metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: D14⋊1SD16, C7⋊C8⋊20D4, C7⋊1(C8⋊8D4), D4⋊C4⋊3D7, C4⋊C4.10D14, C4.159(D4×D7), D14⋊2Q8⋊2C2, (C2×D4).26D14, C28.8(C4○D4), (C2×C8).203D14, C28⋊2D4.3C2, C28.109(C2×D4), C4.Dic14⋊5C2, C2.13(D7×SD16), C4.25(C4○D28), C14.23(C4○D8), C2.9(D8⋊3D7), (C2×Dic7).90D4, C14.25(C2×SD16), (C22×D7).48D4, C22.176(D4×D7), C28.44D4⋊20C2, C14.16(C4⋊D4), (C2×C28).218C23, (C2×C56).185C22, (D4×C14).39C22, C4⋊Dic7.72C22, C2.19(D14⋊D4), (C2×Dic14).57C22, (D7×C2×C8)⋊19C2, (C2×D4.D7)⋊4C2, (C7×D4⋊C4)⋊23C2, (C2×C14).231(C2×D4), (C7×C4⋊C4).19C22, (C2×C7⋊C8).213C22, (C2×C4×D7).225C22, (C2×C4).325(C22×D7), SmallGroup(448,312)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for D14⋊SD16
G = < a,b,c,d | a14=b2=c8=d2=1, bab=cac-1=a-1, ad=da, cbc-1=a12b, dbd=a7b, dcd=c3 >
Subgroups: 660 in 124 conjugacy classes, 41 normal (37 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C8, C2×C4, C2×C4, D4, Q8, C23, D7, C14, C14, C22⋊C4, C4⋊C4, C4⋊C4, C2×C8, C2×C8, SD16, C22×C4, C2×D4, C2×D4, C2×Q8, Dic7, C28, C28, D14, D14, C2×C14, C2×C14, D4⋊C4, Q8⋊C4, C4.Q8, C4⋊D4, C22⋊Q8, C22×C8, C2×SD16, C7⋊C8, C56, Dic14, C4×D7, C2×Dic7, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C7×D4, C22×D7, C22×C14, C8⋊8D4, C8×D7, C2×C7⋊C8, C4⋊Dic7, C4⋊Dic7, D14⋊C4, D4.D7, C23.D7, C7×C4⋊C4, C2×C56, C2×Dic14, C2×C4×D7, C2×C7⋊D4, D4×C14, C4.Dic14, C28.44D4, C7×D4⋊C4, D14⋊2Q8, D7×C2×C8, C2×D4.D7, C28⋊2D4, D14⋊SD16
Quotients: C1, C2, C22, D4, C23, D7, SD16, C2×D4, C4○D4, D14, C4⋊D4, C2×SD16, C4○D8, C22×D7, C8⋊8D4, C4○D28, D4×D7, D14⋊D4, D8⋊3D7, D7×SD16, D14⋊SD16
►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 28)(16 27)(17 26)(18 25)(19 24)(20 23)(21 22)(29 41)(30 40)(31 39)(32 38)(33 37)(34 36)(43 54)(44 53)(45 52)(46 51)(47 50)(48 49)(55 56)(57 69)(58 68)(59 67)(60 66)(61 65)(62 64)(71 78)(72 77)(73 76)(74 75)(79 84)(80 83)(81 82)(85 90)(86 89)(87 88)(91 98)(92 97)(93 96)(94 95)(99 105)(100 104)(101 103)(106 112)(107 111)(108 110)(113 114)(115 126)(116 125)(117 124)(118 123)(119 122)(120 121)(127 137)(128 136)(129 135)(130 134)(131 133)(138 140)(141 153)(142 152)(143 151)(144 150)(145 149)(146 148)(155 160)(156 159)(157 158)(161 168)(162 167)(163 166)(164 165)(170 182)(171 181)(172 180)(173 179)(174 178)(175 177)(183 192)(184 191)(185 190)(186 189)(187 188)(193 196)(194 195)(197 203)(198 202)(199 201)(204 210)(205 209)(206 208)(211 217)(212 216)(213 215)(218 224)(219 223)(220 222)
(1 114 88 56 195 22 75 165)(2 113 89 55 196 21 76 164)(3 126 90 54 183 20 77 163)(4 125 91 53 184 19 78 162)(5 124 92 52 185 18 79 161)(6 123 93 51 186 17 80 160)(7 122 94 50 187 16 81 159)(8 121 95 49 188 15 82 158)(9 120 96 48 189 28 83 157)(10 119 97 47 190 27 84 156)(11 118 98 46 191 26 71 155)(12 117 85 45 192 25 72 168)(13 116 86 44 193 24 73 167)(14 115 87 43 194 23 74 166)(29 221 103 200 170 70 140 147)(30 220 104 199 171 69 127 146)(31 219 105 198 172 68 128 145)(32 218 106 197 173 67 129 144)(33 217 107 210 174 66 130 143)(34 216 108 209 175 65 131 142)(35 215 109 208 176 64 132 141)(36 214 110 207 177 63 133 154)(37 213 111 206 178 62 134 153)(38 212 112 205 179 61 135 152)(39 211 99 204 180 60 136 151)(40 224 100 203 181 59 137 150)(41 223 101 202 182 58 138 149)(42 222 102 201 169 57 139 148)
(1 211)(2 212)(3 213)(4 214)(5 215)(6 216)(7 217)(8 218)(9 219)(10 220)(11 221)(12 222)(13 223)(14 224)(15 32)(16 33)(17 34)(18 35)(19 36)(20 37)(21 38)(22 39)(23 40)(24 41)(25 42)(26 29)(27 30)(28 31)(43 100)(44 101)(45 102)(46 103)(47 104)(48 105)(49 106)(50 107)(51 108)(52 109)(53 110)(54 111)(55 112)(56 99)(57 192)(58 193)(59 194)(60 195)(61 196)(62 183)(63 184)(64 185)(65 186)(66 187)(67 188)(68 189)(69 190)(70 191)(71 200)(72 201)(73 202)(74 203)(75 204)(76 205)(77 206)(78 207)(79 208)(80 209)(81 210)(82 197)(83 198)(84 199)(85 148)(86 149)(87 150)(88 151)(89 152)(90 153)(91 154)(92 141)(93 142)(94 143)(95 144)(96 145)(97 146)(98 147)(113 179)(114 180)(115 181)(116 182)(117 169)(118 170)(119 171)(120 172)(121 173)(122 174)(123 175)(124 176)(125 177)(126 178)(127 156)(128 157)(129 158)(130 159)(131 160)(132 161)(133 162)(134 163)(135 164)(136 165)(137 166)(138 167)(139 168)(140 155)
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)(15,28)(16,27)(17,26)(18,25)(19,24)(20,23)(21,22)(29,41)(30,40)(31,39)(32,38)(33,37)(34,36)(43,54)(44,53)(45,52)(46,51)(47,50)(48,49)(55,56)(57,69)(58,68)(59,67)(60,66)(61,65)(62,64)(71,78)(72,77)(73,76)(74,75)(79,84)(80,83)(81,82)(85,90)(86,89)(87,88)(91,98)(92,97)(93,96)(94,95)(99,105)(100,104)(101,103)(106,112)(107,111)(108,110)(113,114)(115,126)(116,125)(117,124)(118,123)(119,122)(120,121)(127,137)(128,136)(129,135)(130,134)(131,133)(138,140)(141,153)(142,152)(143,151)(144,150)(145,149)(146,148)(155,160)(156,159)(157,158)(161,168)(162,167)(163,166)(164,165)(170,182)(171,181)(172,180)(173,179)(174,178)(175,177)(183,192)(184,191)(185,190)(186,189)(187,188)(193,196)(194,195)(197,203)(198,202)(199,201)(204,210)(205,209)(206,208)(211,217)(212,216)(213,215)(218,224)(219,223)(220,222), (1,114,88,56,195,22,75,165)(2,113,89,55,196,21,76,164)(3,126,90,54,183,20,77,163)(4,125,91,53,184,19,78,162)(5,124,92,52,185,18,79,161)(6,123,93,51,186,17,80,160)(7,122,94,50,187,16,81,159)(8,121,95,49,188,15,82,158)(9,120,96,48,189,28,83,157)(10,119,97,47,190,27,84,156)(11,118,98,46,191,26,71,155)(12,117,85,45,192,25,72,168)(13,116,86,44,193,24,73,167)(14,115,87,43,194,23,74,166)(29,221,103,200,170,70,140,147)(30,220,104,199,171,69,127,146)(31,219,105,198,172,68,128,145)(32,218,106,197,173,67,129,144)(33,217,107,210,174,66,130,143)(34,216,108,209,175,65,131,142)(35,215,109,208,176,64,132,141)(36,214,110,207,177,63,133,154)(37,213,111,206,178,62,134,153)(38,212,112,205,179,61,135,152)(39,211,99,204,180,60,136,151)(40,224,100,203,181,59,137,150)(41,223,101,202,182,58,138,149)(42,222,102,201,169,57,139,148), (1,211)(2,212)(3,213)(4,214)(5,215)(6,216)(7,217)(8,218)(9,219)(10,220)(11,221)(12,222)(13,223)(14,224)(15,32)(16,33)(17,34)(18,35)(19,36)(20,37)(21,38)(22,39)(23,40)(24,41)(25,42)(26,29)(27,30)(28,31)(43,100)(44,101)(45,102)(46,103)(47,104)(48,105)(49,106)(50,107)(51,108)(52,109)(53,110)(54,111)(55,112)(56,99)(57,192)(58,193)(59,194)(60,195)(61,196)(62,183)(63,184)(64,185)(65,186)(66,187)(67,188)(68,189)(69,190)(70,191)(71,200)(72,201)(73,202)(74,203)(75,204)(76,205)(77,206)(78,207)(79,208)(80,209)(81,210)(82,197)(83,198)(84,199)(85,148)(86,149)(87,150)(88,151)(89,152)(90,153)(91,154)(92,141)(93,142)(94,143)(95,144)(96,145)(97,146)(98,147)(113,179)(114,180)(115,181)(116,182)(117,169)(118,170)(119,171)(120,172)(121,173)(122,174)(123,175)(124,176)(125,177)(126,178)(127,156)(128,157)(129,158)(130,159)(131,160)(132,161)(133,162)(134,163)(135,164)(136,165)(137,166)(138,167)(139,168)(140,155)>;
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)(15,28)(16,27)(17,26)(18,25)(19,24)(20,23)(21,22)(29,41)(30,40)(31,39)(32,38)(33,37)(34,36)(43,54)(44,53)(45,52)(46,51)(47,50)(48,49)(55,56)(57,69)(58,68)(59,67)(60,66)(61,65)(62,64)(71,78)(72,77)(73,76)(74,75)(79,84)(80,83)(81,82)(85,90)(86,89)(87,88)(91,98)(92,97)(93,96)(94,95)(99,105)(100,104)(101,103)(106,112)(107,111)(108,110)(113,114)(115,126)(116,125)(117,124)(118,123)(119,122)(120,121)(127,137)(128,136)(129,135)(130,134)(131,133)(138,140)(141,153)(142,152)(143,151)(144,150)(145,149)(146,148)(155,160)(156,159)(157,158)(161,168)(162,167)(163,166)(164,165)(170,182)(171,181)(172,180)(173,179)(174,178)(175,177)(183,192)(184,191)(185,190)(186,189)(187,188)(193,196)(194,195)(197,203)(198,202)(199,201)(204,210)(205,209)(206,208)(211,217)(212,216)(213,215)(218,224)(219,223)(220,222), (1,114,88,56,195,22,75,165)(2,113,89,55,196,21,76,164)(3,126,90,54,183,20,77,163)(4,125,91,53,184,19,78,162)(5,124,92,52,185,18,79,161)(6,123,93,51,186,17,80,160)(7,122,94,50,187,16,81,159)(8,121,95,49,188,15,82,158)(9,120,96,48,189,28,83,157)(10,119,97,47,190,27,84,156)(11,118,98,46,191,26,71,155)(12,117,85,45,192,25,72,168)(13,116,86,44,193,24,73,167)(14,115,87,43,194,23,74,166)(29,221,103,200,170,70,140,147)(30,220,104,199,171,69,127,146)(31,219,105,198,172,68,128,145)(32,218,106,197,173,67,129,144)(33,217,107,210,174,66,130,143)(34,216,108,209,175,65,131,142)(35,215,109,208,176,64,132,141)(36,214,110,207,177,63,133,154)(37,213,111,206,178,62,134,153)(38,212,112,205,179,61,135,152)(39,211,99,204,180,60,136,151)(40,224,100,203,181,59,137,150)(41,223,101,202,182,58,138,149)(42,222,102,201,169,57,139,148), (1,211)(2,212)(3,213)(4,214)(5,215)(6,216)(7,217)(8,218)(9,219)(10,220)(11,221)(12,222)(13,223)(14,224)(15,32)(16,33)(17,34)(18,35)(19,36)(20,37)(21,38)(22,39)(23,40)(24,41)(25,42)(26,29)(27,30)(28,31)(43,100)(44,101)(45,102)(46,103)(47,104)(48,105)(49,106)(50,107)(51,108)(52,109)(53,110)(54,111)(55,112)(56,99)(57,192)(58,193)(59,194)(60,195)(61,196)(62,183)(63,184)(64,185)(65,186)(66,187)(67,188)(68,189)(69,190)(70,191)(71,200)(72,201)(73,202)(74,203)(75,204)(76,205)(77,206)(78,207)(79,208)(80,209)(81,210)(82,197)(83,198)(84,199)(85,148)(86,149)(87,150)(88,151)(89,152)(90,153)(91,154)(92,141)(93,142)(94,143)(95,144)(96,145)(97,146)(98,147)(113,179)(114,180)(115,181)(116,182)(117,169)(118,170)(119,171)(120,172)(121,173)(122,174)(123,175)(124,176)(125,177)(126,178)(127,156)(128,157)(129,158)(130,159)(131,160)(132,161)(133,162)(134,163)(135,164)(136,165)(137,166)(138,167)(139,168)(140,155) );
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),(15,28),(16,27),(17,26),(18,25),(19,24),(20,23),(21,22),(29,41),(30,40),(31,39),(32,38),(33,37),(34,36),(43,54),(44,53),(45,52),(46,51),(47,50),(48,49),(55,56),(57,69),(58,68),(59,67),(60,66),(61,65),(62,64),(71,78),(72,77),(73,76),(74,75),(79,84),(80,83),(81,82),(85,90),(86,89),(87,88),(91,98),(92,97),(93,96),(94,95),(99,105),(100,104),(101,103),(106,112),(107,111),(108,110),(113,114),(115,126),(116,125),(117,124),(118,123),(119,122),(120,121),(127,137),(128,136),(129,135),(130,134),(131,133),(138,140),(141,153),(142,152),(143,151),(144,150),(145,149),(146,148),(155,160),(156,159),(157,158),(161,168),(162,167),(163,166),(164,165),(170,182),(171,181),(172,180),(173,179),(174,178),(175,177),(183,192),(184,191),(185,190),(186,189),(187,188),(193,196),(194,195),(197,203),(198,202),(199,201),(204,210),(205,209),(206,208),(211,217),(212,216),(213,215),(218,224),(219,223),(220,222)], [(1,114,88,56,195,22,75,165),(2,113,89,55,196,21,76,164),(3,126,90,54,183,20,77,163),(4,125,91,53,184,19,78,162),(5,124,92,52,185,18,79,161),(6,123,93,51,186,17,80,160),(7,122,94,50,187,16,81,159),(8,121,95,49,188,15,82,158),(9,120,96,48,189,28,83,157),(10,119,97,47,190,27,84,156),(11,118,98,46,191,26,71,155),(12,117,85,45,192,25,72,168),(13,116,86,44,193,24,73,167),(14,115,87,43,194,23,74,166),(29,221,103,200,170,70,140,147),(30,220,104,199,171,69,127,146),(31,219,105,198,172,68,128,145),(32,218,106,197,173,67,129,144),(33,217,107,210,174,66,130,143),(34,216,108,209,175,65,131,142),(35,215,109,208,176,64,132,141),(36,214,110,207,177,63,133,154),(37,213,111,206,178,62,134,153),(38,212,112,205,179,61,135,152),(39,211,99,204,180,60,136,151),(40,224,100,203,181,59,137,150),(41,223,101,202,182,58,138,149),(42,222,102,201,169,57,139,148)], [(1,211),(2,212),(3,213),(4,214),(5,215),(6,216),(7,217),(8,218),(9,219),(10,220),(11,221),(12,222),(13,223),(14,224),(15,32),(16,33),(17,34),(18,35),(19,36),(20,37),(21,38),(22,39),(23,40),(24,41),(25,42),(26,29),(27,30),(28,31),(43,100),(44,101),(45,102),(46,103),(47,104),(48,105),(49,106),(50,107),(51,108),(52,109),(53,110),(54,111),(55,112),(56,99),(57,192),(58,193),(59,194),(60,195),(61,196),(62,183),(63,184),(64,185),(65,186),(66,187),(67,188),(68,189),(69,190),(70,191),(71,200),(72,201),(73,202),(74,203),(75,204),(76,205),(77,206),(78,207),(79,208),(80,209),(81,210),(82,197),(83,198),(84,199),(85,148),(86,149),(87,150),(88,151),(89,152),(90,153),(91,154),(92,141),(93,142),(94,143),(95,144),(96,145),(97,146),(98,147),(113,179),(114,180),(115,181),(116,182),(117,169),(118,170),(119,171),(120,172),(121,173),(122,174),(123,175),(124,176),(125,177),(126,178),(127,156),(128,157),(129,158),(130,159),(131,160),(132,161),(133,162),(134,163),(135,164),(136,165),(137,166),(138,167),(139,168),(140,155)]])
64 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 7A | 7B | 7C | 8A | 8B | 8C | 8D | 8E | 8F | 8G | 8H | 14A | ··· | 14I | 14J | ··· | 14O | 28A | ··· | 28F | 28G | ··· | 28L | 56A | ··· | 56L |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 | 56 | ··· | 56 |
| size | 1 | 1 | 1 | 1 | 8 | 14 | 14 | 2 | 2 | 8 | 14 | 14 | 56 | 56 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 14 | 14 | 14 | 14 | 2 | ··· | 2 | 8 | ··· | 8 | 4 | ··· | 4 | 8 | ··· | 8 | 4 | ··· | 4 |
64 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | |||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | D4 | D4 | D7 | C4○D4 | SD16 | D14 | D14 | D14 | C4○D8 | C4○D28 | D4×D7 | D4×D7 | D8⋊3D7 | D7×SD16 |
| kernel | D14⋊SD16 | C4.Dic14 | C28.44D4 | C7×D4⋊C4 | D14⋊2Q8 | D7×C2×C8 | C2×D4.D7 | C28⋊2D4 | C7⋊C8 | C2×Dic7 | C22×D7 | D4⋊C4 | C28 | D14 | C4⋊C4 | C2×C8 | C2×D4 | C14 | C4 | C4 | C22 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 1 | 1 | 3 | 2 | 4 | 3 | 3 | 3 | 4 | 12 | 3 | 3 | 6 | 6 |
Matrix representation of D14⋊SD16 ►in GL6(𝔽113)
| 112 | 0 | 0 | 0 | 0 | 0 |
| 0 | 112 | 0 | 0 | 0 | 0 |
| 0 | 0 | 102 | 103 | 0 | 0 |
| 0 | 0 | 20 | 90 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 112 | 0 | 0 | 0 | 0 | 0 |
| 17 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 24 | 24 | 0 | 0 |
| 0 | 0 | 9 | 89 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 112 | 0 | 0 | 0 | 0 | 0 |
| 0 | 112 | 0 | 0 | 0 | 0 |
| 0 | 0 | 98 | 89 | 0 | 0 |
| 0 | 0 | 47 | 15 | 0 | 0 |
| 0 | 0 | 0 | 0 | 87 | 81 |
| 0 | 0 | 0 | 0 | 60 | 0 |
| 17 | 2 | 0 | 0 | 0 | 0 |
| 82 | 96 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 96 | 18 |
| 0 | 0 | 0 | 0 | 97 | 17 |
G:=sub<GL(6,GF(113))| [112,0,0,0,0,0,0,112,0,0,0,0,0,0,102,20,0,0,0,0,103,90,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[112,17,0,0,0,0,0,1,0,0,0,0,0,0,24,9,0,0,0,0,24,89,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[112,0,0,0,0,0,0,112,0,0,0,0,0,0,98,47,0,0,0,0,89,15,0,0,0,0,0,0,87,60,0,0,0,0,81,0],[17,82,0,0,0,0,2,96,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,96,97,0,0,0,0,18,17] >;
D14⋊SD16 in GAP, Magma, Sage, TeX
D_{14}\rtimes {\rm SD}_{16} % in TeX
G:=Group("D14:SD16"); // GroupNames label
G:=SmallGroup(448,312);
// by ID
G=gap.SmallGroup(448,312);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,64,590,219,297,136,438,102,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^14=b^2=c^8=d^2=1,b*a*b=c*a*c^-1=a^-1,a*d=d*a,c*b*c^-1=a^12*b,d*b*d=a^7*b,d*c*d=c^3>;
// generators/relations