metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: D14⋊2Q16, C56.17D4, C8.19D28, C2.D8⋊6D7, C4⋊C4.52D14, C4.55(C2×D28), C2.15(D7×Q16), C28.135(C2×D4), (C2×C8).232D14, C7⋊2(C8.18D4), C14.25(C2×Q16), (C2×Dic28)⋊16C2, C14.29(C4○D8), C28.42(C4○D4), C14.Q16⋊21C2, (C2×C56).84C22, D14⋊2Q8.8C2, (C22×D7).56D4, C22.233(D4×D7), C2.14(D8⋊3D7), C2.21(C4⋊D28), C14.48(C4⋊D4), (C2×C28).303C23, C4.11(Q8⋊2D7), (C2×Dic7).104D4, (C2×Dic14).91C22, (D7×C2×C8).4C2, (C7×C2.D8)⋊6C2, (C2×C14).308(C2×D4), (C7×C4⋊C4).96C22, (C2×C7⋊C8).236C22, (C2×C4×D7).237C22, (C2×C4).406(C22×D7), SmallGroup(448,421)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for D14⋊2Q16
G = < a,b,c,d | a14=b2=c8=1, d2=c4, bab=dad-1=a-1, ac=ca, bc=cb, dbd-1=a5b, dcd-1=c-1 >
Subgroups: 588 in 114 conjugacy classes, 43 normal (27 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C8, C8, C2×C4, C2×C4, Q8, C23, D7, C14, C22⋊C4, C4⋊C4, C4⋊C4, C2×C8, C2×C8, Q16, C22×C4, C2×Q8, Dic7, C28, C28, D14, D14, C2×C14, Q8⋊C4, C2.D8, C22⋊Q8, C22×C8, C2×Q16, C7⋊C8, C56, Dic14, C4×D7, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C22×D7, C8.18D4, C8×D7, Dic28, C2×C7⋊C8, C4⋊Dic7, D14⋊C4, C7×C4⋊C4, C2×C56, C2×Dic14, C2×C4×D7, C14.Q16, C7×C2.D8, D14⋊2Q8, D7×C2×C8, C2×Dic28, D14⋊2Q16
Quotients: C1, C2, C22, D4, C23, D7, Q16, C2×D4, C4○D4, D14, C4⋊D4, C2×Q16, C4○D8, D28, C22×D7, C8.18D4, C2×D28, D4×D7, Q8⋊2D7, C4⋊D28, D8⋊3D7, 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)
(1 223)(2 222)(3 221)(4 220)(5 219)(6 218)(7 217)(8 216)(9 215)(10 214)(11 213)(12 212)(13 211)(14 224)(15 50)(16 49)(17 48)(18 47)(19 46)(20 45)(21 44)(22 43)(23 56)(24 55)(25 54)(26 53)(27 52)(28 51)(29 144)(30 143)(31 142)(32 141)(33 154)(34 153)(35 152)(36 151)(37 150)(38 149)(39 148)(40 147)(41 146)(42 145)(57 198)(58 197)(59 210)(60 209)(61 208)(62 207)(63 206)(64 205)(65 204)(66 203)(67 202)(68 201)(69 200)(70 199)(71 116)(72 115)(73 114)(74 113)(75 126)(76 125)(77 124)(78 123)(79 122)(80 121)(81 120)(82 119)(83 118)(84 117)(85 188)(86 187)(87 186)(88 185)(89 184)(90 183)(91 196)(92 195)(93 194)(94 193)(95 192)(96 191)(97 190)(98 189)(99 130)(100 129)(101 128)(102 127)(103 140)(104 139)(105 138)(106 137)(107 136)(108 135)(109 134)(110 133)(111 132)(112 131)(155 170)(156 169)(157 182)(158 181)(159 180)(160 179)(161 178)(162 177)(163 176)(164 175)(165 174)(166 173)(167 172)(168 171)
(1 99 190 84 224 131 98 118)(2 100 191 71 211 132 85 119)(3 101 192 72 212 133 86 120)(4 102 193 73 213 134 87 121)(5 103 194 74 214 135 88 122)(6 104 195 75 215 136 89 123)(7 105 196 76 216 137 90 124)(8 106 183 77 217 138 91 125)(9 107 184 78 218 139 92 126)(10 108 185 79 219 140 93 113)(11 109 186 80 220 127 94 114)(12 110 187 81 221 128 95 115)(13 111 188 82 222 129 96 116)(14 112 189 83 223 130 97 117)(15 69 175 145 48 198 162 40)(16 70 176 146 49 199 163 41)(17 57 177 147 50 200 164 42)(18 58 178 148 51 201 165 29)(19 59 179 149 52 202 166 30)(20 60 180 150 53 203 167 31)(21 61 181 151 54 204 168 32)(22 62 182 152 55 205 155 33)(23 63 169 153 56 206 156 34)(24 64 170 154 43 207 157 35)(25 65 171 141 44 208 158 36)(26 66 172 142 45 209 159 37)(27 67 173 143 46 210 160 38)(28 68 174 144 47 197 161 39)
(1 38 224 143)(2 37 211 142)(3 36 212 141)(4 35 213 154)(5 34 214 153)(6 33 215 152)(7 32 216 151)(8 31 217 150)(9 30 218 149)(10 29 219 148)(11 42 220 147)(12 41 221 146)(13 40 222 145)(14 39 223 144)(15 82 48 116)(16 81 49 115)(17 80 50 114)(18 79 51 113)(19 78 52 126)(20 77 53 125)(21 76 54 124)(22 75 55 123)(23 74 56 122)(24 73 43 121)(25 72 44 120)(26 71 45 119)(27 84 46 118)(28 83 47 117)(57 186 200 94)(58 185 201 93)(59 184 202 92)(60 183 203 91)(61 196 204 90)(62 195 205 89)(63 194 206 88)(64 193 207 87)(65 192 208 86)(66 191 209 85)(67 190 210 98)(68 189 197 97)(69 188 198 96)(70 187 199 95)(99 160 131 173)(100 159 132 172)(101 158 133 171)(102 157 134 170)(103 156 135 169)(104 155 136 182)(105 168 137 181)(106 167 138 180)(107 166 139 179)(108 165 140 178)(109 164 127 177)(110 163 128 176)(111 162 129 175)(112 161 130 174)
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), (1,223)(2,222)(3,221)(4,220)(5,219)(6,218)(7,217)(8,216)(9,215)(10,214)(11,213)(12,212)(13,211)(14,224)(15,50)(16,49)(17,48)(18,47)(19,46)(20,45)(21,44)(22,43)(23,56)(24,55)(25,54)(26,53)(27,52)(28,51)(29,144)(30,143)(31,142)(32,141)(33,154)(34,153)(35,152)(36,151)(37,150)(38,149)(39,148)(40,147)(41,146)(42,145)(57,198)(58,197)(59,210)(60,209)(61,208)(62,207)(63,206)(64,205)(65,204)(66,203)(67,202)(68,201)(69,200)(70,199)(71,116)(72,115)(73,114)(74,113)(75,126)(76,125)(77,124)(78,123)(79,122)(80,121)(81,120)(82,119)(83,118)(84,117)(85,188)(86,187)(87,186)(88,185)(89,184)(90,183)(91,196)(92,195)(93,194)(94,193)(95,192)(96,191)(97,190)(98,189)(99,130)(100,129)(101,128)(102,127)(103,140)(104,139)(105,138)(106,137)(107,136)(108,135)(109,134)(110,133)(111,132)(112,131)(155,170)(156,169)(157,182)(158,181)(159,180)(160,179)(161,178)(162,177)(163,176)(164,175)(165,174)(166,173)(167,172)(168,171), (1,99,190,84,224,131,98,118)(2,100,191,71,211,132,85,119)(3,101,192,72,212,133,86,120)(4,102,193,73,213,134,87,121)(5,103,194,74,214,135,88,122)(6,104,195,75,215,136,89,123)(7,105,196,76,216,137,90,124)(8,106,183,77,217,138,91,125)(9,107,184,78,218,139,92,126)(10,108,185,79,219,140,93,113)(11,109,186,80,220,127,94,114)(12,110,187,81,221,128,95,115)(13,111,188,82,222,129,96,116)(14,112,189,83,223,130,97,117)(15,69,175,145,48,198,162,40)(16,70,176,146,49,199,163,41)(17,57,177,147,50,200,164,42)(18,58,178,148,51,201,165,29)(19,59,179,149,52,202,166,30)(20,60,180,150,53,203,167,31)(21,61,181,151,54,204,168,32)(22,62,182,152,55,205,155,33)(23,63,169,153,56,206,156,34)(24,64,170,154,43,207,157,35)(25,65,171,141,44,208,158,36)(26,66,172,142,45,209,159,37)(27,67,173,143,46,210,160,38)(28,68,174,144,47,197,161,39), (1,38,224,143)(2,37,211,142)(3,36,212,141)(4,35,213,154)(5,34,214,153)(6,33,215,152)(7,32,216,151)(8,31,217,150)(9,30,218,149)(10,29,219,148)(11,42,220,147)(12,41,221,146)(13,40,222,145)(14,39,223,144)(15,82,48,116)(16,81,49,115)(17,80,50,114)(18,79,51,113)(19,78,52,126)(20,77,53,125)(21,76,54,124)(22,75,55,123)(23,74,56,122)(24,73,43,121)(25,72,44,120)(26,71,45,119)(27,84,46,118)(28,83,47,117)(57,186,200,94)(58,185,201,93)(59,184,202,92)(60,183,203,91)(61,196,204,90)(62,195,205,89)(63,194,206,88)(64,193,207,87)(65,192,208,86)(66,191,209,85)(67,190,210,98)(68,189,197,97)(69,188,198,96)(70,187,199,95)(99,160,131,173)(100,159,132,172)(101,158,133,171)(102,157,134,170)(103,156,135,169)(104,155,136,182)(105,168,137,181)(106,167,138,180)(107,166,139,179)(108,165,140,178)(109,164,127,177)(110,163,128,176)(111,162,129,175)(112,161,130,174)>;
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), (1,223)(2,222)(3,221)(4,220)(5,219)(6,218)(7,217)(8,216)(9,215)(10,214)(11,213)(12,212)(13,211)(14,224)(15,50)(16,49)(17,48)(18,47)(19,46)(20,45)(21,44)(22,43)(23,56)(24,55)(25,54)(26,53)(27,52)(28,51)(29,144)(30,143)(31,142)(32,141)(33,154)(34,153)(35,152)(36,151)(37,150)(38,149)(39,148)(40,147)(41,146)(42,145)(57,198)(58,197)(59,210)(60,209)(61,208)(62,207)(63,206)(64,205)(65,204)(66,203)(67,202)(68,201)(69,200)(70,199)(71,116)(72,115)(73,114)(74,113)(75,126)(76,125)(77,124)(78,123)(79,122)(80,121)(81,120)(82,119)(83,118)(84,117)(85,188)(86,187)(87,186)(88,185)(89,184)(90,183)(91,196)(92,195)(93,194)(94,193)(95,192)(96,191)(97,190)(98,189)(99,130)(100,129)(101,128)(102,127)(103,140)(104,139)(105,138)(106,137)(107,136)(108,135)(109,134)(110,133)(111,132)(112,131)(155,170)(156,169)(157,182)(158,181)(159,180)(160,179)(161,178)(162,177)(163,176)(164,175)(165,174)(166,173)(167,172)(168,171), (1,99,190,84,224,131,98,118)(2,100,191,71,211,132,85,119)(3,101,192,72,212,133,86,120)(4,102,193,73,213,134,87,121)(5,103,194,74,214,135,88,122)(6,104,195,75,215,136,89,123)(7,105,196,76,216,137,90,124)(8,106,183,77,217,138,91,125)(9,107,184,78,218,139,92,126)(10,108,185,79,219,140,93,113)(11,109,186,80,220,127,94,114)(12,110,187,81,221,128,95,115)(13,111,188,82,222,129,96,116)(14,112,189,83,223,130,97,117)(15,69,175,145,48,198,162,40)(16,70,176,146,49,199,163,41)(17,57,177,147,50,200,164,42)(18,58,178,148,51,201,165,29)(19,59,179,149,52,202,166,30)(20,60,180,150,53,203,167,31)(21,61,181,151,54,204,168,32)(22,62,182,152,55,205,155,33)(23,63,169,153,56,206,156,34)(24,64,170,154,43,207,157,35)(25,65,171,141,44,208,158,36)(26,66,172,142,45,209,159,37)(27,67,173,143,46,210,160,38)(28,68,174,144,47,197,161,39), (1,38,224,143)(2,37,211,142)(3,36,212,141)(4,35,213,154)(5,34,214,153)(6,33,215,152)(7,32,216,151)(8,31,217,150)(9,30,218,149)(10,29,219,148)(11,42,220,147)(12,41,221,146)(13,40,222,145)(14,39,223,144)(15,82,48,116)(16,81,49,115)(17,80,50,114)(18,79,51,113)(19,78,52,126)(20,77,53,125)(21,76,54,124)(22,75,55,123)(23,74,56,122)(24,73,43,121)(25,72,44,120)(26,71,45,119)(27,84,46,118)(28,83,47,117)(57,186,200,94)(58,185,201,93)(59,184,202,92)(60,183,203,91)(61,196,204,90)(62,195,205,89)(63,194,206,88)(64,193,207,87)(65,192,208,86)(66,191,209,85)(67,190,210,98)(68,189,197,97)(69,188,198,96)(70,187,199,95)(99,160,131,173)(100,159,132,172)(101,158,133,171)(102,157,134,170)(103,156,135,169)(104,155,136,182)(105,168,137,181)(106,167,138,180)(107,166,139,179)(108,165,140,178)(109,164,127,177)(110,163,128,176)(111,162,129,175)(112,161,130,174) );
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)], [(1,223),(2,222),(3,221),(4,220),(5,219),(6,218),(7,217),(8,216),(9,215),(10,214),(11,213),(12,212),(13,211),(14,224),(15,50),(16,49),(17,48),(18,47),(19,46),(20,45),(21,44),(22,43),(23,56),(24,55),(25,54),(26,53),(27,52),(28,51),(29,144),(30,143),(31,142),(32,141),(33,154),(34,153),(35,152),(36,151),(37,150),(38,149),(39,148),(40,147),(41,146),(42,145),(57,198),(58,197),(59,210),(60,209),(61,208),(62,207),(63,206),(64,205),(65,204),(66,203),(67,202),(68,201),(69,200),(70,199),(71,116),(72,115),(73,114),(74,113),(75,126),(76,125),(77,124),(78,123),(79,122),(80,121),(81,120),(82,119),(83,118),(84,117),(85,188),(86,187),(87,186),(88,185),(89,184),(90,183),(91,196),(92,195),(93,194),(94,193),(95,192),(96,191),(97,190),(98,189),(99,130),(100,129),(101,128),(102,127),(103,140),(104,139),(105,138),(106,137),(107,136),(108,135),(109,134),(110,133),(111,132),(112,131),(155,170),(156,169),(157,182),(158,181),(159,180),(160,179),(161,178),(162,177),(163,176),(164,175),(165,174),(166,173),(167,172),(168,171)], [(1,99,190,84,224,131,98,118),(2,100,191,71,211,132,85,119),(3,101,192,72,212,133,86,120),(4,102,193,73,213,134,87,121),(5,103,194,74,214,135,88,122),(6,104,195,75,215,136,89,123),(7,105,196,76,216,137,90,124),(8,106,183,77,217,138,91,125),(9,107,184,78,218,139,92,126),(10,108,185,79,219,140,93,113),(11,109,186,80,220,127,94,114),(12,110,187,81,221,128,95,115),(13,111,188,82,222,129,96,116),(14,112,189,83,223,130,97,117),(15,69,175,145,48,198,162,40),(16,70,176,146,49,199,163,41),(17,57,177,147,50,200,164,42),(18,58,178,148,51,201,165,29),(19,59,179,149,52,202,166,30),(20,60,180,150,53,203,167,31),(21,61,181,151,54,204,168,32),(22,62,182,152,55,205,155,33),(23,63,169,153,56,206,156,34),(24,64,170,154,43,207,157,35),(25,65,171,141,44,208,158,36),(26,66,172,142,45,209,159,37),(27,67,173,143,46,210,160,38),(28,68,174,144,47,197,161,39)], [(1,38,224,143),(2,37,211,142),(3,36,212,141),(4,35,213,154),(5,34,214,153),(6,33,215,152),(7,32,216,151),(8,31,217,150),(9,30,218,149),(10,29,219,148),(11,42,220,147),(12,41,221,146),(13,40,222,145),(14,39,223,144),(15,82,48,116),(16,81,49,115),(17,80,50,114),(18,79,51,113),(19,78,52,126),(20,77,53,125),(21,76,54,124),(22,75,55,123),(23,74,56,122),(24,73,43,121),(25,72,44,120),(26,71,45,119),(27,84,46,118),(28,83,47,117),(57,186,200,94),(58,185,201,93),(59,184,202,92),(60,183,203,91),(61,196,204,90),(62,195,205,89),(63,194,206,88),(64,193,207,87),(65,192,208,86),(66,191,209,85),(67,190,210,98),(68,189,197,97),(69,188,198,96),(70,187,199,95),(99,160,131,173),(100,159,132,172),(101,158,133,171),(102,157,134,170),(103,156,135,169),(104,155,136,182),(105,168,137,181),(106,167,138,180),(107,166,139,179),(108,165,140,178),(109,164,127,177),(110,163,128,176),(111,162,129,175),(112,161,130,174)]])
64 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 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 | 4 | 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 | 2 | 2 | 8 | 8 | 14 | 14 | 56 | 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 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | - | + | + | + | + | + | - | - | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | D4 | D4 | D4 | D7 | C4○D4 | Q16 | D14 | D14 | C4○D8 | D28 | Q8⋊2D7 | D4×D7 | D8⋊3D7 | D7×Q16 |
| kernel | D14⋊2Q16 | C14.Q16 | C7×C2.D8 | D14⋊2Q8 | D7×C2×C8 | C2×Dic28 | C56 | C2×Dic7 | C22×D7 | C2.D8 | C28 | D14 | C4⋊C4 | C2×C8 | C14 | C8 | C4 | C22 | C2 | C2 |
| # reps | 1 | 2 | 1 | 2 | 1 | 1 | 2 | 1 | 1 | 3 | 2 | 4 | 6 | 3 | 4 | 12 | 3 | 3 | 6 | 6 |
Matrix representation of D14⋊2Q16 ►in GL4(𝔽113) generated by
| 112 | 0 | 0 | 0 |
| 0 | 112 | 0 | 0 |
| 0 | 0 | 0 | 10 |
| 0 | 0 | 79 | 34 |
| 1 | 0 | 0 | 0 |
| 37 | 112 | 0 | 0 |
| 0 | 0 | 34 | 103 |
| 0 | 0 | 59 | 79 |
| 69 | 0 | 0 | 0 |
| 84 | 95 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 68 | 91 | 0 | 0 |
| 51 | 45 | 0 | 0 |
| 0 | 0 | 94 | 96 |
| 0 | 0 | 81 | 19 |
G:=sub<GL(4,GF(113))| [112,0,0,0,0,112,0,0,0,0,0,79,0,0,10,34],[1,37,0,0,0,112,0,0,0,0,34,59,0,0,103,79],[69,84,0,0,0,95,0,0,0,0,1,0,0,0,0,1],[68,51,0,0,91,45,0,0,0,0,94,81,0,0,96,19] >;
D14⋊2Q16 in GAP, Magma, Sage, TeX
D_{14}\rtimes_2Q_{16} % in TeX
G:=Group("D14:2Q16"); // GroupNames label
G:=SmallGroup(448,421);
// by ID
G=gap.SmallGroup(448,421);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,120,254,219,226,438,102,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^14=b^2=c^8=1,d^2=c^4,b*a*b=d*a*d^-1=a^-1,a*c=c*a,b*c=c*b,d*b*d^-1=a^5*b,d*c*d^-1=c^-1>;
// generators/relations