metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: D14.3SD16, D14⋊C8⋊10C2, C8⋊Dic7⋊12C2, D4⋊C4⋊11D7, C4⋊C4.136D14, (C2×D4).25D14, D4⋊Dic7⋊8C2, (C2×C8).115D14, C28⋊2D4.2C2, C4.Dic14⋊4C2, C2.12(D7×SD16), C4.52(C4○D28), (C2×Dic7).21D4, C14.24(C2×SD16), (C22×D7).73D4, C22.175(D4×D7), C28.150(C4○D4), C4.79(D4⋊2D7), C2.14(D8⋊D7), C14.32(C8⋊C22), (C2×C56).126C22, (C2×C28).217C23, (D4×C14).38C22, C7⋊2(C23.46D4), C4⋊Dic7.71C22, C2.13(D14.D4), C14.21(C22.D4), (D7×C4⋊C4)⋊4C2, (C2×C7⋊C8).16C22, (C7×D4⋊C4)⋊11C2, (C2×C4×D7).10C22, (C2×C14).230(C2×D4), (C7×C4⋊C4).18C22, (C2×C4).324(C22×D7), SmallGroup(448,311)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for D14.SD16
G = < a,b,c,d | a14=b2=c8=d2=1, bab=a-1, ac=ca, ad=da, cbc-1=dbd=a7b, dcd=a7c3 >
Subgroups: 628 in 114 conjugacy classes, 39 normal (37 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C8, C2×C4, C2×C4, D4, C23, D7, C14, C14, C22⋊C4, C4⋊C4, C4⋊C4, C2×C8, C2×C8, C22×C4, C2×D4, C2×D4, Dic7, C28, C28, D14, D14, C2×C14, C2×C14, C22⋊C8, D4⋊C4, D4⋊C4, C4.Q8, C2×C4⋊C4, C4⋊D4, C7⋊C8, C56, C4×D7, C2×Dic7, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C7×D4, C22×D7, C22×C14, C23.46D4, C2×C7⋊C8, Dic7⋊C4, C4⋊Dic7, C23.D7, C7×C4⋊C4, C2×C56, C2×C4×D7, C2×C4×D7, C2×C7⋊D4, D4×C14, C4.Dic14, C8⋊Dic7, D14⋊C8, D4⋊Dic7, C7×D4⋊C4, D7×C4⋊C4, C28⋊2D4, D14.SD16
Quotients: C1, C2, C22, D4, C23, D7, SD16, C2×D4, C4○D4, D14, C22.D4, C2×SD16, C8⋊C22, C22×D7, C23.46D4, C4○D28, D4×D7, D4⋊2D7, D14.D4, D8⋊D7, 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 20)(16 19)(17 18)(21 28)(22 27)(23 26)(24 25)(29 33)(30 32)(34 42)(35 41)(36 40)(37 39)(43 51)(44 50)(45 49)(46 48)(52 56)(53 55)(57 68)(58 67)(59 66)(60 65)(61 64)(62 63)(69 70)(71 81)(72 80)(73 79)(74 78)(75 77)(82 84)(85 95)(86 94)(87 93)(88 92)(89 91)(96 98)(99 108)(100 107)(101 106)(102 105)(103 104)(109 112)(110 111)(113 124)(114 123)(115 122)(116 121)(117 120)(118 119)(125 126)(128 140)(129 139)(130 138)(131 137)(132 136)(133 135)(141 151)(142 150)(143 149)(144 148)(145 147)(152 154)(155 164)(156 163)(157 162)(158 161)(159 160)(165 168)(166 167)(169 174)(170 173)(171 172)(175 182)(176 181)(177 180)(178 179)(184 196)(185 195)(186 194)(187 193)(188 192)(189 191)(197 200)(198 199)(201 210)(202 209)(203 208)(204 207)(205 206)(211 217)(212 216)(213 215)(218 224)(219 223)(220 222)
(1 150 111 73 167 42 199 94)(2 151 112 74 168 29 200 95)(3 152 99 75 155 30 201 96)(4 153 100 76 156 31 202 97)(5 154 101 77 157 32 203 98)(6 141 102 78 158 33 204 85)(7 142 103 79 159 34 205 86)(8 143 104 80 160 35 206 87)(9 144 105 81 161 36 207 88)(10 145 106 82 162 37 208 89)(11 146 107 83 163 38 209 90)(12 147 108 84 164 39 210 91)(13 148 109 71 165 40 197 92)(14 149 110 72 166 41 198 93)(15 128 176 48 123 184 60 215)(16 129 177 49 124 185 61 216)(17 130 178 50 125 186 62 217)(18 131 179 51 126 187 63 218)(19 132 180 52 113 188 64 219)(20 133 181 53 114 189 65 220)(21 134 182 54 115 190 66 221)(22 135 169 55 116 191 67 222)(23 136 170 56 117 192 68 223)(24 137 171 43 118 193 69 224)(25 138 172 44 119 194 70 211)(26 139 173 45 120 195 57 212)(27 140 174 46 121 196 58 213)(28 127 175 47 122 183 59 214)
(1 187)(2 188)(3 189)(4 190)(5 191)(6 192)(7 193)(8 194)(9 195)(10 196)(11 183)(12 184)(13 185)(14 186)(15 154)(16 141)(17 142)(18 143)(19 144)(20 145)(21 146)(22 147)(23 148)(24 149)(25 150)(26 151)(27 152)(28 153)(29 120)(30 121)(31 122)(32 123)(33 124)(34 125)(35 126)(36 113)(37 114)(38 115)(39 116)(40 117)(41 118)(42 119)(43 103)(44 104)(45 105)(46 106)(47 107)(48 108)(49 109)(50 110)(51 111)(52 112)(53 99)(54 100)(55 101)(56 102)(57 74)(58 75)(59 76)(60 77)(61 78)(62 79)(63 80)(64 81)(65 82)(66 83)(67 84)(68 71)(69 72)(70 73)(85 177)(86 178)(87 179)(88 180)(89 181)(90 182)(91 169)(92 170)(93 171)(94 172)(95 173)(96 174)(97 175)(98 176)(127 163)(128 164)(129 165)(130 166)(131 167)(132 168)(133 155)(134 156)(135 157)(136 158)(137 159)(138 160)(139 161)(140 162)(197 216)(198 217)(199 218)(200 219)(201 220)(202 221)(203 222)(204 223)(205 224)(206 211)(207 212)(208 213)(209 214)(210 215)
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)(15,20)(16,19)(17,18)(21,28)(22,27)(23,26)(24,25)(29,33)(30,32)(34,42)(35,41)(36,40)(37,39)(43,51)(44,50)(45,49)(46,48)(52,56)(53,55)(57,68)(58,67)(59,66)(60,65)(61,64)(62,63)(69,70)(71,81)(72,80)(73,79)(74,78)(75,77)(82,84)(85,95)(86,94)(87,93)(88,92)(89,91)(96,98)(99,108)(100,107)(101,106)(102,105)(103,104)(109,112)(110,111)(113,124)(114,123)(115,122)(116,121)(117,120)(118,119)(125,126)(128,140)(129,139)(130,138)(131,137)(132,136)(133,135)(141,151)(142,150)(143,149)(144,148)(145,147)(152,154)(155,164)(156,163)(157,162)(158,161)(159,160)(165,168)(166,167)(169,174)(170,173)(171,172)(175,182)(176,181)(177,180)(178,179)(184,196)(185,195)(186,194)(187,193)(188,192)(189,191)(197,200)(198,199)(201,210)(202,209)(203,208)(204,207)(205,206)(211,217)(212,216)(213,215)(218,224)(219,223)(220,222), (1,150,111,73,167,42,199,94)(2,151,112,74,168,29,200,95)(3,152,99,75,155,30,201,96)(4,153,100,76,156,31,202,97)(5,154,101,77,157,32,203,98)(6,141,102,78,158,33,204,85)(7,142,103,79,159,34,205,86)(8,143,104,80,160,35,206,87)(9,144,105,81,161,36,207,88)(10,145,106,82,162,37,208,89)(11,146,107,83,163,38,209,90)(12,147,108,84,164,39,210,91)(13,148,109,71,165,40,197,92)(14,149,110,72,166,41,198,93)(15,128,176,48,123,184,60,215)(16,129,177,49,124,185,61,216)(17,130,178,50,125,186,62,217)(18,131,179,51,126,187,63,218)(19,132,180,52,113,188,64,219)(20,133,181,53,114,189,65,220)(21,134,182,54,115,190,66,221)(22,135,169,55,116,191,67,222)(23,136,170,56,117,192,68,223)(24,137,171,43,118,193,69,224)(25,138,172,44,119,194,70,211)(26,139,173,45,120,195,57,212)(27,140,174,46,121,196,58,213)(28,127,175,47,122,183,59,214), (1,187)(2,188)(3,189)(4,190)(5,191)(6,192)(7,193)(8,194)(9,195)(10,196)(11,183)(12,184)(13,185)(14,186)(15,154)(16,141)(17,142)(18,143)(19,144)(20,145)(21,146)(22,147)(23,148)(24,149)(25,150)(26,151)(27,152)(28,153)(29,120)(30,121)(31,122)(32,123)(33,124)(34,125)(35,126)(36,113)(37,114)(38,115)(39,116)(40,117)(41,118)(42,119)(43,103)(44,104)(45,105)(46,106)(47,107)(48,108)(49,109)(50,110)(51,111)(52,112)(53,99)(54,100)(55,101)(56,102)(57,74)(58,75)(59,76)(60,77)(61,78)(62,79)(63,80)(64,81)(65,82)(66,83)(67,84)(68,71)(69,72)(70,73)(85,177)(86,178)(87,179)(88,180)(89,181)(90,182)(91,169)(92,170)(93,171)(94,172)(95,173)(96,174)(97,175)(98,176)(127,163)(128,164)(129,165)(130,166)(131,167)(132,168)(133,155)(134,156)(135,157)(136,158)(137,159)(138,160)(139,161)(140,162)(197,216)(198,217)(199,218)(200,219)(201,220)(202,221)(203,222)(204,223)(205,224)(206,211)(207,212)(208,213)(209,214)(210,215)>;
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)(15,20)(16,19)(17,18)(21,28)(22,27)(23,26)(24,25)(29,33)(30,32)(34,42)(35,41)(36,40)(37,39)(43,51)(44,50)(45,49)(46,48)(52,56)(53,55)(57,68)(58,67)(59,66)(60,65)(61,64)(62,63)(69,70)(71,81)(72,80)(73,79)(74,78)(75,77)(82,84)(85,95)(86,94)(87,93)(88,92)(89,91)(96,98)(99,108)(100,107)(101,106)(102,105)(103,104)(109,112)(110,111)(113,124)(114,123)(115,122)(116,121)(117,120)(118,119)(125,126)(128,140)(129,139)(130,138)(131,137)(132,136)(133,135)(141,151)(142,150)(143,149)(144,148)(145,147)(152,154)(155,164)(156,163)(157,162)(158,161)(159,160)(165,168)(166,167)(169,174)(170,173)(171,172)(175,182)(176,181)(177,180)(178,179)(184,196)(185,195)(186,194)(187,193)(188,192)(189,191)(197,200)(198,199)(201,210)(202,209)(203,208)(204,207)(205,206)(211,217)(212,216)(213,215)(218,224)(219,223)(220,222), (1,150,111,73,167,42,199,94)(2,151,112,74,168,29,200,95)(3,152,99,75,155,30,201,96)(4,153,100,76,156,31,202,97)(5,154,101,77,157,32,203,98)(6,141,102,78,158,33,204,85)(7,142,103,79,159,34,205,86)(8,143,104,80,160,35,206,87)(9,144,105,81,161,36,207,88)(10,145,106,82,162,37,208,89)(11,146,107,83,163,38,209,90)(12,147,108,84,164,39,210,91)(13,148,109,71,165,40,197,92)(14,149,110,72,166,41,198,93)(15,128,176,48,123,184,60,215)(16,129,177,49,124,185,61,216)(17,130,178,50,125,186,62,217)(18,131,179,51,126,187,63,218)(19,132,180,52,113,188,64,219)(20,133,181,53,114,189,65,220)(21,134,182,54,115,190,66,221)(22,135,169,55,116,191,67,222)(23,136,170,56,117,192,68,223)(24,137,171,43,118,193,69,224)(25,138,172,44,119,194,70,211)(26,139,173,45,120,195,57,212)(27,140,174,46,121,196,58,213)(28,127,175,47,122,183,59,214), (1,187)(2,188)(3,189)(4,190)(5,191)(6,192)(7,193)(8,194)(9,195)(10,196)(11,183)(12,184)(13,185)(14,186)(15,154)(16,141)(17,142)(18,143)(19,144)(20,145)(21,146)(22,147)(23,148)(24,149)(25,150)(26,151)(27,152)(28,153)(29,120)(30,121)(31,122)(32,123)(33,124)(34,125)(35,126)(36,113)(37,114)(38,115)(39,116)(40,117)(41,118)(42,119)(43,103)(44,104)(45,105)(46,106)(47,107)(48,108)(49,109)(50,110)(51,111)(52,112)(53,99)(54,100)(55,101)(56,102)(57,74)(58,75)(59,76)(60,77)(61,78)(62,79)(63,80)(64,81)(65,82)(66,83)(67,84)(68,71)(69,72)(70,73)(85,177)(86,178)(87,179)(88,180)(89,181)(90,182)(91,169)(92,170)(93,171)(94,172)(95,173)(96,174)(97,175)(98,176)(127,163)(128,164)(129,165)(130,166)(131,167)(132,168)(133,155)(134,156)(135,157)(136,158)(137,159)(138,160)(139,161)(140,162)(197,216)(198,217)(199,218)(200,219)(201,220)(202,221)(203,222)(204,223)(205,224)(206,211)(207,212)(208,213)(209,214)(210,215) );
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),(15,20),(16,19),(17,18),(21,28),(22,27),(23,26),(24,25),(29,33),(30,32),(34,42),(35,41),(36,40),(37,39),(43,51),(44,50),(45,49),(46,48),(52,56),(53,55),(57,68),(58,67),(59,66),(60,65),(61,64),(62,63),(69,70),(71,81),(72,80),(73,79),(74,78),(75,77),(82,84),(85,95),(86,94),(87,93),(88,92),(89,91),(96,98),(99,108),(100,107),(101,106),(102,105),(103,104),(109,112),(110,111),(113,124),(114,123),(115,122),(116,121),(117,120),(118,119),(125,126),(128,140),(129,139),(130,138),(131,137),(132,136),(133,135),(141,151),(142,150),(143,149),(144,148),(145,147),(152,154),(155,164),(156,163),(157,162),(158,161),(159,160),(165,168),(166,167),(169,174),(170,173),(171,172),(175,182),(176,181),(177,180),(178,179),(184,196),(185,195),(186,194),(187,193),(188,192),(189,191),(197,200),(198,199),(201,210),(202,209),(203,208),(204,207),(205,206),(211,217),(212,216),(213,215),(218,224),(219,223),(220,222)], [(1,150,111,73,167,42,199,94),(2,151,112,74,168,29,200,95),(3,152,99,75,155,30,201,96),(4,153,100,76,156,31,202,97),(5,154,101,77,157,32,203,98),(6,141,102,78,158,33,204,85),(7,142,103,79,159,34,205,86),(8,143,104,80,160,35,206,87),(9,144,105,81,161,36,207,88),(10,145,106,82,162,37,208,89),(11,146,107,83,163,38,209,90),(12,147,108,84,164,39,210,91),(13,148,109,71,165,40,197,92),(14,149,110,72,166,41,198,93),(15,128,176,48,123,184,60,215),(16,129,177,49,124,185,61,216),(17,130,178,50,125,186,62,217),(18,131,179,51,126,187,63,218),(19,132,180,52,113,188,64,219),(20,133,181,53,114,189,65,220),(21,134,182,54,115,190,66,221),(22,135,169,55,116,191,67,222),(23,136,170,56,117,192,68,223),(24,137,171,43,118,193,69,224),(25,138,172,44,119,194,70,211),(26,139,173,45,120,195,57,212),(27,140,174,46,121,196,58,213),(28,127,175,47,122,183,59,214)], [(1,187),(2,188),(3,189),(4,190),(5,191),(6,192),(7,193),(8,194),(9,195),(10,196),(11,183),(12,184),(13,185),(14,186),(15,154),(16,141),(17,142),(18,143),(19,144),(20,145),(21,146),(22,147),(23,148),(24,149),(25,150),(26,151),(27,152),(28,153),(29,120),(30,121),(31,122),(32,123),(33,124),(34,125),(35,126),(36,113),(37,114),(38,115),(39,116),(40,117),(41,118),(42,119),(43,103),(44,104),(45,105),(46,106),(47,107),(48,108),(49,109),(50,110),(51,111),(52,112),(53,99),(54,100),(55,101),(56,102),(57,74),(58,75),(59,76),(60,77),(61,78),(62,79),(63,80),(64,81),(65,82),(66,83),(67,84),(68,71),(69,72),(70,73),(85,177),(86,178),(87,179),(88,180),(89,181),(90,182),(91,169),(92,170),(93,171),(94,172),(95,173),(96,174),(97,175),(98,176),(127,163),(128,164),(129,165),(130,166),(131,167),(132,168),(133,155),(134,156),(135,157),(136,158),(137,159),(138,160),(139,161),(140,162),(197,216),(198,217),(199,218),(200,219),(201,220),(202,221),(203,222),(204,223),(205,224),(206,211),(207,212),(208,213),(209,214),(210,215)]])
61 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 7A | 7B | 7C | 8A | 8B | 8C | 8D | 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 | 4 | 7 | 7 | 7 | 8 | 8 | 8 | 8 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 | 56 | ··· | 56 |
| size | 1 | 1 | 1 | 1 | 8 | 14 | 14 | 2 | 2 | 4 | 4 | 28 | 28 | 28 | 56 | 2 | 2 | 2 | 4 | 4 | 28 | 28 | 2 | ··· | 2 | 8 | ··· | 8 | 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 | 2 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | + | |||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | D4 | D7 | C4○D4 | SD16 | D14 | D14 | D14 | C4○D28 | C8⋊C22 | D4⋊2D7 | D4×D7 | D8⋊D7 | D7×SD16 |
| kernel | D14.SD16 | C4.Dic14 | C8⋊Dic7 | D14⋊C8 | D4⋊Dic7 | C7×D4⋊C4 | D7×C4⋊C4 | C28⋊2D4 | C2×Dic7 | C22×D7 | D4⋊C4 | C28 | D14 | C4⋊C4 | C2×C8 | C2×D4 | C4 | C14 | C4 | C22 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 3 | 4 | 4 | 3 | 3 | 3 | 12 | 1 | 3 | 3 | 6 | 6 |
Matrix representation of D14.SD16 ►in GL4(𝔽113) generated by
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 1 | 14 |
| 0 | 0 | 88 | 103 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 89 | 13 |
| 0 | 0 | 34 | 24 |
| 13 | 100 | 0 | 0 |
| 13 | 13 | 0 | 0 |
| 0 | 0 | 17 | 33 |
| 0 | 0 | 46 | 96 |
| 38 | 34 | 0 | 0 |
| 34 | 75 | 0 | 0 |
| 0 | 0 | 29 | 43 |
| 0 | 0 | 12 | 84 |
G:=sub<GL(4,GF(113))| [1,0,0,0,0,1,0,0,0,0,1,88,0,0,14,103],[1,0,0,0,0,1,0,0,0,0,89,34,0,0,13,24],[13,13,0,0,100,13,0,0,0,0,17,46,0,0,33,96],[38,34,0,0,34,75,0,0,0,0,29,12,0,0,43,84] >;
D14.SD16 in GAP, Magma, Sage, TeX
D_{14}.{\rm SD}_{16} % in TeX
G:=Group("D14.SD16"); // GroupNames label
G:=SmallGroup(448,311);
// by ID
G=gap.SmallGroup(448,311);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,64,926,219,851,438,102,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^14=b^2=c^8=d^2=1,b*a*b=a^-1,a*c=c*a,a*d=d*a,c*b*c^-1=d*b*d=a^7*b,d*c*d=a^7*c^3>;
// generators/relations