metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: D14⋊1D8, C7⋊C8⋊19D4, C7⋊1(C8⋊7D4), C4⋊C4.9D14, C2.10(D7×D8), D4⋊C4⋊2D7, C4⋊D28⋊2C2, C28⋊2D4⋊1C2, C4.158(D4×D7), C14.24(C2×D8), (C2×D4).24D14, C28.7(C4○D4), (C2×C8).202D14, C28.108(C2×D4), C28.Q8⋊6C2, C2.D56⋊19C2, C4.24(C4○D28), C14.40(C4○D8), (C2×Dic7).89D4, (C22×D7).47D4, C22.173(D4×D7), C14.15(C4⋊D4), (C2×C56).184C22, (C2×C28).215C23, (C2×D28).49C22, (D4×C14).36C22, C4⋊Dic7.70C22, C2.18(D14⋊D4), C2.10(SD16⋊3D7), (D7×C2×C8)⋊18C2, (C2×D4⋊D7)⋊3C2, (C7×D4⋊C4)⋊22C2, (C2×C14).228(C2×D4), (C7×C4⋊C4).17C22, (C2×C7⋊C8).212C22, (C2×C4×D7).224C22, (C2×C4).322(C22×D7), SmallGroup(448,309)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for D14⋊D8
G = < a,b,c,d | a14=b2=c8=d2=1, bab=cac-1=dad=a-1, cbc-1=a12b, dbd=a5b, dcd=c-1 >
Subgroups: 852 in 134 conjugacy classes, 41 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, D8, C22×C4, C2×D4, C2×D4, Dic7, C28, C28, D14, D14, C2×C14, C2×C14, D4⋊C4, D4⋊C4, C2.D8, C4⋊D4, C22×C8, C2×D8, C7⋊C8, C56, C4×D7, D28, C2×Dic7, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C7×D4, C22×D7, C22×D7, C22×C14, C8⋊7D4, C8×D7, C2×C7⋊C8, C4⋊Dic7, D14⋊C4, D4⋊D7, C23.D7, C7×C4⋊C4, C2×C56, C2×C4×D7, C2×D28, C2×D28, C2×C7⋊D4, D4×C14, C28.Q8, C2.D56, C7×D4⋊C4, C4⋊D28, D7×C2×C8, C2×D4⋊D7, C28⋊2D4, D14⋊D8
Quotients: C1, C2, C22, D4, C23, D7, D8, C2×D4, C4○D4, D14, C4⋊D4, C2×D8, C4○D8, C22×D7, C8⋊7D4, C4○D28, D4×D7, D14⋊D4, D7×D8, SD16⋊3D7, 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 23)(16 22)(17 21)(18 20)(24 28)(25 27)(29 34)(30 33)(31 32)(35 42)(36 41)(37 40)(38 39)(43 45)(46 56)(47 55)(48 54)(49 53)(50 52)(57 62)(58 61)(59 60)(63 70)(64 69)(65 68)(66 67)(71 76)(72 75)(73 74)(77 84)(78 83)(79 82)(80 81)(85 95)(86 94)(87 93)(88 92)(89 91)(96 98)(99 105)(100 104)(101 103)(106 112)(107 111)(108 110)(113 126)(114 125)(115 124)(116 123)(117 122)(118 121)(119 120)(127 137)(128 136)(129 135)(130 134)(131 133)(138 140)(141 145)(142 144)(146 154)(147 153)(148 152)(149 151)(155 165)(156 164)(157 163)(158 162)(159 161)(166 168)(169 180)(170 179)(171 178)(172 177)(173 176)(174 175)(181 182)(183 194)(184 193)(185 192)(186 191)(187 190)(188 189)(195 196)(197 203)(198 202)(199 201)(204 210)(205 209)(206 208)(211 224)(212 223)(213 222)(214 221)(215 220)(216 219)(217 218)
(1 182 113 67 74 211 196 32)(2 181 114 66 75 224 183 31)(3 180 115 65 76 223 184 30)(4 179 116 64 77 222 185 29)(5 178 117 63 78 221 186 42)(6 177 118 62 79 220 187 41)(7 176 119 61 80 219 188 40)(8 175 120 60 81 218 189 39)(9 174 121 59 82 217 190 38)(10 173 122 58 83 216 191 37)(11 172 123 57 84 215 192 36)(12 171 124 70 71 214 193 35)(13 170 125 69 72 213 194 34)(14 169 126 68 73 212 195 33)(15 158 112 95 210 130 47 141)(16 157 99 94 197 129 48 154)(17 156 100 93 198 128 49 153)(18 155 101 92 199 127 50 152)(19 168 102 91 200 140 51 151)(20 167 103 90 201 139 52 150)(21 166 104 89 202 138 53 149)(22 165 105 88 203 137 54 148)(23 164 106 87 204 136 55 147)(24 163 107 86 205 135 56 146)(25 162 108 85 206 134 43 145)(26 161 109 98 207 133 44 144)(27 160 110 97 208 132 45 143)(28 159 111 96 209 131 46 142)
(1 197)(2 210)(3 209)(4 208)(5 207)(6 206)(7 205)(8 204)(9 203)(10 202)(11 201)(12 200)(13 199)(14 198)(15 75)(16 74)(17 73)(18 72)(19 71)(20 84)(21 83)(22 82)(23 81)(24 80)(25 79)(26 78)(27 77)(28 76)(29 132)(30 131)(31 130)(32 129)(33 128)(34 127)(35 140)(36 139)(37 138)(38 137)(39 136)(40 135)(41 134)(42 133)(43 187)(44 186)(45 185)(46 184)(47 183)(48 196)(49 195)(50 194)(51 193)(52 192)(53 191)(54 190)(55 189)(56 188)(57 167)(58 166)(59 165)(60 164)(61 163)(62 162)(63 161)(64 160)(65 159)(66 158)(67 157)(68 156)(69 155)(70 168)(85 177)(86 176)(87 175)(88 174)(89 173)(90 172)(91 171)(92 170)(93 169)(94 182)(95 181)(96 180)(97 179)(98 178)(99 113)(100 126)(101 125)(102 124)(103 123)(104 122)(105 121)(106 120)(107 119)(108 118)(109 117)(110 116)(111 115)(112 114)(141 224)(142 223)(143 222)(144 221)(145 220)(146 219)(147 218)(148 217)(149 216)(150 215)(151 214)(152 213)(153 212)(154 211)
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)(29,34)(30,33)(31,32)(35,42)(36,41)(37,40)(38,39)(43,45)(46,56)(47,55)(48,54)(49,53)(50,52)(57,62)(58,61)(59,60)(63,70)(64,69)(65,68)(66,67)(71,76)(72,75)(73,74)(77,84)(78,83)(79,82)(80,81)(85,95)(86,94)(87,93)(88,92)(89,91)(96,98)(99,105)(100,104)(101,103)(106,112)(107,111)(108,110)(113,126)(114,125)(115,124)(116,123)(117,122)(118,121)(119,120)(127,137)(128,136)(129,135)(130,134)(131,133)(138,140)(141,145)(142,144)(146,154)(147,153)(148,152)(149,151)(155,165)(156,164)(157,163)(158,162)(159,161)(166,168)(169,180)(170,179)(171,178)(172,177)(173,176)(174,175)(181,182)(183,194)(184,193)(185,192)(186,191)(187,190)(188,189)(195,196)(197,203)(198,202)(199,201)(204,210)(205,209)(206,208)(211,224)(212,223)(213,222)(214,221)(215,220)(216,219)(217,218), (1,182,113,67,74,211,196,32)(2,181,114,66,75,224,183,31)(3,180,115,65,76,223,184,30)(4,179,116,64,77,222,185,29)(5,178,117,63,78,221,186,42)(6,177,118,62,79,220,187,41)(7,176,119,61,80,219,188,40)(8,175,120,60,81,218,189,39)(9,174,121,59,82,217,190,38)(10,173,122,58,83,216,191,37)(11,172,123,57,84,215,192,36)(12,171,124,70,71,214,193,35)(13,170,125,69,72,213,194,34)(14,169,126,68,73,212,195,33)(15,158,112,95,210,130,47,141)(16,157,99,94,197,129,48,154)(17,156,100,93,198,128,49,153)(18,155,101,92,199,127,50,152)(19,168,102,91,200,140,51,151)(20,167,103,90,201,139,52,150)(21,166,104,89,202,138,53,149)(22,165,105,88,203,137,54,148)(23,164,106,87,204,136,55,147)(24,163,107,86,205,135,56,146)(25,162,108,85,206,134,43,145)(26,161,109,98,207,133,44,144)(27,160,110,97,208,132,45,143)(28,159,111,96,209,131,46,142), (1,197)(2,210)(3,209)(4,208)(5,207)(6,206)(7,205)(8,204)(9,203)(10,202)(11,201)(12,200)(13,199)(14,198)(15,75)(16,74)(17,73)(18,72)(19,71)(20,84)(21,83)(22,82)(23,81)(24,80)(25,79)(26,78)(27,77)(28,76)(29,132)(30,131)(31,130)(32,129)(33,128)(34,127)(35,140)(36,139)(37,138)(38,137)(39,136)(40,135)(41,134)(42,133)(43,187)(44,186)(45,185)(46,184)(47,183)(48,196)(49,195)(50,194)(51,193)(52,192)(53,191)(54,190)(55,189)(56,188)(57,167)(58,166)(59,165)(60,164)(61,163)(62,162)(63,161)(64,160)(65,159)(66,158)(67,157)(68,156)(69,155)(70,168)(85,177)(86,176)(87,175)(88,174)(89,173)(90,172)(91,171)(92,170)(93,169)(94,182)(95,181)(96,180)(97,179)(98,178)(99,113)(100,126)(101,125)(102,124)(103,123)(104,122)(105,121)(106,120)(107,119)(108,118)(109,117)(110,116)(111,115)(112,114)(141,224)(142,223)(143,222)(144,221)(145,220)(146,219)(147,218)(148,217)(149,216)(150,215)(151,214)(152,213)(153,212)(154,211)>;
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)(29,34)(30,33)(31,32)(35,42)(36,41)(37,40)(38,39)(43,45)(46,56)(47,55)(48,54)(49,53)(50,52)(57,62)(58,61)(59,60)(63,70)(64,69)(65,68)(66,67)(71,76)(72,75)(73,74)(77,84)(78,83)(79,82)(80,81)(85,95)(86,94)(87,93)(88,92)(89,91)(96,98)(99,105)(100,104)(101,103)(106,112)(107,111)(108,110)(113,126)(114,125)(115,124)(116,123)(117,122)(118,121)(119,120)(127,137)(128,136)(129,135)(130,134)(131,133)(138,140)(141,145)(142,144)(146,154)(147,153)(148,152)(149,151)(155,165)(156,164)(157,163)(158,162)(159,161)(166,168)(169,180)(170,179)(171,178)(172,177)(173,176)(174,175)(181,182)(183,194)(184,193)(185,192)(186,191)(187,190)(188,189)(195,196)(197,203)(198,202)(199,201)(204,210)(205,209)(206,208)(211,224)(212,223)(213,222)(214,221)(215,220)(216,219)(217,218), (1,182,113,67,74,211,196,32)(2,181,114,66,75,224,183,31)(3,180,115,65,76,223,184,30)(4,179,116,64,77,222,185,29)(5,178,117,63,78,221,186,42)(6,177,118,62,79,220,187,41)(7,176,119,61,80,219,188,40)(8,175,120,60,81,218,189,39)(9,174,121,59,82,217,190,38)(10,173,122,58,83,216,191,37)(11,172,123,57,84,215,192,36)(12,171,124,70,71,214,193,35)(13,170,125,69,72,213,194,34)(14,169,126,68,73,212,195,33)(15,158,112,95,210,130,47,141)(16,157,99,94,197,129,48,154)(17,156,100,93,198,128,49,153)(18,155,101,92,199,127,50,152)(19,168,102,91,200,140,51,151)(20,167,103,90,201,139,52,150)(21,166,104,89,202,138,53,149)(22,165,105,88,203,137,54,148)(23,164,106,87,204,136,55,147)(24,163,107,86,205,135,56,146)(25,162,108,85,206,134,43,145)(26,161,109,98,207,133,44,144)(27,160,110,97,208,132,45,143)(28,159,111,96,209,131,46,142), (1,197)(2,210)(3,209)(4,208)(5,207)(6,206)(7,205)(8,204)(9,203)(10,202)(11,201)(12,200)(13,199)(14,198)(15,75)(16,74)(17,73)(18,72)(19,71)(20,84)(21,83)(22,82)(23,81)(24,80)(25,79)(26,78)(27,77)(28,76)(29,132)(30,131)(31,130)(32,129)(33,128)(34,127)(35,140)(36,139)(37,138)(38,137)(39,136)(40,135)(41,134)(42,133)(43,187)(44,186)(45,185)(46,184)(47,183)(48,196)(49,195)(50,194)(51,193)(52,192)(53,191)(54,190)(55,189)(56,188)(57,167)(58,166)(59,165)(60,164)(61,163)(62,162)(63,161)(64,160)(65,159)(66,158)(67,157)(68,156)(69,155)(70,168)(85,177)(86,176)(87,175)(88,174)(89,173)(90,172)(91,171)(92,170)(93,169)(94,182)(95,181)(96,180)(97,179)(98,178)(99,113)(100,126)(101,125)(102,124)(103,123)(104,122)(105,121)(106,120)(107,119)(108,118)(109,117)(110,116)(111,115)(112,114)(141,224)(142,223)(143,222)(144,221)(145,220)(146,219)(147,218)(148,217)(149,216)(150,215)(151,214)(152,213)(153,212)(154,211) );
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),(29,34),(30,33),(31,32),(35,42),(36,41),(37,40),(38,39),(43,45),(46,56),(47,55),(48,54),(49,53),(50,52),(57,62),(58,61),(59,60),(63,70),(64,69),(65,68),(66,67),(71,76),(72,75),(73,74),(77,84),(78,83),(79,82),(80,81),(85,95),(86,94),(87,93),(88,92),(89,91),(96,98),(99,105),(100,104),(101,103),(106,112),(107,111),(108,110),(113,126),(114,125),(115,124),(116,123),(117,122),(118,121),(119,120),(127,137),(128,136),(129,135),(130,134),(131,133),(138,140),(141,145),(142,144),(146,154),(147,153),(148,152),(149,151),(155,165),(156,164),(157,163),(158,162),(159,161),(166,168),(169,180),(170,179),(171,178),(172,177),(173,176),(174,175),(181,182),(183,194),(184,193),(185,192),(186,191),(187,190),(188,189),(195,196),(197,203),(198,202),(199,201),(204,210),(205,209),(206,208),(211,224),(212,223),(213,222),(214,221),(215,220),(216,219),(217,218)], [(1,182,113,67,74,211,196,32),(2,181,114,66,75,224,183,31),(3,180,115,65,76,223,184,30),(4,179,116,64,77,222,185,29),(5,178,117,63,78,221,186,42),(6,177,118,62,79,220,187,41),(7,176,119,61,80,219,188,40),(8,175,120,60,81,218,189,39),(9,174,121,59,82,217,190,38),(10,173,122,58,83,216,191,37),(11,172,123,57,84,215,192,36),(12,171,124,70,71,214,193,35),(13,170,125,69,72,213,194,34),(14,169,126,68,73,212,195,33),(15,158,112,95,210,130,47,141),(16,157,99,94,197,129,48,154),(17,156,100,93,198,128,49,153),(18,155,101,92,199,127,50,152),(19,168,102,91,200,140,51,151),(20,167,103,90,201,139,52,150),(21,166,104,89,202,138,53,149),(22,165,105,88,203,137,54,148),(23,164,106,87,204,136,55,147),(24,163,107,86,205,135,56,146),(25,162,108,85,206,134,43,145),(26,161,109,98,207,133,44,144),(27,160,110,97,208,132,45,143),(28,159,111,96,209,131,46,142)], [(1,197),(2,210),(3,209),(4,208),(5,207),(6,206),(7,205),(8,204),(9,203),(10,202),(11,201),(12,200),(13,199),(14,198),(15,75),(16,74),(17,73),(18,72),(19,71),(20,84),(21,83),(22,82),(23,81),(24,80),(25,79),(26,78),(27,77),(28,76),(29,132),(30,131),(31,130),(32,129),(33,128),(34,127),(35,140),(36,139),(37,138),(38,137),(39,136),(40,135),(41,134),(42,133),(43,187),(44,186),(45,185),(46,184),(47,183),(48,196),(49,195),(50,194),(51,193),(52,192),(53,191),(54,190),(55,189),(56,188),(57,167),(58,166),(59,165),(60,164),(61,163),(62,162),(63,161),(64,160),(65,159),(66,158),(67,157),(68,156),(69,155),(70,168),(85,177),(86,176),(87,175),(88,174),(89,173),(90,172),(91,171),(92,170),(93,169),(94,182),(95,181),(96,180),(97,179),(98,178),(99,113),(100,126),(101,125),(102,124),(103,123),(104,122),(105,121),(106,120),(107,119),(108,118),(109,117),(110,116),(111,115),(112,114),(141,224),(142,223),(143,222),(144,221),(145,220),(146,219),(147,218),(148,217),(149,216),(150,215),(151,214),(152,213),(153,212),(154,211)]])
64 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 4A | 4B | 4C | 4D | 4E | 4F | 7A | 7B | 7C | 8A | 8B | 8C | 8D | 8E | 8F | 8G | 8H | 14A | ··· | 14I | 14J | ··· | 14O | 28A | ··· | 28F | 28G | ··· | 28L | 56A | ··· | 56L |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 | 56 | ··· | 56 |
| size | 1 | 1 | 1 | 1 | 8 | 14 | 14 | 56 | 2 | 2 | 8 | 14 | 14 | 56 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 14 | 14 | 14 | 14 | 2 | ··· | 2 | 8 | ··· | 8 | 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 | D8 | D14 | D14 | D14 | C4○D8 | C4○D28 | D4×D7 | D4×D7 | D7×D8 | SD16⋊3D7 |
| kernel | D14⋊D8 | C28.Q8 | C2.D56 | C7×D4⋊C4 | C4⋊D28 | D7×C2×C8 | C2×D4⋊D7 | C28⋊2D4 | C7⋊C8 | C2×Dic7 | C22×D7 | D4⋊C4 | C28 | D14 | C4⋊C4 | C2×C8 | C2×D4 | 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⋊D8 ►in GL6(𝔽113)
| 112 | 0 | 0 | 0 | 0 | 0 |
| 0 | 112 | 0 | 0 | 0 | 0 |
| 0 | 0 | 32 | 33 | 0 | 0 |
| 0 | 0 | 47 | 105 | 0 | 0 |
| 0 | 0 | 0 | 0 | 112 | 0 |
| 0 | 0 | 0 | 0 | 0 | 112 |
| 112 | 0 | 0 | 0 | 0 | 0 |
| 48 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 9 | 9 | 0 | 0 |
| 0 | 0 | 79 | 104 | 0 | 0 |
| 0 | 0 | 0 | 0 | 112 | 0 |
| 0 | 0 | 0 | 0 | 20 | 1 |
| 112 | 0 | 0 | 0 | 0 | 0 |
| 0 | 112 | 0 | 0 | 0 | 0 |
| 0 | 0 | 43 | 9 | 0 | 0 |
| 0 | 0 | 96 | 70 | 0 | 0 |
| 0 | 0 | 0 | 0 | 18 | 0 |
| 0 | 0 | 0 | 0 | 34 | 44 |
| 55 | 7 | 0 | 0 | 0 | 0 |
| 20 | 58 | 0 | 0 | 0 | 0 |
| 0 | 0 | 43 | 9 | 0 | 0 |
| 0 | 0 | 96 | 70 | 0 | 0 |
| 0 | 0 | 0 | 0 | 73 | 109 |
| 0 | 0 | 0 | 0 | 89 | 40 |
G:=sub<GL(6,GF(113))| [112,0,0,0,0,0,0,112,0,0,0,0,0,0,32,47,0,0,0,0,33,105,0,0,0,0,0,0,112,0,0,0,0,0,0,112],[112,48,0,0,0,0,0,1,0,0,0,0,0,0,9,79,0,0,0,0,9,104,0,0,0,0,0,0,112,20,0,0,0,0,0,1],[112,0,0,0,0,0,0,112,0,0,0,0,0,0,43,96,0,0,0,0,9,70,0,0,0,0,0,0,18,34,0,0,0,0,0,44],[55,20,0,0,0,0,7,58,0,0,0,0,0,0,43,96,0,0,0,0,9,70,0,0,0,0,0,0,73,89,0,0,0,0,109,40] >;
D14⋊D8 in GAP, Magma, Sage, TeX
D_{14}\rtimes D_8 % in TeX
G:=Group("D14:D8"); // GroupNames label
G:=SmallGroup(448,309);
// by ID
G=gap.SmallGroup(448,309);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,64,590,555,297,136,438,102,18822]);
// 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^-1>;
// generators/relations