metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: Dic14⋊24D4, C42.111D14, C14.1042+ 1+4, (C4×D4)⋊15D7, (D4×C28)⋊17C2, C28⋊3(C4○D4), C4⋊1(C4○D28), C28⋊D4⋊9C2, C7⋊1(Q8⋊6D4), C4.142(D4×D7), D14⋊D4⋊8C2, C28⋊7D4⋊19C2, C28⋊4D4⋊12C2, C4⋊C4.317D14, C28.348(C2×D4), D28⋊C4⋊15C2, (C4×Dic14)⋊32C2, (C2×D4).216D14, (C2×C14).97C24, Dic7.18(C2×D4), C14.52(C22×D4), (C2×C28).785C23, (C4×C28).154C22, D14⋊C4.54C22, C22⋊C4.112D14, (C22×C4).210D14, C2.16(D4⋊8D14), C23.97(C22×D7), (D4×C14).258C22, (C2×D28).138C22, C4⋊Dic7.299C22, (C4×Dic7).75C22, (C22×D7).32C23, C22.122(C23×D7), Dic7⋊C4.111C22, (C22×C14).167C23, (C22×C28).109C22, (C2×Dic7).205C23, (C2×Dic14).316C22, C2.25(C2×D4×D7), (C2×C4○D28)⋊10C2, C2.48(C2×C4○D28), C14.44(C2×C4○D4), (C2×C4×D7).200C22, (C7×C4⋊C4).328C22, (C2×C4).580(C22×D7), (C2×C7⋊D4).14C22, (C7×C22⋊C4).124C22, SmallGroup(448,1006)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for Dic14⋊24D4
G = < a,b,c,d | a28=c4=d2=1, b2=a14, bab-1=a-1, ac=ca, ad=da, bc=cb, dbd=a14b, dcd=c-1 >
Subgroups: 1652 in 312 conjugacy classes, 107 normal (29 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C2×C4, C2×C4, C2×C4, D4, Q8, C23, C23, D7, C14, C14, C42, C42, C22⋊C4, C22⋊C4, C4⋊C4, C4⋊C4, C22×C4, C22×C4, C2×D4, C2×D4, C2×Q8, C4○D4, Dic7, Dic7, C28, C28, D14, C2×C14, C2×C14, C4×D4, C4×D4, C4×Q8, C4⋊D4, C4⋊1D4, C2×C4○D4, Dic14, C4×D7, D28, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C2×C28, C7×D4, C22×D7, C22×C14, Q8⋊6D4, C4×Dic7, Dic7⋊C4, C4⋊Dic7, D14⋊C4, C4×C28, C7×C22⋊C4, C7×C4⋊C4, C2×Dic14, C2×C4×D7, C2×D28, C4○D28, C2×C7⋊D4, C22×C28, D4×C14, C4×Dic14, C28⋊4D4, D14⋊D4, D28⋊C4, C28⋊7D4, C28⋊D4, D4×C28, C2×C4○D28, Dic14⋊24D4
Quotients: C1, C2, C22, D4, C23, D7, C2×D4, C4○D4, C24, D14, C22×D4, C2×C4○D4, 2+ 1+4, C22×D7, Q8⋊6D4, C4○D28, D4×D7, C23×D7, C2×C4○D28, C2×D4×D7, D4⋊8D14, Dic14⋊24D4
►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 50 15 36)(2 49 16 35)(3 48 17 34)(4 47 18 33)(5 46 19 32)(6 45 20 31)(7 44 21 30)(8 43 22 29)(9 42 23 56)(10 41 24 55)(11 40 25 54)(12 39 26 53)(13 38 27 52)(14 37 28 51)(57 94 71 108)(58 93 72 107)(59 92 73 106)(60 91 74 105)(61 90 75 104)(62 89 76 103)(63 88 77 102)(64 87 78 101)(65 86 79 100)(66 85 80 99)(67 112 81 98)(68 111 82 97)(69 110 83 96)(70 109 84 95)(113 164 127 150)(114 163 128 149)(115 162 129 148)(116 161 130 147)(117 160 131 146)(118 159 132 145)(119 158 133 144)(120 157 134 143)(121 156 135 142)(122 155 136 141)(123 154 137 168)(124 153 138 167)(125 152 139 166)(126 151 140 165)(169 219 183 205)(170 218 184 204)(171 217 185 203)(172 216 186 202)(173 215 187 201)(174 214 188 200)(175 213 189 199)(176 212 190 198)(177 211 191 197)(178 210 192 224)(179 209 193 223)(180 208 194 222)(181 207 195 221)(182 206 196 220)
(1 195 146 63)(2 196 147 64)(3 169 148 65)(4 170 149 66)(5 171 150 67)(6 172 151 68)(7 173 152 69)(8 174 153 70)(9 175 154 71)(10 176 155 72)(11 177 156 73)(12 178 157 74)(13 179 158 75)(14 180 159 76)(15 181 160 77)(16 182 161 78)(17 183 162 79)(18 184 163 80)(19 185 164 81)(20 186 165 82)(21 187 166 83)(22 188 167 84)(23 189 168 57)(24 190 141 58)(25 191 142 59)(26 192 143 60)(27 193 144 61)(28 194 145 62)(29 200 124 95)(30 201 125 96)(31 202 126 97)(32 203 127 98)(33 204 128 99)(34 205 129 100)(35 206 130 101)(36 207 131 102)(37 208 132 103)(38 209 133 104)(39 210 134 105)(40 211 135 106)(41 212 136 107)(42 213 137 108)(43 214 138 109)(44 215 139 110)(45 216 140 111)(46 217 113 112)(47 218 114 85)(48 219 115 86)(49 220 116 87)(50 221 117 88)(51 222 118 89)(52 223 119 90)(53 224 120 91)(54 197 121 92)(55 198 122 93)(56 199 123 94)
(1 117)(2 118)(3 119)(4 120)(5 121)(6 122)(7 123)(8 124)(9 125)(10 126)(11 127)(12 128)(13 129)(14 130)(15 131)(16 132)(17 133)(18 134)(19 135)(20 136)(21 137)(22 138)(23 139)(24 140)(25 113)(26 114)(27 115)(28 116)(29 153)(30 154)(31 155)(32 156)(33 157)(34 158)(35 159)(36 160)(37 161)(38 162)(39 163)(40 164)(41 165)(42 166)(43 167)(44 168)(45 141)(46 142)(47 143)(48 144)(49 145)(50 146)(51 147)(52 148)(53 149)(54 150)(55 151)(56 152)(57 110)(58 111)(59 112)(60 85)(61 86)(62 87)(63 88)(64 89)(65 90)(66 91)(67 92)(68 93)(69 94)(70 95)(71 96)(72 97)(73 98)(74 99)(75 100)(76 101)(77 102)(78 103)(79 104)(80 105)(81 106)(82 107)(83 108)(84 109)(169 223)(170 224)(171 197)(172 198)(173 199)(174 200)(175 201)(176 202)(177 203)(178 204)(179 205)(180 206)(181 207)(182 208)(183 209)(184 210)(185 211)(186 212)(187 213)(188 214)(189 215)(190 216)(191 217)(192 218)(193 219)(194 220)(195 221)(196 222)
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), (1,50,15,36)(2,49,16,35)(3,48,17,34)(4,47,18,33)(5,46,19,32)(6,45,20,31)(7,44,21,30)(8,43,22,29)(9,42,23,56)(10,41,24,55)(11,40,25,54)(12,39,26,53)(13,38,27,52)(14,37,28,51)(57,94,71,108)(58,93,72,107)(59,92,73,106)(60,91,74,105)(61,90,75,104)(62,89,76,103)(63,88,77,102)(64,87,78,101)(65,86,79,100)(66,85,80,99)(67,112,81,98)(68,111,82,97)(69,110,83,96)(70,109,84,95)(113,164,127,150)(114,163,128,149)(115,162,129,148)(116,161,130,147)(117,160,131,146)(118,159,132,145)(119,158,133,144)(120,157,134,143)(121,156,135,142)(122,155,136,141)(123,154,137,168)(124,153,138,167)(125,152,139,166)(126,151,140,165)(169,219,183,205)(170,218,184,204)(171,217,185,203)(172,216,186,202)(173,215,187,201)(174,214,188,200)(175,213,189,199)(176,212,190,198)(177,211,191,197)(178,210,192,224)(179,209,193,223)(180,208,194,222)(181,207,195,221)(182,206,196,220), (1,195,146,63)(2,196,147,64)(3,169,148,65)(4,170,149,66)(5,171,150,67)(6,172,151,68)(7,173,152,69)(8,174,153,70)(9,175,154,71)(10,176,155,72)(11,177,156,73)(12,178,157,74)(13,179,158,75)(14,180,159,76)(15,181,160,77)(16,182,161,78)(17,183,162,79)(18,184,163,80)(19,185,164,81)(20,186,165,82)(21,187,166,83)(22,188,167,84)(23,189,168,57)(24,190,141,58)(25,191,142,59)(26,192,143,60)(27,193,144,61)(28,194,145,62)(29,200,124,95)(30,201,125,96)(31,202,126,97)(32,203,127,98)(33,204,128,99)(34,205,129,100)(35,206,130,101)(36,207,131,102)(37,208,132,103)(38,209,133,104)(39,210,134,105)(40,211,135,106)(41,212,136,107)(42,213,137,108)(43,214,138,109)(44,215,139,110)(45,216,140,111)(46,217,113,112)(47,218,114,85)(48,219,115,86)(49,220,116,87)(50,221,117,88)(51,222,118,89)(52,223,119,90)(53,224,120,91)(54,197,121,92)(55,198,122,93)(56,199,123,94), (1,117)(2,118)(3,119)(4,120)(5,121)(6,122)(7,123)(8,124)(9,125)(10,126)(11,127)(12,128)(13,129)(14,130)(15,131)(16,132)(17,133)(18,134)(19,135)(20,136)(21,137)(22,138)(23,139)(24,140)(25,113)(26,114)(27,115)(28,116)(29,153)(30,154)(31,155)(32,156)(33,157)(34,158)(35,159)(36,160)(37,161)(38,162)(39,163)(40,164)(41,165)(42,166)(43,167)(44,168)(45,141)(46,142)(47,143)(48,144)(49,145)(50,146)(51,147)(52,148)(53,149)(54,150)(55,151)(56,152)(57,110)(58,111)(59,112)(60,85)(61,86)(62,87)(63,88)(64,89)(65,90)(66,91)(67,92)(68,93)(69,94)(70,95)(71,96)(72,97)(73,98)(74,99)(75,100)(76,101)(77,102)(78,103)(79,104)(80,105)(81,106)(82,107)(83,108)(84,109)(169,223)(170,224)(171,197)(172,198)(173,199)(174,200)(175,201)(176,202)(177,203)(178,204)(179,205)(180,206)(181,207)(182,208)(183,209)(184,210)(185,211)(186,212)(187,213)(188,214)(189,215)(190,216)(191,217)(192,218)(193,219)(194,220)(195,221)(196,222)>;
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), (1,50,15,36)(2,49,16,35)(3,48,17,34)(4,47,18,33)(5,46,19,32)(6,45,20,31)(7,44,21,30)(8,43,22,29)(9,42,23,56)(10,41,24,55)(11,40,25,54)(12,39,26,53)(13,38,27,52)(14,37,28,51)(57,94,71,108)(58,93,72,107)(59,92,73,106)(60,91,74,105)(61,90,75,104)(62,89,76,103)(63,88,77,102)(64,87,78,101)(65,86,79,100)(66,85,80,99)(67,112,81,98)(68,111,82,97)(69,110,83,96)(70,109,84,95)(113,164,127,150)(114,163,128,149)(115,162,129,148)(116,161,130,147)(117,160,131,146)(118,159,132,145)(119,158,133,144)(120,157,134,143)(121,156,135,142)(122,155,136,141)(123,154,137,168)(124,153,138,167)(125,152,139,166)(126,151,140,165)(169,219,183,205)(170,218,184,204)(171,217,185,203)(172,216,186,202)(173,215,187,201)(174,214,188,200)(175,213,189,199)(176,212,190,198)(177,211,191,197)(178,210,192,224)(179,209,193,223)(180,208,194,222)(181,207,195,221)(182,206,196,220), (1,195,146,63)(2,196,147,64)(3,169,148,65)(4,170,149,66)(5,171,150,67)(6,172,151,68)(7,173,152,69)(8,174,153,70)(9,175,154,71)(10,176,155,72)(11,177,156,73)(12,178,157,74)(13,179,158,75)(14,180,159,76)(15,181,160,77)(16,182,161,78)(17,183,162,79)(18,184,163,80)(19,185,164,81)(20,186,165,82)(21,187,166,83)(22,188,167,84)(23,189,168,57)(24,190,141,58)(25,191,142,59)(26,192,143,60)(27,193,144,61)(28,194,145,62)(29,200,124,95)(30,201,125,96)(31,202,126,97)(32,203,127,98)(33,204,128,99)(34,205,129,100)(35,206,130,101)(36,207,131,102)(37,208,132,103)(38,209,133,104)(39,210,134,105)(40,211,135,106)(41,212,136,107)(42,213,137,108)(43,214,138,109)(44,215,139,110)(45,216,140,111)(46,217,113,112)(47,218,114,85)(48,219,115,86)(49,220,116,87)(50,221,117,88)(51,222,118,89)(52,223,119,90)(53,224,120,91)(54,197,121,92)(55,198,122,93)(56,199,123,94), (1,117)(2,118)(3,119)(4,120)(5,121)(6,122)(7,123)(8,124)(9,125)(10,126)(11,127)(12,128)(13,129)(14,130)(15,131)(16,132)(17,133)(18,134)(19,135)(20,136)(21,137)(22,138)(23,139)(24,140)(25,113)(26,114)(27,115)(28,116)(29,153)(30,154)(31,155)(32,156)(33,157)(34,158)(35,159)(36,160)(37,161)(38,162)(39,163)(40,164)(41,165)(42,166)(43,167)(44,168)(45,141)(46,142)(47,143)(48,144)(49,145)(50,146)(51,147)(52,148)(53,149)(54,150)(55,151)(56,152)(57,110)(58,111)(59,112)(60,85)(61,86)(62,87)(63,88)(64,89)(65,90)(66,91)(67,92)(68,93)(69,94)(70,95)(71,96)(72,97)(73,98)(74,99)(75,100)(76,101)(77,102)(78,103)(79,104)(80,105)(81,106)(82,107)(83,108)(84,109)(169,223)(170,224)(171,197)(172,198)(173,199)(174,200)(175,201)(176,202)(177,203)(178,204)(179,205)(180,206)(181,207)(182,208)(183,209)(184,210)(185,211)(186,212)(187,213)(188,214)(189,215)(190,216)(191,217)(192,218)(193,219)(194,220)(195,221)(196,222) );
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)], [(1,50,15,36),(2,49,16,35),(3,48,17,34),(4,47,18,33),(5,46,19,32),(6,45,20,31),(7,44,21,30),(8,43,22,29),(9,42,23,56),(10,41,24,55),(11,40,25,54),(12,39,26,53),(13,38,27,52),(14,37,28,51),(57,94,71,108),(58,93,72,107),(59,92,73,106),(60,91,74,105),(61,90,75,104),(62,89,76,103),(63,88,77,102),(64,87,78,101),(65,86,79,100),(66,85,80,99),(67,112,81,98),(68,111,82,97),(69,110,83,96),(70,109,84,95),(113,164,127,150),(114,163,128,149),(115,162,129,148),(116,161,130,147),(117,160,131,146),(118,159,132,145),(119,158,133,144),(120,157,134,143),(121,156,135,142),(122,155,136,141),(123,154,137,168),(124,153,138,167),(125,152,139,166),(126,151,140,165),(169,219,183,205),(170,218,184,204),(171,217,185,203),(172,216,186,202),(173,215,187,201),(174,214,188,200),(175,213,189,199),(176,212,190,198),(177,211,191,197),(178,210,192,224),(179,209,193,223),(180,208,194,222),(181,207,195,221),(182,206,196,220)], [(1,195,146,63),(2,196,147,64),(3,169,148,65),(4,170,149,66),(5,171,150,67),(6,172,151,68),(7,173,152,69),(8,174,153,70),(9,175,154,71),(10,176,155,72),(11,177,156,73),(12,178,157,74),(13,179,158,75),(14,180,159,76),(15,181,160,77),(16,182,161,78),(17,183,162,79),(18,184,163,80),(19,185,164,81),(20,186,165,82),(21,187,166,83),(22,188,167,84),(23,189,168,57),(24,190,141,58),(25,191,142,59),(26,192,143,60),(27,193,144,61),(28,194,145,62),(29,200,124,95),(30,201,125,96),(31,202,126,97),(32,203,127,98),(33,204,128,99),(34,205,129,100),(35,206,130,101),(36,207,131,102),(37,208,132,103),(38,209,133,104),(39,210,134,105),(40,211,135,106),(41,212,136,107),(42,213,137,108),(43,214,138,109),(44,215,139,110),(45,216,140,111),(46,217,113,112),(47,218,114,85),(48,219,115,86),(49,220,116,87),(50,221,117,88),(51,222,118,89),(52,223,119,90),(53,224,120,91),(54,197,121,92),(55,198,122,93),(56,199,123,94)], [(1,117),(2,118),(3,119),(4,120),(5,121),(6,122),(7,123),(8,124),(9,125),(10,126),(11,127),(12,128),(13,129),(14,130),(15,131),(16,132),(17,133),(18,134),(19,135),(20,136),(21,137),(22,138),(23,139),(24,140),(25,113),(26,114),(27,115),(28,116),(29,153),(30,154),(31,155),(32,156),(33,157),(34,158),(35,159),(36,160),(37,161),(38,162),(39,163),(40,164),(41,165),(42,166),(43,167),(44,168),(45,141),(46,142),(47,143),(48,144),(49,145),(50,146),(51,147),(52,148),(53,149),(54,150),(55,151),(56,152),(57,110),(58,111),(59,112),(60,85),(61,86),(62,87),(63,88),(64,89),(65,90),(66,91),(67,92),(68,93),(69,94),(70,95),(71,96),(72,97),(73,98),(74,99),(75,100),(76,101),(77,102),(78,103),(79,104),(80,105),(81,106),(82,107),(83,108),(84,109),(169,223),(170,224),(171,197),(172,198),(173,199),(174,200),(175,201),(176,202),(177,203),(178,204),(179,205),(180,206),(181,207),(182,208),(183,209),(184,210),(185,211),(186,212),(187,213),(188,214),(189,215),(190,216),(191,217),(192,218),(193,219),(194,220),(195,221),(196,222)]])
85 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 2H | 2I | 4A | ··· | 4H | 4I | 4J | 4K | 4L | 4M | 4N | 4O | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14U | 28A | ··· | 28L | 28M | ··· | 28AJ |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 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 | 4 | 4 | 28 | 28 | 28 | 28 | 2 | ··· | 2 | 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 | D4 | D7 | C4○D4 | D14 | D14 | D14 | D14 | D14 | C4○D28 | 2+ 1+4 | D4×D7 | D4⋊8D14 |
| kernel | Dic14⋊24D4 | C4×Dic14 | C28⋊4D4 | D14⋊D4 | D28⋊C4 | C28⋊7D4 | C28⋊D4 | D4×C28 | C2×C4○D28 | Dic14 | C4×D4 | C28 | C42 | C22⋊C4 | C4⋊C4 | C22×C4 | C2×D4 | C4 | C14 | C4 | C2 |
| # reps | 1 | 1 | 1 | 4 | 2 | 2 | 2 | 1 | 2 | 4 | 3 | 4 | 3 | 6 | 3 | 6 | 3 | 24 | 1 | 6 | 6 |
Matrix representation of Dic14⋊24D4 ►in GL4(𝔽29) generated by
| 17 | 21 | 0 | 0 |
| 14 | 2 | 0 | 0 |
| 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 28 |
| 13 | 21 | 0 | 0 |
| 14 | 16 | 0 | 0 |
| 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 28 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 28 |
| 0 | 0 | 1 | 0 |
| 24 | 15 | 0 | 0 |
| 10 | 5 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 28 |
G:=sub<GL(4,GF(29))| [17,14,0,0,21,2,0,0,0,0,28,0,0,0,0,28],[13,14,0,0,21,16,0,0,0,0,28,0,0,0,0,28],[1,0,0,0,0,1,0,0,0,0,0,1,0,0,28,0],[24,10,0,0,15,5,0,0,0,0,1,0,0,0,0,28] >;
Dic14⋊24D4 in GAP, Magma, Sage, TeX
{\rm Dic}_{14}\rtimes_{24}D_4 % in TeX
G:=Group("Dic14:24D4"); // GroupNames label
G:=SmallGroup(448,1006);
// by ID
G=gap.SmallGroup(448,1006);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,477,232,387,100,675,570,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^28=c^4=d^2=1,b^2=a^14,b*a*b^-1=a^-1,a*c=c*a,a*d=d*a,b*c=c*b,d*b*d=a^14*b,d*c*d=c^-1>;
// generators/relations