218,220), (1,114,36,28,87,43,168,223)(2,115,37,15,88,44,155,224)(3,116,38,16,89,45,156,211)(4,117,39,17,90,46,157,212)(5,118,40,18,91,47,158,213)(6,119,41,19,92,48,159,214)(7,120,42,20,93,49,160,215)(8,121,29,21,94,50,161,216)(9,122,30,22,95,51,162,217)(10,123,31,23,96,52,163,218)(11,124,32,24,97,53,164,219)(12,125,33,25,98,54,165,220)(13,126,34,26,85,55,166,221)(14,113,35,27,86,56,167,222)(57,138,143,83,195,178,101,197)(58,139,144,84,196,179,102,198)(59,140,145,71,183,180,103,199)(60,127,146,72,184,181,104,200)(61,128,147,73,185,182,105,201)(62,129,148,74,186,169,106,202)(63,130,149,75,187,170,107,203)(64,131,150,76,188,171,108,204)(65,132,151,77,189,172,109,205)(66,133,152,78,190,173,110,206)(67,134,153,79,191,174,111,207)(68,135,154,80,192,175,112,208)(69,136,141,81,193,176,99,209)(70,137,142,82,194,177,100,210), (1,200,8,207)(2,201,9,208)(3,202,10,209)(4,203,11,210)(5,204,12,197)(6,205,13,198)(7,206,14,199)(15,61,22,68)(16,62,23,69)(17,63,24,70)(18,64,25,57)(19,65,26,58)(20,66,27,59)(21,67,28,60)(29,174,36,181)(30,175,37,182)(31,176,38,169)(32,177,39,170)(33,178,40,171)(34,179,41,172)(35,180,42,173)(43,104,50,111)(44,105,51,112)(45,106,52,99)(46,107,53,100)(47,108,54,101)(48,109,55,102)(49,110,56,103)(71,93,78,86)(72,94,79,87)(73,95,80,88)(74,96,81,89)(75,97,82,90)(76,98,83,91)(77,85,84,92)(113,145,120,152)(114,146,121,153)(115,147,122,154)(116,148,123,141)(117,149,124,142)(118,150,125,143)(119,151,126,144)(127,161,134,168)(128,162,135,155)(129,163,136,156)(130,164,137,157)(131,165,138,158)(132,166,139,159)(133,167,140,160)(183,215,190,222)(184,216,191,223)(185,217,192,224)(186,218,193,211)(187,219,194,212)(188,220,195,213)(189,221,196,214) );
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),(15,19),(16,18),(20,28),(21,27),(22,26),(23,25),(29,42),(30,41),(31,40),(32,39),(33,38),(34,37),(35,36),(43,49),(44,48),(45,47),(50,56),(51,55),(52,54),(57,69),(58,68),(59,67),(60,66),(61,65),(62,64),(71,72),(73,84),(74,83),(75,82),(76,81),(77,80),(78,79),(85,88),(86,87),(89,98),(90,97),(91,96),(92,95),(93,94),(99,101),(102,112),(103,111),(104,110),(105,109),(106,108),(113,121),(114,120),(115,119),(116,118),(122,126),(123,125),(127,140),(128,139),(129,138),(130,137),(131,136),(132,135),(133,134),(141,143),(144,154),(145,153),(146,152),(147,151),(148,150),(155,166),(156,165),(157,164),(158,163),(159,162),(160,161),(167,168),(169,178),(170,177),(171,176),(172,175),(173,174),(179,182),(180,181),(183,191),(184,190),(185,189),(186,188),(192,196),(193,195),(197,202),(198,201),(199,200),(203,210),(204,209),(205,208),(206,207),(211,213),(214,224),(215,223),(216,222),(217,221),(218,220)], [(1,114,36,28,87,43,168,223),(2,115,37,15,88,44,155,224),(3,116,38,16,89,45,156,211),(4,117,39,17,90,46,157,212),(5,118,40,18,91,47,158,213),(6,119,41,19,92,48,159,214),(7,120,42,20,93,49,160,215),(8,121,29,21,94,50,161,216),(9,122,30,22,95,51,162,217),(10,123,31,23,96,52,163,218),(11,124,32,24,97,53,164,219),(12,125,33,25,98,54,165,220),(13,126,34,26,85,55,166,221),(14,113,35,27,86,56,167,222),(57,138,143,83,195,178,101,197),(58,139,144,84,196,179,102,198),(59,140,145,71,183,180,103,199),(60,127,146,72,184,181,104,200),(61,128,147,73,185,182,105,201),(62,129,148,74,186,169,106,202),(63,130,149,75,187,170,107,203),(64,131,150,76,188,171,108,204),(65,132,151,77,189,172,109,205),(66,133,152,78,190,173,110,206),(67,134,153,79,191,174,111,207),(68,135,154,80,192,175,112,208),(69,136,141,81,193,176,99,209),(70,137,142,82,194,177,100,210)], [(1,200,8,207),(2,201,9,208),(3,202,10,209),(4,203,11,210),(5,204,12,197),(6,205,13,198),(7,206,14,199),(15,61,22,68),(16,62,23,69),(17,63,24,70),(18,64,25,57),(19,65,26,58),(20,66,27,59),(21,67,28,60),(29,174,36,181),(30,175,37,182),(31,176,38,169),(32,177,39,170),(33,178,40,171),(34,179,41,172),(35,180,42,173),(43,104,50,111),(44,105,51,112),(45,106,52,99),(46,107,53,100),(47,108,54,101),(48,109,55,102),(49,110,56,103),(71,93,78,86),(72,94,79,87),(73,95,80,88),(74,96,81,89),(75,97,82,90),(76,98,83,91),(77,85,84,92),(113,145,120,152),(114,146,121,153),(115,147,122,154),(116,148,123,141),(117,149,124,142),(118,150,125,143),(119,151,126,144),(127,161,134,168),(128,162,135,155),(129,163,136,156),(130,164,137,157),(131,165,138,158),(132,166,139,159),(133,167,140,160),(183,215,190,222),(184,216,191,223),(185,217,192,224),(186,218,193,211),(187,219,194,212),(188,220,195,213),(189,221,196,214)]])
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 | SD16 | D14 | D14 | C4○D28 | C8.C22 | Q8⋊2D7 | D4×D7 | D7×SD16 | SD16⋊D7 |
| kernel | D14.2SD16 | C4.Dic14 | C14.Q16 | C28.44D4 | D14⋊C8 | C7×C4.Q8 | D7×C4⋊C4 | D14⋊2Q8 | 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 D14.2SD16 ►in GL4(𝔽113) generated by
| 33 | 10 | 0 | 0 |
| 71 | 1 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 104 | 89 | 0 | 0 |
| 41 | 9 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 34 | 106 | 0 | 0 |
| 52 | 79 | 0 | 0 |
| 0 | 0 | 0 | 7 |
| 0 | 0 | 97 | 26 |
| 15 | 0 | 0 | 0 |
| 0 | 15 | 0 | 0 |
| 0 | 0 | 92 | 33 |
| 0 | 0 | 62 | 21 |
G:=sub<GL(4,GF(113))| [33,71,0,0,10,1,0,0,0,0,1,0,0,0,0,1],[104,41,0,0,89,9,0,0,0,0,1,0,0,0,0,1],[34,52,0,0,106,79,0,0,0,0,0,97,0,0,7,26],[15,0,0,0,0,15,0,0,0,0,92,62,0,0,33,21] >;
D14.2SD16 in GAP, Magma, Sage, TeX
D_{14}._2{\rm SD}_{16} % in TeX
G:=Group("D14.2SD16"); // GroupNames label
G:=SmallGroup(448,396);
// by ID
G=gap.SmallGroup(448,396);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,64,254,219,100,851,102,18822]);
// 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=a^7*b,b*d=d*b,d*c*d^-1=c^3>;
// generators/relations