D14:2SD16 - GroupNames

G = D₁₄⋊₂SD₁₆ order 448 = 2⁶·7

2^nd semidirect product of D₁₄ and SD₁₆ acting via SD₁₆/C₈=C₂

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: D₁₄⋊₂SD₁₆, C₇⋊C₈⋊₂₁D₄, C₇⋊₂(C₈⋊₈D₄), C₄⋊C₄.₂₄D₁₄, Q₈⋊C₄⋊₂D₇, C₄.₁₆₆(D₄×D₇), D₁₄⋊₃Q₈⋊₁C₂, C₄⋊D₂₈.₂C₂, C₂₈.₁₂₁(C₂×D₄), (C₂×C₈).₂₁₀D₁₄, (C₂×Q₈).₁₆D₁₄, C₂.D₅₆⋊₂₄C₂, C₂.₁₈(D₇×SD₁₆), C₂₈.₁₉(C₄○D₄), C₁₄.₆₉(C₄○D₈), C₄.₃₂(C₄○D₂₈), C₄.Dic₁₄⋊₁₁C₂, (C₂×Dic₇).₉₄D₄, C₁₄.₃₂(C₂×SD₁₆), (C₂²×D₇).₅₀D₄, C₂².₁₉₇(D₄×D₇), C₂.₈(Q₈.D₁₄), C₁₄.₂₃(C₄⋊D₄), (C₂×C₂₈).₂₄₇C₂³, (C₂×C₅₆).₂₀₀C₂², (C₂×D₂₈).₆₃C₂², C₄⋊Dic₇.₉₄C₂², (Q₈×C₁₄).₃₀C₂², C₂.₂₆(D₁₄⋊D₄), (D₇×C₂×C₈)⋊₂₁C₂, (C₂×Q₈⋊D₇)⋊₃C₂, (C₇×Q₈⋊C₄)⋊₂₂C₂, (C₂×C₁₄).₂₆₀(C₂×D₄), (C₇×C₄⋊C₄).₄₈C₂², (C₂×C₇⋊C₈).₂₂₀C₂², (C₂×C₄×D₇).₂₂₈C₂², (C₂×C₄).₃₅₄(C₂²×D₇), SmallGroup(448,341)

Series: Derived ►Chief ►Lower central ►Upper central

Derived series

C₁ — C₂×C₂₈ — D₁₄⋊₂SD₁₆

Chief series

C₁ — C₇ — C₁₄ — C₂₈ — C₂×C₂₈ — C₂×C₄×D₇ — D₇×C₂×C₈ — D₁₄⋊₂SD₁₆

Lower central

C₇ — C₁₄ — C₂×C₂₈ — D₁₄⋊₂SD₁₆

Upper central

C₁ — C₂² — C₂×C₄ — Q₈⋊C₄

Generators and relations for D₁₄⋊₂SD₁₆
G = < a,b,c,d | a¹⁴=b²=c⁸=d²=1, bab=cac^-1=dad=a^-1, cbc^-1=a¹²b, dbd=a⁵b, dcd=c³ >

Subgroups: 756 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, C₂²⋊C₄, C₄⋊C₄, C₄⋊C₄, C₂×C₈, C₂×C₈, SD₁₆, C₂²×C₄, C₂×D₄, C₂×Q₈, Dic₇, C₂₈, C₂₈, D₁₄, D₁₄, C₂×C₁₄, D₄⋊C₄, Q₈⋊C₄, C₄.Q₈, C₄⋊D₄, C₂²⋊Q₈, C₂²×C₈, C₂×SD₁₆, C₇⋊C₈, C₅₆, C₄×D₇, D₂₈, C₂×Dic₇, C₂×Dic₇, C₂×C₂₈, C₂×C₂₈, C₇×Q₈, C₂²×D₇, C₂²×D₇, C₈⋊₈D₄, C₈×D₇, C₂×C₇⋊C₈, Dic₇⋊C₄, C₄⋊Dic₇, D₁₄⋊C₄, Q₈⋊D₇, C₇×C₄⋊C₄, C₂×C₅₆, C₂×C₄×D₇, C₂×D₂₈, C₂×D₂₈, Q₈×C₁₄, C₄.Dic₁₄, C₂.D₅₆, C₇×Q₈⋊C₄, C₄⋊D₂₈, D₇×C₂×C₈, C₂×Q₈⋊D₇, D₁₄⋊₃Q₈, D₁₄⋊₂SD₁₆
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, D₇×SD₁₆, Q₈.D₁₄, D₁₄⋊₂SD₁₆

Smallest permutation representation of 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)

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

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

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

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

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

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

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	28A	···	28F	28G	···	28R	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	28	···	28	28	···	28	56	···	56
size	1	1	1	1	14	14	56	2	2	8	8	14	14	56	2	2	2	2	2	2	2	14	14	14	14	2	···	2	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	D₇×SD₁₆	Q₈.D₁₄
kernel	D₁₄⋊₂SD₁₆	C₄.Dic₁₄	C₂.D₅₆	C₇×Q₈⋊C₄	C₄⋊D₂₈	D₇×C₂×C₈	C₂×Q₈⋊D₇	D₁₄⋊₃Q₈	C₇⋊C₈	C₂×Dic₇	C₂²×D₇	Q₈⋊C₄	C₂₈	D₁₄	C₄⋊C₄	C₂×C₈	C₂×Q₈	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⋊₂SD₁₆ ►in GL₆(𝔽₁₁₃)

112	0	0	0	0	0
0	112	0	0	0	0
0	0	112	103	0	0
0	0	42	80	0	0
0	0	0	0	1	0
0	0	0	0	0	1

112	0	0	0	0	0
32	1	0	0	0	0
0	0	80	112	0	0
0	0	71	33	0	0
0	0	0	0	112	0
0	0	0	0	0	112

112	0	0	0	0	0
0	112	0	0	0	0
0	0	112	103	0	0
0	0	0	1	0	0
0	0	0	0	26	91
0	0	0	0	77	0

102	77	0	0	0	0
41	11	0	0	0	0
0	0	1	10	0	0
0	0	0	112	0	0
0	0	0	0	1	0
0	0	0	0	32	112

G:=sub<GL(6,GF(113))| [112,0,0,0,0,0,0,112,0,0,0,0,0,0,112,42,0,0,0,0,103,80,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[112,32,0,0,0,0,0,1,0,0,0,0,0,0,80,71,0,0,0,0,112,33,0,0,0,0,0,0,112,0,0,0,0,0,0,112],[112,0,0,0,0,0,0,112,0,0,0,0,0,0,112,0,0,0,0,0,103,1,0,0,0,0,0,0,26,77,0,0,0,0,91,0],[102,41,0,0,0,0,77,11,0,0,0,0,0,0,1,0,0,0,0,0,10,112,0,0,0,0,0,0,1,32,0,0,0,0,0,112] >;

D₁₄⋊₂SD₁₆ in GAP, Magma, Sage, TeX

D_{14}\rtimes_2{\rm SD}_{16}

% in TeX

G:=Group("D14:2SD16");

// GroupNames label

G:=SmallGroup(448,341);

// by ID

G=gap.SmallGroup(448,341);

# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,64,590,219,184,297,136,438,102,18822]);

// Polycyclic

G:=Group<a,b,c,d|a^14=b^2=c^8=d^2=1,b*a*b=c*a*c^-1=d*a*d=a^-1,c*b*c^-1=a^12*b,d*b*d=a^5*b,d*c*d=c^3>;

// generators/relations

G = D14⋊2SD16 order 448 = 26·7

2nd semidirect product of D14 and SD16 acting via SD16/C8=C2

G = D₁₄⋊₂SD₁₆ order 448 = 2⁶·7

2^nd semidirect product of D₁₄ and SD₁₆ acting via SD₁₆/C₈=C₂