metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: D14.4D8, C2.9(D7×D8), D14⋊C8⋊5C2, C56⋊1C4⋊8C2, (C2×C8).9D14, D4⋊C4⋊5D7, C14.23(C2×D8), C4⋊C4.135D14, (C2×D4).23D14, D4⋊Dic7⋊7C2, C28⋊2D4.1C2, C28.Q8⋊5C2, (C2×C56).9C22, C4.51(C4○D28), (C2×Dic7).19D4, (C22×D7).71D4, C22.172(D4×D7), C7⋊2(C22.D8), C28.149(C4○D4), C4.78(D4⋊2D7), (C2×C28).214C23, (D4×C14).35C22, C4⋊Dic7.69C22, C2.11(SD16⋊D7), C14.29(C8.C22), C2.12(D14.D4), C14.20(C22.D4), (D7×C4⋊C4)⋊3C2, (C7×D4⋊C4)⋊5C2, (C2×C4×D7).8C22, (C2×C7⋊C8).15C22, (C2×C14).227(C2×D4), (C7×C4⋊C4).16C22, (C2×C4).321(C22×D7), SmallGroup(448,308)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for D14.D8
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=a7c-1 >
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, C2.D8, 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, C22.D8, 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, C28.Q8, C56⋊1C4, D14⋊C8, D4⋊Dic7, C7×D4⋊C4, D7×C4⋊C4, C28⋊2D4, D14.D8
Quotients: C1, C2, C22, D4, C23, D7, D8, C2×D4, C4○D4, D14, C22.D4, C2×D8, C8.C22, C22×D7, C22.D8, C4○D28, D4×D7, D4⋊2D7, D14.D4, D7×D8, SD16⋊D7, D14.D8
►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 19)(16 18)(20 28)(21 27)(22 26)(23 25)(29 35)(30 34)(31 33)(36 42)(37 41)(38 40)(43 49)(44 48)(45 47)(50 56)(51 55)(52 54)(57 58)(59 70)(60 69)(61 68)(62 67)(63 66)(64 65)(71 83)(72 82)(73 81)(74 80)(75 79)(76 78)(85 94)(86 93)(87 92)(88 91)(89 90)(95 98)(96 97)(100 112)(101 111)(102 110)(103 109)(104 108)(105 107)(113 123)(114 122)(115 121)(116 120)(117 119)(124 126)(127 134)(128 133)(129 132)(130 131)(135 140)(136 139)(137 138)(141 144)(142 143)(145 154)(146 153)(147 152)(148 151)(149 150)(155 163)(156 162)(157 161)(158 160)(164 168)(165 167)(169 171)(172 182)(173 181)(174 180)(175 179)(176 178)(183 194)(184 193)(185 192)(186 191)(187 190)(188 189)(195 196)(197 206)(198 205)(199 204)(200 203)(201 202)(207 210)(208 209)(211 218)(212 217)(213 216)(214 215)(219 224)(220 223)(221 222)
(1 74 196 110 131 115 215 28)(2 75 183 111 132 116 216 15)(3 76 184 112 133 117 217 16)(4 77 185 99 134 118 218 17)(5 78 186 100 135 119 219 18)(6 79 187 101 136 120 220 19)(7 80 188 102 137 121 221 20)(8 81 189 103 138 122 222 21)(9 82 190 104 139 123 223 22)(10 83 191 105 140 124 224 23)(11 84 192 106 127 125 211 24)(12 71 193 107 128 126 212 25)(13 72 194 108 129 113 213 26)(14 73 195 109 130 114 214 27)(29 97 163 150 50 58 174 202)(30 98 164 151 51 59 175 203)(31 85 165 152 52 60 176 204)(32 86 166 153 53 61 177 205)(33 87 167 154 54 62 178 206)(34 88 168 141 55 63 179 207)(35 89 155 142 56 64 180 208)(36 90 156 143 43 65 181 209)(37 91 157 144 44 66 182 210)(38 92 158 145 45 67 169 197)(39 93 159 146 46 68 170 198)(40 94 160 147 47 69 171 199)(41 95 161 148 48 70 172 200)(42 96 162 149 49 57 173 201)
(1 209 8 202)(2 210 9 203)(3 197 10 204)(4 198 11 205)(5 199 12 206)(6 200 13 207)(7 201 14 208)(15 30 22 37)(16 31 23 38)(17 32 24 39)(18 33 25 40)(19 34 26 41)(20 35 27 42)(21 36 28 29)(43 110 50 103)(44 111 51 104)(45 112 52 105)(46 99 53 106)(47 100 54 107)(48 101 55 108)(49 102 56 109)(57 195 64 188)(58 196 65 189)(59 183 66 190)(60 184 67 191)(61 185 68 192)(62 186 69 193)(63 187 70 194)(71 171 78 178)(72 172 79 179)(73 173 80 180)(74 174 81 181)(75 175 82 182)(76 176 83 169)(77 177 84 170)(85 217 92 224)(86 218 93 211)(87 219 94 212)(88 220 95 213)(89 221 96 214)(90 222 97 215)(91 223 98 216)(113 161 120 168)(114 162 121 155)(115 163 122 156)(116 164 123 157)(117 165 124 158)(118 166 125 159)(119 167 126 160)(127 153 134 146)(128 154 135 147)(129 141 136 148)(130 142 137 149)(131 143 138 150)(132 144 139 151)(133 145 140 152)
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)(15,19)(16,18)(20,28)(21,27)(22,26)(23,25)(29,35)(30,34)(31,33)(36,42)(37,41)(38,40)(43,49)(44,48)(45,47)(50,56)(51,55)(52,54)(57,58)(59,70)(60,69)(61,68)(62,67)(63,66)(64,65)(71,83)(72,82)(73,81)(74,80)(75,79)(76,78)(85,94)(86,93)(87,92)(88,91)(89,90)(95,98)(96,97)(100,112)(101,111)(102,110)(103,109)(104,108)(105,107)(113,123)(114,122)(115,121)(116,120)(117,119)(124,126)(127,134)(128,133)(129,132)(130,131)(135,140)(136,139)(137,138)(141,144)(142,143)(145,154)(146,153)(147,152)(148,151)(149,150)(155,163)(156,162)(157,161)(158,160)(164,168)(165,167)(169,171)(172,182)(173,181)(174,180)(175,179)(176,178)(183,194)(184,193)(185,192)(186,191)(187,190)(188,189)(195,196)(197,206)(198,205)(199,204)(200,203)(201,202)(207,210)(208,209)(211,218)(212,217)(213,216)(214,215)(219,224)(220,223)(221,222), (1,74,196,110,131,115,215,28)(2,75,183,111,132,116,216,15)(3,76,184,112,133,117,217,16)(4,77,185,99,134,118,218,17)(5,78,186,100,135,119,219,18)(6,79,187,101,136,120,220,19)(7,80,188,102,137,121,221,20)(8,81,189,103,138,122,222,21)(9,82,190,104,139,123,223,22)(10,83,191,105,140,124,224,23)(11,84,192,106,127,125,211,24)(12,71,193,107,128,126,212,25)(13,72,194,108,129,113,213,26)(14,73,195,109,130,114,214,27)(29,97,163,150,50,58,174,202)(30,98,164,151,51,59,175,203)(31,85,165,152,52,60,176,204)(32,86,166,153,53,61,177,205)(33,87,167,154,54,62,178,206)(34,88,168,141,55,63,179,207)(35,89,155,142,56,64,180,208)(36,90,156,143,43,65,181,209)(37,91,157,144,44,66,182,210)(38,92,158,145,45,67,169,197)(39,93,159,146,46,68,170,198)(40,94,160,147,47,69,171,199)(41,95,161,148,48,70,172,200)(42,96,162,149,49,57,173,201), (1,209,8,202)(2,210,9,203)(3,197,10,204)(4,198,11,205)(5,199,12,206)(6,200,13,207)(7,201,14,208)(15,30,22,37)(16,31,23,38)(17,32,24,39)(18,33,25,40)(19,34,26,41)(20,35,27,42)(21,36,28,29)(43,110,50,103)(44,111,51,104)(45,112,52,105)(46,99,53,106)(47,100,54,107)(48,101,55,108)(49,102,56,109)(57,195,64,188)(58,196,65,189)(59,183,66,190)(60,184,67,191)(61,185,68,192)(62,186,69,193)(63,187,70,194)(71,171,78,178)(72,172,79,179)(73,173,80,180)(74,174,81,181)(75,175,82,182)(76,176,83,169)(77,177,84,170)(85,217,92,224)(86,218,93,211)(87,219,94,212)(88,220,95,213)(89,221,96,214)(90,222,97,215)(91,223,98,216)(113,161,120,168)(114,162,121,155)(115,163,122,156)(116,164,123,157)(117,165,124,158)(118,166,125,159)(119,167,126,160)(127,153,134,146)(128,154,135,147)(129,141,136,148)(130,142,137,149)(131,143,138,150)(132,144,139,151)(133,145,140,152)>;
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)(15,19)(16,18)(20,28)(21,27)(22,26)(23,25)(29,35)(30,34)(31,33)(36,42)(37,41)(38,40)(43,49)(44,48)(45,47)(50,56)(51,55)(52,54)(57,58)(59,70)(60,69)(61,68)(62,67)(63,66)(64,65)(71,83)(72,82)(73,81)(74,80)(75,79)(76,78)(85,94)(86,93)(87,92)(88,91)(89,90)(95,98)(96,97)(100,112)(101,111)(102,110)(103,109)(104,108)(105,107)(113,123)(114,122)(115,121)(116,120)(117,119)(124,126)(127,134)(128,133)(129,132)(130,131)(135,140)(136,139)(137,138)(141,144)(142,143)(145,154)(146,153)(147,152)(148,151)(149,150)(155,163)(156,162)(157,161)(158,160)(164,168)(165,167)(169,171)(172,182)(173,181)(174,180)(175,179)(176,178)(183,194)(184,193)(185,192)(186,191)(187,190)(188,189)(195,196)(197,206)(198,205)(199,204)(200,203)(201,202)(207,210)(208,209)(211,218)(212,217)(213,216)(214,215)(219,224)(220,223)(221,222), (1,74,196,110,131,115,215,28)(2,75,183,111,132,116,216,15)(3,76,184,112,133,117,217,16)(4,77,185,99,134,118,218,17)(5,78,186,100,135,119,219,18)(6,79,187,101,136,120,220,19)(7,80,188,102,137,121,221,20)(8,81,189,103,138,122,222,21)(9,82,190,104,139,123,223,22)(10,83,191,105,140,124,224,23)(11,84,192,106,127,125,211,24)(12,71,193,107,128,126,212,25)(13,72,194,108,129,113,213,26)(14,73,195,109,130,114,214,27)(29,97,163,150,50,58,174,202)(30,98,164,151,51,59,175,203)(31,85,165,152,52,60,176,204)(32,86,166,153,53,61,177,205)(33,87,167,154,54,62,178,206)(34,88,168,141,55,63,179,207)(35,89,155,142,56,64,180,208)(36,90,156,143,43,65,181,209)(37,91,157,144,44,66,182,210)(38,92,158,145,45,67,169,197)(39,93,159,146,46,68,170,198)(40,94,160,147,47,69,171,199)(41,95,161,148,48,70,172,200)(42,96,162,149,49,57,173,201), (1,209,8,202)(2,210,9,203)(3,197,10,204)(4,198,11,205)(5,199,12,206)(6,200,13,207)(7,201,14,208)(15,30,22,37)(16,31,23,38)(17,32,24,39)(18,33,25,40)(19,34,26,41)(20,35,27,42)(21,36,28,29)(43,110,50,103)(44,111,51,104)(45,112,52,105)(46,99,53,106)(47,100,54,107)(48,101,55,108)(49,102,56,109)(57,195,64,188)(58,196,65,189)(59,183,66,190)(60,184,67,191)(61,185,68,192)(62,186,69,193)(63,187,70,194)(71,171,78,178)(72,172,79,179)(73,173,80,180)(74,174,81,181)(75,175,82,182)(76,176,83,169)(77,177,84,170)(85,217,92,224)(86,218,93,211)(87,219,94,212)(88,220,95,213)(89,221,96,214)(90,222,97,215)(91,223,98,216)(113,161,120,168)(114,162,121,155)(115,163,122,156)(116,164,123,157)(117,165,124,158)(118,166,125,159)(119,167,126,160)(127,153,134,146)(128,154,135,147)(129,141,136,148)(130,142,137,149)(131,143,138,150)(132,144,139,151)(133,145,140,152) );
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),(15,19),(16,18),(20,28),(21,27),(22,26),(23,25),(29,35),(30,34),(31,33),(36,42),(37,41),(38,40),(43,49),(44,48),(45,47),(50,56),(51,55),(52,54),(57,58),(59,70),(60,69),(61,68),(62,67),(63,66),(64,65),(71,83),(72,82),(73,81),(74,80),(75,79),(76,78),(85,94),(86,93),(87,92),(88,91),(89,90),(95,98),(96,97),(100,112),(101,111),(102,110),(103,109),(104,108),(105,107),(113,123),(114,122),(115,121),(116,120),(117,119),(124,126),(127,134),(128,133),(129,132),(130,131),(135,140),(136,139),(137,138),(141,144),(142,143),(145,154),(146,153),(147,152),(148,151),(149,150),(155,163),(156,162),(157,161),(158,160),(164,168),(165,167),(169,171),(172,182),(173,181),(174,180),(175,179),(176,178),(183,194),(184,193),(185,192),(186,191),(187,190),(188,189),(195,196),(197,206),(198,205),(199,204),(200,203),(201,202),(207,210),(208,209),(211,218),(212,217),(213,216),(214,215),(219,224),(220,223),(221,222)], [(1,74,196,110,131,115,215,28),(2,75,183,111,132,116,216,15),(3,76,184,112,133,117,217,16),(4,77,185,99,134,118,218,17),(5,78,186,100,135,119,219,18),(6,79,187,101,136,120,220,19),(7,80,188,102,137,121,221,20),(8,81,189,103,138,122,222,21),(9,82,190,104,139,123,223,22),(10,83,191,105,140,124,224,23),(11,84,192,106,127,125,211,24),(12,71,193,107,128,126,212,25),(13,72,194,108,129,113,213,26),(14,73,195,109,130,114,214,27),(29,97,163,150,50,58,174,202),(30,98,164,151,51,59,175,203),(31,85,165,152,52,60,176,204),(32,86,166,153,53,61,177,205),(33,87,167,154,54,62,178,206),(34,88,168,141,55,63,179,207),(35,89,155,142,56,64,180,208),(36,90,156,143,43,65,181,209),(37,91,157,144,44,66,182,210),(38,92,158,145,45,67,169,197),(39,93,159,146,46,68,170,198),(40,94,160,147,47,69,171,199),(41,95,161,148,48,70,172,200),(42,96,162,149,49,57,173,201)], [(1,209,8,202),(2,210,9,203),(3,197,10,204),(4,198,11,205),(5,199,12,206),(6,200,13,207),(7,201,14,208),(15,30,22,37),(16,31,23,38),(17,32,24,39),(18,33,25,40),(19,34,26,41),(20,35,27,42),(21,36,28,29),(43,110,50,103),(44,111,51,104),(45,112,52,105),(46,99,53,106),(47,100,54,107),(48,101,55,108),(49,102,56,109),(57,195,64,188),(58,196,65,189),(59,183,66,190),(60,184,67,191),(61,185,68,192),(62,186,69,193),(63,187,70,194),(71,171,78,178),(72,172,79,179),(73,173,80,180),(74,174,81,181),(75,175,82,182),(76,176,83,169),(77,177,84,170),(85,217,92,224),(86,218,93,211),(87,219,94,212),(88,220,95,213),(89,221,96,214),(90,222,97,215),(91,223,98,216),(113,161,120,168),(114,162,121,155),(115,163,122,156),(116,164,123,157),(117,165,124,158),(118,166,125,159),(119,167,126,160),(127,153,134,146),(128,154,135,147),(129,141,136,148),(130,142,137,149),(131,143,138,150),(132,144,139,151),(133,145,140,152)]])
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 | D8 | D14 | D14 | D14 | C4○D28 | C8.C22 | D4⋊2D7 | D4×D7 | D7×D8 | SD16⋊D7 |
| kernel | D14.D8 | C28.Q8 | C56⋊1C4 | 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.D8 ►in GL6(𝔽113)
| 103 | 103 | 0 | 0 | 0 | 0 |
| 10 | 89 | 0 | 0 | 0 | 0 |
| 0 | 0 | 112 | 0 | 0 | 0 |
| 0 | 0 | 0 | 112 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 103 | 103 | 0 | 0 | 0 | 0 |
| 89 | 10 | 0 | 0 | 0 | 0 |
| 0 | 0 | 112 | 0 | 0 | 0 |
| 0 | 0 | 22 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 51 | 56 | 0 | 0 |
| 0 | 0 | 6 | 62 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 62 |
| 0 | 0 | 0 | 0 | 82 | 62 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 15 | 0 | 0 | 0 |
| 0 | 0 | 0 | 15 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 62 |
| 0 | 0 | 0 | 0 | 31 | 0 |
G:=sub<GL(6,GF(113))| [103,10,0,0,0,0,103,89,0,0,0,0,0,0,112,0,0,0,0,0,0,112,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[103,89,0,0,0,0,103,10,0,0,0,0,0,0,112,22,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,51,6,0,0,0,0,56,62,0,0,0,0,0,0,0,82,0,0,0,0,62,62],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,15,0,0,0,0,0,0,15,0,0,0,0,0,0,0,31,0,0,0,0,62,0] >;
D14.D8 in GAP, Magma, Sage, TeX
D_{14}.D_8 % in TeX
G:=Group("D14.D8"); // GroupNames label
G:=SmallGroup(448,308);
// by ID
G=gap.SmallGroup(448,308);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,64,254,219,851,438,102,18822]);
// 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^-1>;
// generators/relations