metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: D14.1SD16, D14⋊C8.5C2, C8⋊Dic7⋊14C2, C4⋊C4.151D14, Q8⋊C4⋊10D7, Q8⋊Dic7⋊7C2, (C2×C8).122D14, (C2×Q8).15D14, C2.16(D7×SD16), C4.55(C4○D28), D14⋊3Q8.1C2, C4.Dic14⋊10C2, (C2×Dic7).29D4, C14.30(C2×SD16), (C22×D7).76D4, C22.195(D4×D7), C28.161(C4○D4), C4.86(D4⋊2D7), (C2×C28).245C23, (C2×C56).133C22, C7⋊2(C23.47D4), C4⋊Dic7.93C22, (Q8×C14).28C22, C2.13(Q16⋊D7), C14.59(C8.C22), C2.16(D14.D4), C14.24(C22.D4), (D7×C4⋊C4).2C2, (C2×C7⋊C8).37C22, (C2×C4×D7).19C22, (C7×Q8⋊C4)⋊10C2, (C2×C14).258(C2×D4), (C7×C4⋊C4).46C22, (C2×C4).352(C22×D7), SmallGroup(448,339)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for D14.1SD16
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=a7c3 >
Subgroups: 532 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, Q8⋊C4, C4.Q8, C2×C4⋊C4, C22⋊Q8, C7⋊C8, C56, C4×D7, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C7×Q8, C22×D7, C23.47D4, C2×C7⋊C8, Dic7⋊C4, C4⋊Dic7, D14⋊C4, C7×C4⋊C4, C2×C56, C2×C4×D7, C2×C4×D7, Q8×C14, C4.Dic14, C8⋊Dic7, D14⋊C8, Q8⋊Dic7, C7×Q8⋊C4, D7×C4⋊C4, D14⋊3Q8, D14.1SD16
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, D4⋊2D7, D14.D4, D7×SD16, Q16⋊D7, D14.1SD16
►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 23)(16 22)(17 21)(18 20)(24 28)(25 27)(30 42)(31 41)(32 40)(33 39)(34 38)(35 37)(43 49)(44 48)(45 47)(50 56)(51 55)(52 54)(57 66)(58 65)(59 64)(60 63)(61 62)(67 70)(68 69)(71 80)(72 79)(73 78)(74 77)(75 76)(81 84)(82 83)(85 95)(86 94)(87 93)(88 92)(89 91)(96 98)(99 102)(100 101)(103 112)(104 111)(105 110)(106 109)(107 108)(113 117)(114 116)(118 126)(119 125)(120 124)(121 123)(127 129)(130 140)(131 139)(132 138)(133 137)(134 136)(141 142)(143 154)(144 153)(145 152)(146 151)(147 150)(148 149)(155 167)(156 166)(157 165)(158 164)(159 163)(160 162)(169 170)(171 182)(172 181)(173 180)(174 179)(175 178)(176 177)(183 188)(184 187)(185 186)(189 196)(190 195)(191 194)(192 193)(197 205)(198 204)(199 203)(200 202)(206 210)(207 209)(211 220)(212 219)(213 218)(214 217)(215 216)(221 224)(222 223)
(1 23 177 205 149 50 186 165)(2 24 178 206 150 51 187 166)(3 25 179 207 151 52 188 167)(4 26 180 208 152 53 189 168)(5 27 181 209 153 54 190 155)(6 28 182 210 154 55 191 156)(7 15 169 197 141 56 192 157)(8 16 170 198 142 43 193 158)(9 17 171 199 143 44 194 159)(10 18 172 200 144 45 195 160)(11 19 173 201 145 46 196 161)(12 20 174 202 146 47 183 162)(13 21 175 203 147 48 184 163)(14 22 176 204 148 49 185 164)(29 104 115 65 90 79 128 219)(30 105 116 66 91 80 129 220)(31 106 117 67 92 81 130 221)(32 107 118 68 93 82 131 222)(33 108 119 69 94 83 132 223)(34 109 120 70 95 84 133 224)(35 110 121 57 96 71 134 211)(36 111 122 58 97 72 135 212)(37 112 123 59 98 73 136 213)(38 99 124 60 85 74 137 214)(39 100 125 61 86 75 138 215)(40 101 126 62 87 76 139 216)(41 102 113 63 88 77 140 217)(42 103 114 64 89 78 127 218)
(1 69 8 62)(2 70 9 63)(3 57 10 64)(4 58 11 65)(5 59 12 66)(6 60 13 67)(7 61 14 68)(15 131 22 138)(16 132 23 139)(17 133 24 140)(18 134 25 127)(19 135 26 128)(20 136 27 129)(21 137 28 130)(29 161 36 168)(30 162 37 155)(31 163 38 156)(32 164 39 157)(33 165 40 158)(34 166 41 159)(35 167 42 160)(43 119 50 126)(44 120 51 113)(45 121 52 114)(46 122 53 115)(47 123 54 116)(48 124 55 117)(49 125 56 118)(71 195 78 188)(72 196 79 189)(73 183 80 190)(74 184 81 191)(75 185 82 192)(76 186 83 193)(77 187 84 194)(85 210 92 203)(86 197 93 204)(87 198 94 205)(88 199 95 206)(89 200 96 207)(90 201 97 208)(91 202 98 209)(99 175 106 182)(100 176 107 169)(101 177 108 170)(102 178 109 171)(103 179 110 172)(104 180 111 173)(105 181 112 174)(141 215 148 222)(142 216 149 223)(143 217 150 224)(144 218 151 211)(145 219 152 212)(146 220 153 213)(147 221 154 214)
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)(15,23)(16,22)(17,21)(18,20)(24,28)(25,27)(30,42)(31,41)(32,40)(33,39)(34,38)(35,37)(43,49)(44,48)(45,47)(50,56)(51,55)(52,54)(57,66)(58,65)(59,64)(60,63)(61,62)(67,70)(68,69)(71,80)(72,79)(73,78)(74,77)(75,76)(81,84)(82,83)(85,95)(86,94)(87,93)(88,92)(89,91)(96,98)(99,102)(100,101)(103,112)(104,111)(105,110)(106,109)(107,108)(113,117)(114,116)(118,126)(119,125)(120,124)(121,123)(127,129)(130,140)(131,139)(132,138)(133,137)(134,136)(141,142)(143,154)(144,153)(145,152)(146,151)(147,150)(148,149)(155,167)(156,166)(157,165)(158,164)(159,163)(160,162)(169,170)(171,182)(172,181)(173,180)(174,179)(175,178)(176,177)(183,188)(184,187)(185,186)(189,196)(190,195)(191,194)(192,193)(197,205)(198,204)(199,203)(200,202)(206,210)(207,209)(211,220)(212,219)(213,218)(214,217)(215,216)(221,224)(222,223), (1,23,177,205,149,50,186,165)(2,24,178,206,150,51,187,166)(3,25,179,207,151,52,188,167)(4,26,180,208,152,53,189,168)(5,27,181,209,153,54,190,155)(6,28,182,210,154,55,191,156)(7,15,169,197,141,56,192,157)(8,16,170,198,142,43,193,158)(9,17,171,199,143,44,194,159)(10,18,172,200,144,45,195,160)(11,19,173,201,145,46,196,161)(12,20,174,202,146,47,183,162)(13,21,175,203,147,48,184,163)(14,22,176,204,148,49,185,164)(29,104,115,65,90,79,128,219)(30,105,116,66,91,80,129,220)(31,106,117,67,92,81,130,221)(32,107,118,68,93,82,131,222)(33,108,119,69,94,83,132,223)(34,109,120,70,95,84,133,224)(35,110,121,57,96,71,134,211)(36,111,122,58,97,72,135,212)(37,112,123,59,98,73,136,213)(38,99,124,60,85,74,137,214)(39,100,125,61,86,75,138,215)(40,101,126,62,87,76,139,216)(41,102,113,63,88,77,140,217)(42,103,114,64,89,78,127,218), (1,69,8,62)(2,70,9,63)(3,57,10,64)(4,58,11,65)(5,59,12,66)(6,60,13,67)(7,61,14,68)(15,131,22,138)(16,132,23,139)(17,133,24,140)(18,134,25,127)(19,135,26,128)(20,136,27,129)(21,137,28,130)(29,161,36,168)(30,162,37,155)(31,163,38,156)(32,164,39,157)(33,165,40,158)(34,166,41,159)(35,167,42,160)(43,119,50,126)(44,120,51,113)(45,121,52,114)(46,122,53,115)(47,123,54,116)(48,124,55,117)(49,125,56,118)(71,195,78,188)(72,196,79,189)(73,183,80,190)(74,184,81,191)(75,185,82,192)(76,186,83,193)(77,187,84,194)(85,210,92,203)(86,197,93,204)(87,198,94,205)(88,199,95,206)(89,200,96,207)(90,201,97,208)(91,202,98,209)(99,175,106,182)(100,176,107,169)(101,177,108,170)(102,178,109,171)(103,179,110,172)(104,180,111,173)(105,181,112,174)(141,215,148,222)(142,216,149,223)(143,217,150,224)(144,218,151,211)(145,219,152,212)(146,220,153,213)(147,221,154,214)>;
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)(15,23)(16,22)(17,21)(18,20)(24,28)(25,27)(30,42)(31,41)(32,40)(33,39)(34,38)(35,37)(43,49)(44,48)(45,47)(50,56)(51,55)(52,54)(57,66)(58,65)(59,64)(60,63)(61,62)(67,70)(68,69)(71,80)(72,79)(73,78)(74,77)(75,76)(81,84)(82,83)(85,95)(86,94)(87,93)(88,92)(89,91)(96,98)(99,102)(100,101)(103,112)(104,111)(105,110)(106,109)(107,108)(113,117)(114,116)(118,126)(119,125)(120,124)(121,123)(127,129)(130,140)(131,139)(132,138)(133,137)(134,136)(141,142)(143,154)(144,153)(145,152)(146,151)(147,150)(148,149)(155,167)(156,166)(157,165)(158,164)(159,163)(160,162)(169,170)(171,182)(172,181)(173,180)(174,179)(175,178)(176,177)(183,188)(184,187)(185,186)(189,196)(190,195)(191,194)(192,193)(197,205)(198,204)(199,203)(200,202)(206,210)(207,209)(211,220)(212,219)(213,218)(214,217)(215,216)(221,224)(222,223), (1,23,177,205,149,50,186,165)(2,24,178,206,150,51,187,166)(3,25,179,207,151,52,188,167)(4,26,180,208,152,53,189,168)(5,27,181,209,153,54,190,155)(6,28,182,210,154,55,191,156)(7,15,169,197,141,56,192,157)(8,16,170,198,142,43,193,158)(9,17,171,199,143,44,194,159)(10,18,172,200,144,45,195,160)(11,19,173,201,145,46,196,161)(12,20,174,202,146,47,183,162)(13,21,175,203,147,48,184,163)(14,22,176,204,148,49,185,164)(29,104,115,65,90,79,128,219)(30,105,116,66,91,80,129,220)(31,106,117,67,92,81,130,221)(32,107,118,68,93,82,131,222)(33,108,119,69,94,83,132,223)(34,109,120,70,95,84,133,224)(35,110,121,57,96,71,134,211)(36,111,122,58,97,72,135,212)(37,112,123,59,98,73,136,213)(38,99,124,60,85,74,137,214)(39,100,125,61,86,75,138,215)(40,101,126,62,87,76,139,216)(41,102,113,63,88,77,140,217)(42,103,114,64,89,78,127,218), (1,69,8,62)(2,70,9,63)(3,57,10,64)(4,58,11,65)(5,59,12,66)(6,60,13,67)(7,61,14,68)(15,131,22,138)(16,132,23,139)(17,133,24,140)(18,134,25,127)(19,135,26,128)(20,136,27,129)(21,137,28,130)(29,161,36,168)(30,162,37,155)(31,163,38,156)(32,164,39,157)(33,165,40,158)(34,166,41,159)(35,167,42,160)(43,119,50,126)(44,120,51,113)(45,121,52,114)(46,122,53,115)(47,123,54,116)(48,124,55,117)(49,125,56,118)(71,195,78,188)(72,196,79,189)(73,183,80,190)(74,184,81,191)(75,185,82,192)(76,186,83,193)(77,187,84,194)(85,210,92,203)(86,197,93,204)(87,198,94,205)(88,199,95,206)(89,200,96,207)(90,201,97,208)(91,202,98,209)(99,175,106,182)(100,176,107,169)(101,177,108,170)(102,178,109,171)(103,179,110,172)(104,180,111,173)(105,181,112,174)(141,215,148,222)(142,216,149,223)(143,217,150,224)(144,218,151,211)(145,219,152,212)(146,220,153,213)(147,221,154,214) );
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),(15,23),(16,22),(17,21),(18,20),(24,28),(25,27),(30,42),(31,41),(32,40),(33,39),(34,38),(35,37),(43,49),(44,48),(45,47),(50,56),(51,55),(52,54),(57,66),(58,65),(59,64),(60,63),(61,62),(67,70),(68,69),(71,80),(72,79),(73,78),(74,77),(75,76),(81,84),(82,83),(85,95),(86,94),(87,93),(88,92),(89,91),(96,98),(99,102),(100,101),(103,112),(104,111),(105,110),(106,109),(107,108),(113,117),(114,116),(118,126),(119,125),(120,124),(121,123),(127,129),(130,140),(131,139),(132,138),(133,137),(134,136),(141,142),(143,154),(144,153),(145,152),(146,151),(147,150),(148,149),(155,167),(156,166),(157,165),(158,164),(159,163),(160,162),(169,170),(171,182),(172,181),(173,180),(174,179),(175,178),(176,177),(183,188),(184,187),(185,186),(189,196),(190,195),(191,194),(192,193),(197,205),(198,204),(199,203),(200,202),(206,210),(207,209),(211,220),(212,219),(213,218),(214,217),(215,216),(221,224),(222,223)], [(1,23,177,205,149,50,186,165),(2,24,178,206,150,51,187,166),(3,25,179,207,151,52,188,167),(4,26,180,208,152,53,189,168),(5,27,181,209,153,54,190,155),(6,28,182,210,154,55,191,156),(7,15,169,197,141,56,192,157),(8,16,170,198,142,43,193,158),(9,17,171,199,143,44,194,159),(10,18,172,200,144,45,195,160),(11,19,173,201,145,46,196,161),(12,20,174,202,146,47,183,162),(13,21,175,203,147,48,184,163),(14,22,176,204,148,49,185,164),(29,104,115,65,90,79,128,219),(30,105,116,66,91,80,129,220),(31,106,117,67,92,81,130,221),(32,107,118,68,93,82,131,222),(33,108,119,69,94,83,132,223),(34,109,120,70,95,84,133,224),(35,110,121,57,96,71,134,211),(36,111,122,58,97,72,135,212),(37,112,123,59,98,73,136,213),(38,99,124,60,85,74,137,214),(39,100,125,61,86,75,138,215),(40,101,126,62,87,76,139,216),(41,102,113,63,88,77,140,217),(42,103,114,64,89,78,127,218)], [(1,69,8,62),(2,70,9,63),(3,57,10,64),(4,58,11,65),(5,59,12,66),(6,60,13,67),(7,61,14,68),(15,131,22,138),(16,132,23,139),(17,133,24,140),(18,134,25,127),(19,135,26,128),(20,136,27,129),(21,137,28,130),(29,161,36,168),(30,162,37,155),(31,163,38,156),(32,164,39,157),(33,165,40,158),(34,166,41,159),(35,167,42,160),(43,119,50,126),(44,120,51,113),(45,121,52,114),(46,122,53,115),(47,123,54,116),(48,124,55,117),(49,125,56,118),(71,195,78,188),(72,196,79,189),(73,183,80,190),(74,184,81,191),(75,185,82,192),(76,186,83,193),(77,187,84,194),(85,210,92,203),(86,197,93,204),(87,198,94,205),(88,199,95,206),(89,200,96,207),(90,201,97,208),(91,202,98,209),(99,175,106,182),(100,176,107,169),(101,177,108,170),(102,178,109,171),(103,179,110,172),(104,180,111,173),(105,181,112,174),(141,215,148,222),(142,216,149,223),(143,217,150,224),(144,218,151,211),(145,219,152,212),(146,220,153,213),(147,221,154,214)]])
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 | 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 | D7×SD16 | Q16⋊D7 |
| kernel | D14.1SD16 | C4.Dic14 | C8⋊Dic7 | D14⋊C8 | Q8⋊Dic7 | C7×Q8⋊C4 | D7×C4⋊C4 | D14⋊3Q8 | C2×Dic7 | C22×D7 | Q8⋊C4 | C28 | D14 | C4⋊C4 | C2×C8 | C2×Q8 | 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 D14.1SD16 ►in GL4(𝔽113) generated by
| 8 | 80 | 0 | 0 |
| 66 | 81 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 33 | 1 | 0 | 0 |
| 42 | 80 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 47 | 75 | 0 | 0 |
| 76 | 66 | 0 | 0 |
| 0 | 0 | 87 | 77 |
| 0 | 0 | 91 | 0 |
| 98 | 0 | 0 | 0 |
| 0 | 98 | 0 | 0 |
| 0 | 0 | 72 | 27 |
| 0 | 0 | 101 | 41 |
G:=sub<GL(4,GF(113))| [8,66,0,0,80,81,0,0,0,0,1,0,0,0,0,1],[33,42,0,0,1,80,0,0,0,0,1,0,0,0,0,1],[47,76,0,0,75,66,0,0,0,0,87,91,0,0,77,0],[98,0,0,0,0,98,0,0,0,0,72,101,0,0,27,41] >;
D14.1SD16 in GAP, Magma, Sage, TeX
D_{14}._1{\rm SD}_{16} % in TeX
G:=Group("D14.1SD16"); // GroupNames label
G:=SmallGroup(448,339);
// by ID
G=gap.SmallGroup(448,339);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,64,254,219,184,851,438,102,18822]);
// 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=a^7*c^3>;
// generators/relations