metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: D28⋊3D4, Dic7⋊2D8, (C2×D56)⋊5C2, C7⋊1(C4⋊D8), C2.11(D7×D8), C4.88(D4×D7), D4⋊C4⋊8D7, C28⋊D4⋊2C2, Dic7⋊C8⋊7C2, C14.25(C2×D8), (C2×C8).12D14, C14.D8⋊8C2, D28⋊C4⋊3C2, C4⋊C4.140D14, (C2×D4).31D14, C4.3(C4○D28), C28.112(C2×D4), C28.11(C4○D4), (C2×C56).12C22, (C2×Dic7).24D4, C22.183(D4×D7), C14.19(C4⋊D4), C2.13(D56⋊C2), C14.58(C8⋊C22), (C2×C28).226C23, (C2×D28).54C22, (D4×C14).47C22, C2.22(D14⋊D4), (C4×Dic7).13C22, (C2×D4⋊D7)⋊6C2, (C7×D4⋊C4)⋊8C2, (C2×C7⋊C8).24C22, (C2×C14).239(C2×D4), (C7×C4⋊C4).27C22, (C2×C4).333(C22×D7), SmallGroup(448,320)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for D28⋊3D4
G = < a,b,c,d | a28=b2=c4=d2=1, bab=dad=a-1, cac-1=a13, cbc-1=a12b, dbd=a19b, dcd=c-1 >
Subgroups: 980 in 140 conjugacy classes, 41 normal (37 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C8, C2×C4, C2×C4, D4, C23, D7, C14, C14, C42, C22⋊C4, C4⋊C4, C2×C8, C2×C8, D8, C22×C4, C2×D4, C2×D4, Dic7, Dic7, C28, C28, D14, C2×C14, C2×C14, D4⋊C4, D4⋊C4, C4⋊C8, C4×D4, C4⋊1D4, C2×D8, C7⋊C8, C56, C4×D7, D28, D28, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C7×D4, C22×D7, C22×C14, C4⋊D8, D56, C2×C7⋊C8, C4×Dic7, D14⋊C4, D4⋊D7, C7×C4⋊C4, C2×C56, C2×C4×D7, C2×D28, C2×C7⋊D4, D4×C14, C14.D8, Dic7⋊C8, C7×D4⋊C4, D28⋊C4, C2×D56, C2×D4⋊D7, C28⋊D4, D28⋊3D4
Quotients: C1, C2, C22, D4, C23, D7, D8, C2×D4, C4○D4, D14, C4⋊D4, C2×D8, C8⋊C22, C22×D7, C4⋊D8, C4○D28, D4×D7, D14⋊D4, D7×D8, D56⋊C2, D28⋊3D4
►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 93)(2 92)(3 91)(4 90)(5 89)(6 88)(7 87)(8 86)(9 85)(10 112)(11 111)(12 110)(13 109)(14 108)(15 107)(16 106)(17 105)(18 104)(19 103)(20 102)(21 101)(22 100)(23 99)(24 98)(25 97)(26 96)(27 95)(28 94)(29 157)(30 156)(31 155)(32 154)(33 153)(34 152)(35 151)(36 150)(37 149)(38 148)(39 147)(40 146)(41 145)(42 144)(43 143)(44 142)(45 141)(46 168)(47 167)(48 166)(49 165)(50 164)(51 163)(52 162)(53 161)(54 160)(55 159)(56 158)(57 197)(58 224)(59 223)(60 222)(61 221)(62 220)(63 219)(64 218)(65 217)(66 216)(67 215)(68 214)(69 213)(70 212)(71 211)(72 210)(73 209)(74 208)(75 207)(76 206)(77 205)(78 204)(79 203)(80 202)(81 201)(82 200)(83 199)(84 198)(113 171)(114 170)(115 169)(116 196)(117 195)(118 194)(119 193)(120 192)(121 191)(122 190)(123 189)(124 188)(125 187)(126 186)(127 185)(128 184)(129 183)(130 182)(131 181)(132 180)(133 179)(134 178)(135 177)(136 176)(137 175)(138 174)(139 173)(140 172)
(1 177 87 129)(2 190 88 114)(3 175 89 127)(4 188 90 140)(5 173 91 125)(6 186 92 138)(7 171 93 123)(8 184 94 136)(9 169 95 121)(10 182 96 134)(11 195 97 119)(12 180 98 132)(13 193 99 117)(14 178 100 130)(15 191 101 115)(16 176 102 128)(17 189 103 113)(18 174 104 126)(19 187 105 139)(20 172 106 124)(21 185 107 137)(22 170 108 122)(23 183 109 135)(24 196 110 120)(25 181 111 133)(26 194 112 118)(27 179 85 131)(28 192 86 116)(29 71 160 210)(30 84 161 223)(31 69 162 208)(32 82 163 221)(33 67 164 206)(34 80 165 219)(35 65 166 204)(36 78 167 217)(37 63 168 202)(38 76 141 215)(39 61 142 200)(40 74 143 213)(41 59 144 198)(42 72 145 211)(43 57 146 224)(44 70 147 209)(45 83 148 222)(46 68 149 207)(47 81 150 220)(48 66 151 205)(49 79 152 218)(50 64 153 203)(51 77 154 216)(52 62 155 201)(53 75 156 214)(54 60 157 199)(55 73 158 212)(56 58 159 197)
(1 204)(2 203)(3 202)(4 201)(5 200)(6 199)(7 198)(8 197)(9 224)(10 223)(11 222)(12 221)(13 220)(14 219)(15 218)(16 217)(17 216)(18 215)(19 214)(20 213)(21 212)(22 211)(23 210)(24 209)(25 208)(26 207)(27 206)(28 205)(29 135)(30 134)(31 133)(32 132)(33 131)(34 130)(35 129)(36 128)(37 127)(38 126)(39 125)(40 124)(41 123)(42 122)(43 121)(44 120)(45 119)(46 118)(47 117)(48 116)(49 115)(50 114)(51 113)(52 140)(53 139)(54 138)(55 137)(56 136)(57 95)(58 94)(59 93)(60 92)(61 91)(62 90)(63 89)(64 88)(65 87)(66 86)(67 85)(68 112)(69 111)(70 110)(71 109)(72 108)(73 107)(74 106)(75 105)(76 104)(77 103)(78 102)(79 101)(80 100)(81 99)(82 98)(83 97)(84 96)(141 174)(142 173)(143 172)(144 171)(145 170)(146 169)(147 196)(148 195)(149 194)(150 193)(151 192)(152 191)(153 190)(154 189)(155 188)(156 187)(157 186)(158 185)(159 184)(160 183)(161 182)(162 181)(163 180)(164 179)(165 178)(166 177)(167 176)(168 175)
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), (1,93)(2,92)(3,91)(4,90)(5,89)(6,88)(7,87)(8,86)(9,85)(10,112)(11,111)(12,110)(13,109)(14,108)(15,107)(16,106)(17,105)(18,104)(19,103)(20,102)(21,101)(22,100)(23,99)(24,98)(25,97)(26,96)(27,95)(28,94)(29,157)(30,156)(31,155)(32,154)(33,153)(34,152)(35,151)(36,150)(37,149)(38,148)(39,147)(40,146)(41,145)(42,144)(43,143)(44,142)(45,141)(46,168)(47,167)(48,166)(49,165)(50,164)(51,163)(52,162)(53,161)(54,160)(55,159)(56,158)(57,197)(58,224)(59,223)(60,222)(61,221)(62,220)(63,219)(64,218)(65,217)(66,216)(67,215)(68,214)(69,213)(70,212)(71,211)(72,210)(73,209)(74,208)(75,207)(76,206)(77,205)(78,204)(79,203)(80,202)(81,201)(82,200)(83,199)(84,198)(113,171)(114,170)(115,169)(116,196)(117,195)(118,194)(119,193)(120,192)(121,191)(122,190)(123,189)(124,188)(125,187)(126,186)(127,185)(128,184)(129,183)(130,182)(131,181)(132,180)(133,179)(134,178)(135,177)(136,176)(137,175)(138,174)(139,173)(140,172), (1,177,87,129)(2,190,88,114)(3,175,89,127)(4,188,90,140)(5,173,91,125)(6,186,92,138)(7,171,93,123)(8,184,94,136)(9,169,95,121)(10,182,96,134)(11,195,97,119)(12,180,98,132)(13,193,99,117)(14,178,100,130)(15,191,101,115)(16,176,102,128)(17,189,103,113)(18,174,104,126)(19,187,105,139)(20,172,106,124)(21,185,107,137)(22,170,108,122)(23,183,109,135)(24,196,110,120)(25,181,111,133)(26,194,112,118)(27,179,85,131)(28,192,86,116)(29,71,160,210)(30,84,161,223)(31,69,162,208)(32,82,163,221)(33,67,164,206)(34,80,165,219)(35,65,166,204)(36,78,167,217)(37,63,168,202)(38,76,141,215)(39,61,142,200)(40,74,143,213)(41,59,144,198)(42,72,145,211)(43,57,146,224)(44,70,147,209)(45,83,148,222)(46,68,149,207)(47,81,150,220)(48,66,151,205)(49,79,152,218)(50,64,153,203)(51,77,154,216)(52,62,155,201)(53,75,156,214)(54,60,157,199)(55,73,158,212)(56,58,159,197), (1,204)(2,203)(3,202)(4,201)(5,200)(6,199)(7,198)(8,197)(9,224)(10,223)(11,222)(12,221)(13,220)(14,219)(15,218)(16,217)(17,216)(18,215)(19,214)(20,213)(21,212)(22,211)(23,210)(24,209)(25,208)(26,207)(27,206)(28,205)(29,135)(30,134)(31,133)(32,132)(33,131)(34,130)(35,129)(36,128)(37,127)(38,126)(39,125)(40,124)(41,123)(42,122)(43,121)(44,120)(45,119)(46,118)(47,117)(48,116)(49,115)(50,114)(51,113)(52,140)(53,139)(54,138)(55,137)(56,136)(57,95)(58,94)(59,93)(60,92)(61,91)(62,90)(63,89)(64,88)(65,87)(66,86)(67,85)(68,112)(69,111)(70,110)(71,109)(72,108)(73,107)(74,106)(75,105)(76,104)(77,103)(78,102)(79,101)(80,100)(81,99)(82,98)(83,97)(84,96)(141,174)(142,173)(143,172)(144,171)(145,170)(146,169)(147,196)(148,195)(149,194)(150,193)(151,192)(152,191)(153,190)(154,189)(155,188)(156,187)(157,186)(158,185)(159,184)(160,183)(161,182)(162,181)(163,180)(164,179)(165,178)(166,177)(167,176)(168,175)>;
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), (1,93)(2,92)(3,91)(4,90)(5,89)(6,88)(7,87)(8,86)(9,85)(10,112)(11,111)(12,110)(13,109)(14,108)(15,107)(16,106)(17,105)(18,104)(19,103)(20,102)(21,101)(22,100)(23,99)(24,98)(25,97)(26,96)(27,95)(28,94)(29,157)(30,156)(31,155)(32,154)(33,153)(34,152)(35,151)(36,150)(37,149)(38,148)(39,147)(40,146)(41,145)(42,144)(43,143)(44,142)(45,141)(46,168)(47,167)(48,166)(49,165)(50,164)(51,163)(52,162)(53,161)(54,160)(55,159)(56,158)(57,197)(58,224)(59,223)(60,222)(61,221)(62,220)(63,219)(64,218)(65,217)(66,216)(67,215)(68,214)(69,213)(70,212)(71,211)(72,210)(73,209)(74,208)(75,207)(76,206)(77,205)(78,204)(79,203)(80,202)(81,201)(82,200)(83,199)(84,198)(113,171)(114,170)(115,169)(116,196)(117,195)(118,194)(119,193)(120,192)(121,191)(122,190)(123,189)(124,188)(125,187)(126,186)(127,185)(128,184)(129,183)(130,182)(131,181)(132,180)(133,179)(134,178)(135,177)(136,176)(137,175)(138,174)(139,173)(140,172), (1,177,87,129)(2,190,88,114)(3,175,89,127)(4,188,90,140)(5,173,91,125)(6,186,92,138)(7,171,93,123)(8,184,94,136)(9,169,95,121)(10,182,96,134)(11,195,97,119)(12,180,98,132)(13,193,99,117)(14,178,100,130)(15,191,101,115)(16,176,102,128)(17,189,103,113)(18,174,104,126)(19,187,105,139)(20,172,106,124)(21,185,107,137)(22,170,108,122)(23,183,109,135)(24,196,110,120)(25,181,111,133)(26,194,112,118)(27,179,85,131)(28,192,86,116)(29,71,160,210)(30,84,161,223)(31,69,162,208)(32,82,163,221)(33,67,164,206)(34,80,165,219)(35,65,166,204)(36,78,167,217)(37,63,168,202)(38,76,141,215)(39,61,142,200)(40,74,143,213)(41,59,144,198)(42,72,145,211)(43,57,146,224)(44,70,147,209)(45,83,148,222)(46,68,149,207)(47,81,150,220)(48,66,151,205)(49,79,152,218)(50,64,153,203)(51,77,154,216)(52,62,155,201)(53,75,156,214)(54,60,157,199)(55,73,158,212)(56,58,159,197), (1,204)(2,203)(3,202)(4,201)(5,200)(6,199)(7,198)(8,197)(9,224)(10,223)(11,222)(12,221)(13,220)(14,219)(15,218)(16,217)(17,216)(18,215)(19,214)(20,213)(21,212)(22,211)(23,210)(24,209)(25,208)(26,207)(27,206)(28,205)(29,135)(30,134)(31,133)(32,132)(33,131)(34,130)(35,129)(36,128)(37,127)(38,126)(39,125)(40,124)(41,123)(42,122)(43,121)(44,120)(45,119)(46,118)(47,117)(48,116)(49,115)(50,114)(51,113)(52,140)(53,139)(54,138)(55,137)(56,136)(57,95)(58,94)(59,93)(60,92)(61,91)(62,90)(63,89)(64,88)(65,87)(66,86)(67,85)(68,112)(69,111)(70,110)(71,109)(72,108)(73,107)(74,106)(75,105)(76,104)(77,103)(78,102)(79,101)(80,100)(81,99)(82,98)(83,97)(84,96)(141,174)(142,173)(143,172)(144,171)(145,170)(146,169)(147,196)(148,195)(149,194)(150,193)(151,192)(152,191)(153,190)(154,189)(155,188)(156,187)(157,186)(158,185)(159,184)(160,183)(161,182)(162,181)(163,180)(164,179)(165,178)(166,177)(167,176)(168,175) );
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)], [(1,93),(2,92),(3,91),(4,90),(5,89),(6,88),(7,87),(8,86),(9,85),(10,112),(11,111),(12,110),(13,109),(14,108),(15,107),(16,106),(17,105),(18,104),(19,103),(20,102),(21,101),(22,100),(23,99),(24,98),(25,97),(26,96),(27,95),(28,94),(29,157),(30,156),(31,155),(32,154),(33,153),(34,152),(35,151),(36,150),(37,149),(38,148),(39,147),(40,146),(41,145),(42,144),(43,143),(44,142),(45,141),(46,168),(47,167),(48,166),(49,165),(50,164),(51,163),(52,162),(53,161),(54,160),(55,159),(56,158),(57,197),(58,224),(59,223),(60,222),(61,221),(62,220),(63,219),(64,218),(65,217),(66,216),(67,215),(68,214),(69,213),(70,212),(71,211),(72,210),(73,209),(74,208),(75,207),(76,206),(77,205),(78,204),(79,203),(80,202),(81,201),(82,200),(83,199),(84,198),(113,171),(114,170),(115,169),(116,196),(117,195),(118,194),(119,193),(120,192),(121,191),(122,190),(123,189),(124,188),(125,187),(126,186),(127,185),(128,184),(129,183),(130,182),(131,181),(132,180),(133,179),(134,178),(135,177),(136,176),(137,175),(138,174),(139,173),(140,172)], [(1,177,87,129),(2,190,88,114),(3,175,89,127),(4,188,90,140),(5,173,91,125),(6,186,92,138),(7,171,93,123),(8,184,94,136),(9,169,95,121),(10,182,96,134),(11,195,97,119),(12,180,98,132),(13,193,99,117),(14,178,100,130),(15,191,101,115),(16,176,102,128),(17,189,103,113),(18,174,104,126),(19,187,105,139),(20,172,106,124),(21,185,107,137),(22,170,108,122),(23,183,109,135),(24,196,110,120),(25,181,111,133),(26,194,112,118),(27,179,85,131),(28,192,86,116),(29,71,160,210),(30,84,161,223),(31,69,162,208),(32,82,163,221),(33,67,164,206),(34,80,165,219),(35,65,166,204),(36,78,167,217),(37,63,168,202),(38,76,141,215),(39,61,142,200),(40,74,143,213),(41,59,144,198),(42,72,145,211),(43,57,146,224),(44,70,147,209),(45,83,148,222),(46,68,149,207),(47,81,150,220),(48,66,151,205),(49,79,152,218),(50,64,153,203),(51,77,154,216),(52,62,155,201),(53,75,156,214),(54,60,157,199),(55,73,158,212),(56,58,159,197)], [(1,204),(2,203),(3,202),(4,201),(5,200),(6,199),(7,198),(8,197),(9,224),(10,223),(11,222),(12,221),(13,220),(14,219),(15,218),(16,217),(17,216),(18,215),(19,214),(20,213),(21,212),(22,211),(23,210),(24,209),(25,208),(26,207),(27,206),(28,205),(29,135),(30,134),(31,133),(32,132),(33,131),(34,130),(35,129),(36,128),(37,127),(38,126),(39,125),(40,124),(41,123),(42,122),(43,121),(44,120),(45,119),(46,118),(47,117),(48,116),(49,115),(50,114),(51,113),(52,140),(53,139),(54,138),(55,137),(56,136),(57,95),(58,94),(59,93),(60,92),(61,91),(62,90),(63,89),(64,88),(65,87),(66,86),(67,85),(68,112),(69,111),(70,110),(71,109),(72,108),(73,107),(74,106),(75,105),(76,104),(77,103),(78,102),(79,101),(80,100),(81,99),(82,98),(83,97),(84,96),(141,174),(142,173),(143,172),(144,171),(145,170),(146,169),(147,196),(148,195),(149,194),(150,193),(151,192),(152,191),(153,190),(154,189),(155,188),(156,187),(157,186),(158,185),(159,184),(160,183),(161,182),(162,181),(163,180),(164,179),(165,178),(166,177),(167,176),(168,175)]])
61 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 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 | 2 | 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 | 28 | 28 | 56 | 2 | 2 | 4 | 4 | 14 | 14 | 28 | 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 | D8 | C4○D4 | D14 | D14 | D14 | C4○D28 | C8⋊C22 | D4×D7 | D4×D7 | D7×D8 | D56⋊C2 |
| kernel | D28⋊3D4 | C14.D8 | Dic7⋊C8 | C7×D4⋊C4 | D28⋊C4 | C2×D56 | C2×D4⋊D7 | C28⋊D4 | D28 | C2×Dic7 | D4⋊C4 | Dic7 | C28 | C4⋊C4 | C2×C8 | C2×D4 | C4 | C14 | C4 | C22 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 3 | 4 | 2 | 3 | 3 | 3 | 12 | 1 | 3 | 3 | 6 | 6 |
Matrix representation of D28⋊3D4 ►in GL4(𝔽113) generated by
| 15 | 48 | 0 | 0 |
| 89 | 89 | 0 | 0 |
| 0 | 0 | 0 | 1 |
| 0 | 0 | 112 | 0 |
| 98 | 66 | 0 | 0 |
| 24 | 15 | 0 | 0 |
| 0 | 0 | 112 | 0 |
| 0 | 0 | 0 | 1 |
| 6 | 112 | 0 | 0 |
| 37 | 107 | 0 | 0 |
| 0 | 0 | 112 | 0 |
| 0 | 0 | 0 | 112 |
| 27 | 12 | 0 | 0 |
| 90 | 86 | 0 | 0 |
| 0 | 0 | 31 | 82 |
| 0 | 0 | 82 | 82 |
G:=sub<GL(4,GF(113))| [15,89,0,0,48,89,0,0,0,0,0,112,0,0,1,0],[98,24,0,0,66,15,0,0,0,0,112,0,0,0,0,1],[6,37,0,0,112,107,0,0,0,0,112,0,0,0,0,112],[27,90,0,0,12,86,0,0,0,0,31,82,0,0,82,82] >;
D28⋊3D4 in GAP, Magma, Sage, TeX
D_{28}\rtimes_3D_4 % in TeX
G:=Group("D28:3D4"); // GroupNames label
G:=SmallGroup(448,320);
// by ID
G=gap.SmallGroup(448,320);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,64,590,219,1684,851,438,102,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^28=b^2=c^4=d^2=1,b*a*b=d*a*d=a^-1,c*a*c^-1=a^13,c*b*c^-1=a^12*b,d*b*d=a^19*b,d*c*d=c^-1>;
// generators/relations