metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: D4⋊6Dic14, C42.107D14, C14.1012+ 1+4, (C7×D4)⋊7Q8, (C4×D4).14D7, C7⋊3(D4⋊3Q8), C28.43(C2×Q8), C4⋊C4.281D14, C28⋊2Q8⋊23C2, (D4×C28).15C2, (C4×Dic14)⋊29C2, (C2×D4).243D14, C28.48D4⋊9C2, (C2×C14).87C24, C28.3Q8⋊15C2, (D4×Dic7).12C2, C4.16(C2×Dic14), C28.292(C4○D4), C14.14(C22×Q8), (C2×C28).156C23, (C4×C28).149C22, C22⋊C4.108D14, C22⋊Dic14⋊8C2, (C22×C4).206D14, Dic7⋊C4.6C22, C2.13(D4⋊8D14), C4.117(D4⋊2D7), C22.2(C2×Dic14), (D4×C14).251C22, C4⋊Dic7.198C22, (C22×C28).80C22, (C4×Dic7).74C22, (C2×Dic7).37C23, C2.16(C22×Dic14), C23.166(C22×D7), C22.115(C23×D7), C23.D7.10C22, (C22×C14).157C23, (C2×Dic14).26C22, (C22×Dic7).94C22, (C2×C14).4(C2×Q8), (C2×C4⋊Dic7)⋊24C2, C14.73(C2×C4○D4), C2.21(C2×D4⋊2D7), (C7×C4⋊C4).323C22, (C2×C4).731(C22×D7), (C7×C22⋊C4).105C22, SmallGroup(448,996)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for D4⋊6Dic14
G = < a,b,c,d | a4=b2=c28=1, d2=c14, bab=a-1, ac=ca, ad=da, bc=cb, dbd-1=a2b, dcd-1=c-1 >
Subgroups: 884 in 228 conjugacy classes, 115 normal (29 characteristic)
C1, C2, C2, C4, C4, C22, C22, C22, C7, C2×C4, C2×C4, C2×C4, D4, Q8, C23, C14, C14, C42, C42, C22⋊C4, C22⋊C4, C4⋊C4, C4⋊C4, C22×C4, C22×C4, C2×D4, C2×Q8, Dic7, C28, C28, C2×C14, C2×C14, C2×C14, C2×C4⋊C4, C4×D4, C4×D4, C4×Q8, C22⋊Q8, C42.C2, C4⋊Q8, Dic14, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C2×C28, C7×D4, C22×C14, D4⋊3Q8, C4×Dic7, Dic7⋊C4, C4⋊Dic7, C4⋊Dic7, C23.D7, C4×C28, C7×C22⋊C4, C7×C4⋊C4, C2×Dic14, C2×Dic14, C22×Dic7, C22×C28, D4×C14, C4×Dic14, C28⋊2Q8, C22⋊Dic14, C28.3Q8, C28.48D4, C2×C4⋊Dic7, D4×Dic7, D4×C28, D4⋊6Dic14
Quotients: C1, C2, C22, Q8, C23, D7, C2×Q8, C4○D4, C24, D14, C22×Q8, C2×C4○D4, 2+ 1+4, Dic14, C22×D7, D4⋊3Q8, C2×Dic14, D4⋊2D7, C23×D7, C22×Dic14, C2×D4⋊2D7, D4⋊8D14, D4⋊6Dic14
►On 224 points
Generators in S224
(1 189 91 79)(2 190 92 80)(3 191 93 81)(4 192 94 82)(5 193 95 83)(6 194 96 84)(7 195 97 57)(8 196 98 58)(9 169 99 59)(10 170 100 60)(11 171 101 61)(12 172 102 62)(13 173 103 63)(14 174 104 64)(15 175 105 65)(16 176 106 66)(17 177 107 67)(18 178 108 68)(19 179 109 69)(20 180 110 70)(21 181 111 71)(22 182 112 72)(23 183 85 73)(24 184 86 74)(25 185 87 75)(26 186 88 76)(27 187 89 77)(28 188 90 78)(29 138 166 219)(30 139 167 220)(31 140 168 221)(32 113 141 222)(33 114 142 223)(34 115 143 224)(35 116 144 197)(36 117 145 198)(37 118 146 199)(38 119 147 200)(39 120 148 201)(40 121 149 202)(41 122 150 203)(42 123 151 204)(43 124 152 205)(44 125 153 206)(45 126 154 207)(46 127 155 208)(47 128 156 209)(48 129 157 210)(49 130 158 211)(50 131 159 212)(51 132 160 213)(52 133 161 214)(53 134 162 215)(54 135 163 216)(55 136 164 217)(56 137 165 218)
(1 105)(2 106)(3 107)(4 108)(5 109)(6 110)(7 111)(8 112)(9 85)(10 86)(11 87)(12 88)(13 89)(14 90)(15 91)(16 92)(17 93)(18 94)(19 95)(20 96)(21 97)(22 98)(23 99)(24 100)(25 101)(26 102)(27 103)(28 104)(29 43)(30 44)(31 45)(32 46)(33 47)(34 48)(35 49)(36 50)(37 51)(38 52)(39 53)(40 54)(41 55)(42 56)(57 71)(58 72)(59 73)(60 74)(61 75)(62 76)(63 77)(64 78)(65 79)(66 80)(67 81)(68 82)(69 83)(70 84)(113 208)(114 209)(115 210)(116 211)(117 212)(118 213)(119 214)(120 215)(121 216)(122 217)(123 218)(124 219)(125 220)(126 221)(127 222)(128 223)(129 224)(130 197)(131 198)(132 199)(133 200)(134 201)(135 202)(136 203)(137 204)(138 205)(139 206)(140 207)(141 155)(142 156)(143 157)(144 158)(145 159)(146 160)(147 161)(148 162)(149 163)(150 164)(151 165)(152 166)(153 167)(154 168)(169 183)(170 184)(171 185)(172 186)(173 187)(174 188)(175 189)(176 190)(177 191)(178 192)(179 193)(180 194)(181 195)(182 196)
(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)
(1 161 15 147)(2 160 16 146)(3 159 17 145)(4 158 18 144)(5 157 19 143)(6 156 20 142)(7 155 21 141)(8 154 22 168)(9 153 23 167)(10 152 24 166)(11 151 25 165)(12 150 26 164)(13 149 27 163)(14 148 28 162)(29 100 43 86)(30 99 44 85)(31 98 45 112)(32 97 46 111)(33 96 47 110)(34 95 48 109)(35 94 49 108)(36 93 50 107)(37 92 51 106)(38 91 52 105)(39 90 53 104)(40 89 54 103)(41 88 55 102)(42 87 56 101)(57 127 71 113)(58 126 72 140)(59 125 73 139)(60 124 74 138)(61 123 75 137)(62 122 76 136)(63 121 77 135)(64 120 78 134)(65 119 79 133)(66 118 80 132)(67 117 81 131)(68 116 82 130)(69 115 83 129)(70 114 84 128)(169 206 183 220)(170 205 184 219)(171 204 185 218)(172 203 186 217)(173 202 187 216)(174 201 188 215)(175 200 189 214)(176 199 190 213)(177 198 191 212)(178 197 192 211)(179 224 193 210)(180 223 194 209)(181 222 195 208)(182 221 196 207)
G:=sub<Sym(224)| (1,189,91,79)(2,190,92,80)(3,191,93,81)(4,192,94,82)(5,193,95,83)(6,194,96,84)(7,195,97,57)(8,196,98,58)(9,169,99,59)(10,170,100,60)(11,171,101,61)(12,172,102,62)(13,173,103,63)(14,174,104,64)(15,175,105,65)(16,176,106,66)(17,177,107,67)(18,178,108,68)(19,179,109,69)(20,180,110,70)(21,181,111,71)(22,182,112,72)(23,183,85,73)(24,184,86,74)(25,185,87,75)(26,186,88,76)(27,187,89,77)(28,188,90,78)(29,138,166,219)(30,139,167,220)(31,140,168,221)(32,113,141,222)(33,114,142,223)(34,115,143,224)(35,116,144,197)(36,117,145,198)(37,118,146,199)(38,119,147,200)(39,120,148,201)(40,121,149,202)(41,122,150,203)(42,123,151,204)(43,124,152,205)(44,125,153,206)(45,126,154,207)(46,127,155,208)(47,128,156,209)(48,129,157,210)(49,130,158,211)(50,131,159,212)(51,132,160,213)(52,133,161,214)(53,134,162,215)(54,135,163,216)(55,136,164,217)(56,137,165,218), (1,105)(2,106)(3,107)(4,108)(5,109)(6,110)(7,111)(8,112)(9,85)(10,86)(11,87)(12,88)(13,89)(14,90)(15,91)(16,92)(17,93)(18,94)(19,95)(20,96)(21,97)(22,98)(23,99)(24,100)(25,101)(26,102)(27,103)(28,104)(29,43)(30,44)(31,45)(32,46)(33,47)(34,48)(35,49)(36,50)(37,51)(38,52)(39,53)(40,54)(41,55)(42,56)(57,71)(58,72)(59,73)(60,74)(61,75)(62,76)(63,77)(64,78)(65,79)(66,80)(67,81)(68,82)(69,83)(70,84)(113,208)(114,209)(115,210)(116,211)(117,212)(118,213)(119,214)(120,215)(121,216)(122,217)(123,218)(124,219)(125,220)(126,221)(127,222)(128,223)(129,224)(130,197)(131,198)(132,199)(133,200)(134,201)(135,202)(136,203)(137,204)(138,205)(139,206)(140,207)(141,155)(142,156)(143,157)(144,158)(145,159)(146,160)(147,161)(148,162)(149,163)(150,164)(151,165)(152,166)(153,167)(154,168)(169,183)(170,184)(171,185)(172,186)(173,187)(174,188)(175,189)(176,190)(177,191)(178,192)(179,193)(180,194)(181,195)(182,196), (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), (1,161,15,147)(2,160,16,146)(3,159,17,145)(4,158,18,144)(5,157,19,143)(6,156,20,142)(7,155,21,141)(8,154,22,168)(9,153,23,167)(10,152,24,166)(11,151,25,165)(12,150,26,164)(13,149,27,163)(14,148,28,162)(29,100,43,86)(30,99,44,85)(31,98,45,112)(32,97,46,111)(33,96,47,110)(34,95,48,109)(35,94,49,108)(36,93,50,107)(37,92,51,106)(38,91,52,105)(39,90,53,104)(40,89,54,103)(41,88,55,102)(42,87,56,101)(57,127,71,113)(58,126,72,140)(59,125,73,139)(60,124,74,138)(61,123,75,137)(62,122,76,136)(63,121,77,135)(64,120,78,134)(65,119,79,133)(66,118,80,132)(67,117,81,131)(68,116,82,130)(69,115,83,129)(70,114,84,128)(169,206,183,220)(170,205,184,219)(171,204,185,218)(172,203,186,217)(173,202,187,216)(174,201,188,215)(175,200,189,214)(176,199,190,213)(177,198,191,212)(178,197,192,211)(179,224,193,210)(180,223,194,209)(181,222,195,208)(182,221,196,207)>;
G:=Group( (1,189,91,79)(2,190,92,80)(3,191,93,81)(4,192,94,82)(5,193,95,83)(6,194,96,84)(7,195,97,57)(8,196,98,58)(9,169,99,59)(10,170,100,60)(11,171,101,61)(12,172,102,62)(13,173,103,63)(14,174,104,64)(15,175,105,65)(16,176,106,66)(17,177,107,67)(18,178,108,68)(19,179,109,69)(20,180,110,70)(21,181,111,71)(22,182,112,72)(23,183,85,73)(24,184,86,74)(25,185,87,75)(26,186,88,76)(27,187,89,77)(28,188,90,78)(29,138,166,219)(30,139,167,220)(31,140,168,221)(32,113,141,222)(33,114,142,223)(34,115,143,224)(35,116,144,197)(36,117,145,198)(37,118,146,199)(38,119,147,200)(39,120,148,201)(40,121,149,202)(41,122,150,203)(42,123,151,204)(43,124,152,205)(44,125,153,206)(45,126,154,207)(46,127,155,208)(47,128,156,209)(48,129,157,210)(49,130,158,211)(50,131,159,212)(51,132,160,213)(52,133,161,214)(53,134,162,215)(54,135,163,216)(55,136,164,217)(56,137,165,218), (1,105)(2,106)(3,107)(4,108)(5,109)(6,110)(7,111)(8,112)(9,85)(10,86)(11,87)(12,88)(13,89)(14,90)(15,91)(16,92)(17,93)(18,94)(19,95)(20,96)(21,97)(22,98)(23,99)(24,100)(25,101)(26,102)(27,103)(28,104)(29,43)(30,44)(31,45)(32,46)(33,47)(34,48)(35,49)(36,50)(37,51)(38,52)(39,53)(40,54)(41,55)(42,56)(57,71)(58,72)(59,73)(60,74)(61,75)(62,76)(63,77)(64,78)(65,79)(66,80)(67,81)(68,82)(69,83)(70,84)(113,208)(114,209)(115,210)(116,211)(117,212)(118,213)(119,214)(120,215)(121,216)(122,217)(123,218)(124,219)(125,220)(126,221)(127,222)(128,223)(129,224)(130,197)(131,198)(132,199)(133,200)(134,201)(135,202)(136,203)(137,204)(138,205)(139,206)(140,207)(141,155)(142,156)(143,157)(144,158)(145,159)(146,160)(147,161)(148,162)(149,163)(150,164)(151,165)(152,166)(153,167)(154,168)(169,183)(170,184)(171,185)(172,186)(173,187)(174,188)(175,189)(176,190)(177,191)(178,192)(179,193)(180,194)(181,195)(182,196), (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), (1,161,15,147)(2,160,16,146)(3,159,17,145)(4,158,18,144)(5,157,19,143)(6,156,20,142)(7,155,21,141)(8,154,22,168)(9,153,23,167)(10,152,24,166)(11,151,25,165)(12,150,26,164)(13,149,27,163)(14,148,28,162)(29,100,43,86)(30,99,44,85)(31,98,45,112)(32,97,46,111)(33,96,47,110)(34,95,48,109)(35,94,49,108)(36,93,50,107)(37,92,51,106)(38,91,52,105)(39,90,53,104)(40,89,54,103)(41,88,55,102)(42,87,56,101)(57,127,71,113)(58,126,72,140)(59,125,73,139)(60,124,74,138)(61,123,75,137)(62,122,76,136)(63,121,77,135)(64,120,78,134)(65,119,79,133)(66,118,80,132)(67,117,81,131)(68,116,82,130)(69,115,83,129)(70,114,84,128)(169,206,183,220)(170,205,184,219)(171,204,185,218)(172,203,186,217)(173,202,187,216)(174,201,188,215)(175,200,189,214)(176,199,190,213)(177,198,191,212)(178,197,192,211)(179,224,193,210)(180,223,194,209)(181,222,195,208)(182,221,196,207) );
G=PermutationGroup([[(1,189,91,79),(2,190,92,80),(3,191,93,81),(4,192,94,82),(5,193,95,83),(6,194,96,84),(7,195,97,57),(8,196,98,58),(9,169,99,59),(10,170,100,60),(11,171,101,61),(12,172,102,62),(13,173,103,63),(14,174,104,64),(15,175,105,65),(16,176,106,66),(17,177,107,67),(18,178,108,68),(19,179,109,69),(20,180,110,70),(21,181,111,71),(22,182,112,72),(23,183,85,73),(24,184,86,74),(25,185,87,75),(26,186,88,76),(27,187,89,77),(28,188,90,78),(29,138,166,219),(30,139,167,220),(31,140,168,221),(32,113,141,222),(33,114,142,223),(34,115,143,224),(35,116,144,197),(36,117,145,198),(37,118,146,199),(38,119,147,200),(39,120,148,201),(40,121,149,202),(41,122,150,203),(42,123,151,204),(43,124,152,205),(44,125,153,206),(45,126,154,207),(46,127,155,208),(47,128,156,209),(48,129,157,210),(49,130,158,211),(50,131,159,212),(51,132,160,213),(52,133,161,214),(53,134,162,215),(54,135,163,216),(55,136,164,217),(56,137,165,218)], [(1,105),(2,106),(3,107),(4,108),(5,109),(6,110),(7,111),(8,112),(9,85),(10,86),(11,87),(12,88),(13,89),(14,90),(15,91),(16,92),(17,93),(18,94),(19,95),(20,96),(21,97),(22,98),(23,99),(24,100),(25,101),(26,102),(27,103),(28,104),(29,43),(30,44),(31,45),(32,46),(33,47),(34,48),(35,49),(36,50),(37,51),(38,52),(39,53),(40,54),(41,55),(42,56),(57,71),(58,72),(59,73),(60,74),(61,75),(62,76),(63,77),(64,78),(65,79),(66,80),(67,81),(68,82),(69,83),(70,84),(113,208),(114,209),(115,210),(116,211),(117,212),(118,213),(119,214),(120,215),(121,216),(122,217),(123,218),(124,219),(125,220),(126,221),(127,222),(128,223),(129,224),(130,197),(131,198),(132,199),(133,200),(134,201),(135,202),(136,203),(137,204),(138,205),(139,206),(140,207),(141,155),(142,156),(143,157),(144,158),(145,159),(146,160),(147,161),(148,162),(149,163),(150,164),(151,165),(152,166),(153,167),(154,168),(169,183),(170,184),(171,185),(172,186),(173,187),(174,188),(175,189),(176,190),(177,191),(178,192),(179,193),(180,194),(181,195),(182,196)], [(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)], [(1,161,15,147),(2,160,16,146),(3,159,17,145),(4,158,18,144),(5,157,19,143),(6,156,20,142),(7,155,21,141),(8,154,22,168),(9,153,23,167),(10,152,24,166),(11,151,25,165),(12,150,26,164),(13,149,27,163),(14,148,28,162),(29,100,43,86),(30,99,44,85),(31,98,45,112),(32,97,46,111),(33,96,47,110),(34,95,48,109),(35,94,49,108),(36,93,50,107),(37,92,51,106),(38,91,52,105),(39,90,53,104),(40,89,54,103),(41,88,55,102),(42,87,56,101),(57,127,71,113),(58,126,72,140),(59,125,73,139),(60,124,74,138),(61,123,75,137),(62,122,76,136),(63,121,77,135),(64,120,78,134),(65,119,79,133),(66,118,80,132),(67,117,81,131),(68,116,82,130),(69,115,83,129),(70,114,84,128),(169,206,183,220),(170,205,184,219),(171,204,185,218),(172,203,186,217),(173,202,187,216),(174,201,188,215),(175,200,189,214),(176,199,190,213),(177,198,191,212),(178,197,192,211),(179,224,193,210),(180,223,194,209),(181,222,195,208),(182,221,196,207)]])
85 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 4K | 4L | ··· | 4Q | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14U | 28A | ··· | 28L | 28M | ··· | 28AJ |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 14 | 14 | 14 | 14 | 28 | ··· | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 2 | ··· | 2 | 4 | ··· | 4 |
85 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | - | + | + | + | + | + | + | - | + | - | + | |
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | Q8 | D7 | C4○D4 | D14 | D14 | D14 | D14 | D14 | Dic14 | 2+ 1+4 | D4⋊2D7 | D4⋊8D14 |
| kernel | D4⋊6Dic14 | C4×Dic14 | C28⋊2Q8 | C22⋊Dic14 | C28.3Q8 | C28.48D4 | C2×C4⋊Dic7 | D4×Dic7 | D4×C28 | C7×D4 | C4×D4 | C28 | C42 | C22⋊C4 | C4⋊C4 | C22×C4 | C2×D4 | D4 | C14 | C4 | C2 |
| # reps | 1 | 1 | 1 | 4 | 2 | 2 | 2 | 2 | 1 | 4 | 3 | 4 | 3 | 6 | 3 | 6 | 3 | 24 | 1 | 6 | 6 |
Matrix representation of D4⋊6Dic14 ►in GL4(𝔽29) generated by
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 28 |
| 0 | 0 | 1 | 0 |
| 28 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 |
| 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 1 |
| 26 | 2 | 0 | 0 |
| 19 | 16 | 0 | 0 |
| 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 28 |
| 17 | 0 | 0 | 0 |
| 2 | 12 | 0 | 0 |
| 0 | 0 | 0 | 12 |
| 0 | 0 | 17 | 0 |
G:=sub<GL(4,GF(29))| [1,0,0,0,0,1,0,0,0,0,0,1,0,0,28,0],[28,0,0,0,0,28,0,0,0,0,28,0,0,0,0,1],[26,19,0,0,2,16,0,0,0,0,28,0,0,0,0,28],[17,2,0,0,0,12,0,0,0,0,0,17,0,0,12,0] >;
D4⋊6Dic14 in GAP, Magma, Sage, TeX
D_4\rtimes_6{\rm Dic}_{14} % in TeX
G:=Group("D4:6Dic14"); // GroupNames label
G:=SmallGroup(448,996);
// by ID
G=gap.SmallGroup(448,996);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,112,387,1571,192,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^2=c^28=1,d^2=c^14,b*a*b=a^-1,a*c=c*a,a*d=d*a,b*c=c*b,d*b*d^-1=a^2*b,d*c*d^-1=c^-1>;
// generators/relations