metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: D28⋊4D4, Q8⋊3D28, (C7×Q8)⋊2D4, D14⋊C8⋊8C2, (C2×D56)⋊6C2, C4.95(D4×D7), C4.8(C2×D28), C4⋊D28⋊5C2, C7⋊3(D4⋊D4), C4⋊C4.27D14, Q8⋊C4⋊6D7, (C2×C8).18D14, C28.124(C2×D4), C14.D8⋊12C2, C14.26C22≀C2, C14.70(C4○D8), (C2×C56).18C22, (C2×Q8).110D14, (C22×D7).18D4, C22.201(D4×D7), C2.9(Q8.D14), C2.17(D56⋊C2), C14.63(C8⋊C22), (C2×C28).251C23, (C2×Dic7).155D4, (C2×D28).65C22, (Q8×C14).34C22, C2.29(C22⋊D28), (C2×Q8⋊D7)⋊4C2, (C7×Q8⋊C4)⋊6C2, (C2×Q8⋊2D7)⋊1C2, (C2×C7⋊C8).42C22, (C2×C4×D7).24C22, (C2×C14).264(C2×D4), (C7×C4⋊C4).52C22, (C2×C4).358(C22×D7), SmallGroup(448,345)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for D28⋊4D4
G = < a,b,c,d | a28=b2=c4=d2=1, bab=dad=a-1, cac-1=a15, cbc-1=a21b, dbd=a19b, dcd=c-1 >
Subgroups: 1108 in 162 conjugacy classes, 43 normal (37 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C8, C2×C4, C2×C4, D4, Q8, Q8, C23, D7, C14, C22⋊C4, C4⋊C4, C2×C8, C2×C8, D8, SD16, C22×C4, C2×D4, C2×Q8, C4○D4, Dic7, C28, C28, D14, C2×C14, C22⋊C8, D4⋊C4, Q8⋊C4, C4⋊D4, C2×D8, C2×SD16, C2×C4○D4, C7⋊C8, C56, C4×D7, D28, D28, C2×Dic7, C2×C28, C2×C28, C7×Q8, C7×Q8, C22×D7, C22×D7, D4⋊D4, D56, C2×C7⋊C8, D14⋊C4, Q8⋊D7, C7×C4⋊C4, C2×C56, C2×C4×D7, C2×C4×D7, C2×D28, C2×D28, Q8⋊2D7, Q8×C14, C14.D8, D14⋊C8, C7×Q8⋊C4, C4⋊D28, C2×D56, C2×Q8⋊D7, C2×Q8⋊2D7, D28⋊4D4
Quotients: C1, C2, C22, D4, C23, D7, C2×D4, D14, C22≀C2, C4○D8, C8⋊C22, D28, C22×D7, D4⋊D4, C2×D28, D4×D7, C22⋊D28, D56⋊C2, Q8.D14, D28⋊4D4
►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)
(1 193)(2 192)(3 191)(4 190)(5 189)(6 188)(7 187)(8 186)(9 185)(10 184)(11 183)(12 182)(13 181)(14 180)(15 179)(16 178)(17 177)(18 176)(19 175)(20 174)(21 173)(22 172)(23 171)(24 170)(25 169)(26 196)(27 195)(28 194)(29 156)(30 155)(31 154)(32 153)(33 152)(34 151)(35 150)(36 149)(37 148)(38 147)(39 146)(40 145)(41 144)(42 143)(43 142)(44 141)(45 168)(46 167)(47 166)(48 165)(49 164)(50 163)(51 162)(52 161)(53 160)(54 159)(55 158)(56 157)(57 203)(58 202)(59 201)(60 200)(61 199)(62 198)(63 197)(64 224)(65 223)(66 222)(67 221)(68 220)(69 219)(70 218)(71 217)(72 216)(73 215)(74 214)(75 213)(76 212)(77 211)(78 210)(79 209)(80 208)(81 207)(82 206)(83 205)(84 204)(85 121)(86 120)(87 119)(88 118)(89 117)(90 116)(91 115)(92 114)(93 113)(94 140)(95 139)(96 138)(97 137)(98 136)(99 135)(100 134)(101 133)(102 132)(103 131)(104 130)(105 129)(106 128)(107 127)(108 126)(109 125)(110 124)(111 123)(112 122)
(1 45 74 108)(2 32 75 95)(3 47 76 110)(4 34 77 97)(5 49 78 112)(6 36 79 99)(7 51 80 86)(8 38 81 101)(9 53 82 88)(10 40 83 103)(11 55 84 90)(12 42 57 105)(13 29 58 92)(14 44 59 107)(15 31 60 94)(16 46 61 109)(17 33 62 96)(18 48 63 111)(19 35 64 98)(20 50 65 85)(21 37 66 100)(22 52 67 87)(23 39 68 102)(24 54 69 89)(25 41 70 104)(26 56 71 91)(27 43 72 106)(28 30 73 93)(113 173 155 222)(114 188 156 209)(115 175 157 224)(116 190 158 211)(117 177 159 198)(118 192 160 213)(119 179 161 200)(120 194 162 215)(121 181 163 202)(122 196 164 217)(123 183 165 204)(124 170 166 219)(125 185 167 206)(126 172 168 221)(127 187 141 208)(128 174 142 223)(129 189 143 210)(130 176 144 197)(131 191 145 212)(132 178 146 199)(133 193 147 214)(134 180 148 201)(135 195 149 216)(136 182 150 203)(137 169 151 218)(138 184 152 205)(139 171 153 220)(140 186 154 207)
(1 45)(2 44)(3 43)(4 42)(5 41)(6 40)(7 39)(8 38)(9 37)(10 36)(11 35)(12 34)(13 33)(14 32)(15 31)(16 30)(17 29)(18 56)(19 55)(20 54)(21 53)(22 52)(23 51)(24 50)(25 49)(26 48)(27 47)(28 46)(57 97)(58 96)(59 95)(60 94)(61 93)(62 92)(63 91)(64 90)(65 89)(66 88)(67 87)(68 86)(69 85)(70 112)(71 111)(72 110)(73 109)(74 108)(75 107)(76 106)(77 105)(78 104)(79 103)(80 102)(81 101)(82 100)(83 99)(84 98)(113 208)(114 207)(115 206)(116 205)(117 204)(118 203)(119 202)(120 201)(121 200)(122 199)(123 198)(124 197)(125 224)(126 223)(127 222)(128 221)(129 220)(130 219)(131 218)(132 217)(133 216)(134 215)(135 214)(136 213)(137 212)(138 211)(139 210)(140 209)(141 173)(142 172)(143 171)(144 170)(145 169)(146 196)(147 195)(148 194)(149 193)(150 192)(151 191)(152 190)(153 189)(154 188)(155 187)(156 186)(157 185)(158 184)(159 183)(160 182)(161 181)(162 180)(163 179)(164 178)(165 177)(166 176)(167 175)(168 174)
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), (1,193)(2,192)(3,191)(4,190)(5,189)(6,188)(7,187)(8,186)(9,185)(10,184)(11,183)(12,182)(13,181)(14,180)(15,179)(16,178)(17,177)(18,176)(19,175)(20,174)(21,173)(22,172)(23,171)(24,170)(25,169)(26,196)(27,195)(28,194)(29,156)(30,155)(31,154)(32,153)(33,152)(34,151)(35,150)(36,149)(37,148)(38,147)(39,146)(40,145)(41,144)(42,143)(43,142)(44,141)(45,168)(46,167)(47,166)(48,165)(49,164)(50,163)(51,162)(52,161)(53,160)(54,159)(55,158)(56,157)(57,203)(58,202)(59,201)(60,200)(61,199)(62,198)(63,197)(64,224)(65,223)(66,222)(67,221)(68,220)(69,219)(70,218)(71,217)(72,216)(73,215)(74,214)(75,213)(76,212)(77,211)(78,210)(79,209)(80,208)(81,207)(82,206)(83,205)(84,204)(85,121)(86,120)(87,119)(88,118)(89,117)(90,116)(91,115)(92,114)(93,113)(94,140)(95,139)(96,138)(97,137)(98,136)(99,135)(100,134)(101,133)(102,132)(103,131)(104,130)(105,129)(106,128)(107,127)(108,126)(109,125)(110,124)(111,123)(112,122), (1,45,74,108)(2,32,75,95)(3,47,76,110)(4,34,77,97)(5,49,78,112)(6,36,79,99)(7,51,80,86)(8,38,81,101)(9,53,82,88)(10,40,83,103)(11,55,84,90)(12,42,57,105)(13,29,58,92)(14,44,59,107)(15,31,60,94)(16,46,61,109)(17,33,62,96)(18,48,63,111)(19,35,64,98)(20,50,65,85)(21,37,66,100)(22,52,67,87)(23,39,68,102)(24,54,69,89)(25,41,70,104)(26,56,71,91)(27,43,72,106)(28,30,73,93)(113,173,155,222)(114,188,156,209)(115,175,157,224)(116,190,158,211)(117,177,159,198)(118,192,160,213)(119,179,161,200)(120,194,162,215)(121,181,163,202)(122,196,164,217)(123,183,165,204)(124,170,166,219)(125,185,167,206)(126,172,168,221)(127,187,141,208)(128,174,142,223)(129,189,143,210)(130,176,144,197)(131,191,145,212)(132,178,146,199)(133,193,147,214)(134,180,148,201)(135,195,149,216)(136,182,150,203)(137,169,151,218)(138,184,152,205)(139,171,153,220)(140,186,154,207), (1,45)(2,44)(3,43)(4,42)(5,41)(6,40)(7,39)(8,38)(9,37)(10,36)(11,35)(12,34)(13,33)(14,32)(15,31)(16,30)(17,29)(18,56)(19,55)(20,54)(21,53)(22,52)(23,51)(24,50)(25,49)(26,48)(27,47)(28,46)(57,97)(58,96)(59,95)(60,94)(61,93)(62,92)(63,91)(64,90)(65,89)(66,88)(67,87)(68,86)(69,85)(70,112)(71,111)(72,110)(73,109)(74,108)(75,107)(76,106)(77,105)(78,104)(79,103)(80,102)(81,101)(82,100)(83,99)(84,98)(113,208)(114,207)(115,206)(116,205)(117,204)(118,203)(119,202)(120,201)(121,200)(122,199)(123,198)(124,197)(125,224)(126,223)(127,222)(128,221)(129,220)(130,219)(131,218)(132,217)(133,216)(134,215)(135,214)(136,213)(137,212)(138,211)(139,210)(140,209)(141,173)(142,172)(143,171)(144,170)(145,169)(146,196)(147,195)(148,194)(149,193)(150,192)(151,191)(152,190)(153,189)(154,188)(155,187)(156,186)(157,185)(158,184)(159,183)(160,182)(161,181)(162,180)(163,179)(164,178)(165,177)(166,176)(167,175)(168,174)>;
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), (1,193)(2,192)(3,191)(4,190)(5,189)(6,188)(7,187)(8,186)(9,185)(10,184)(11,183)(12,182)(13,181)(14,180)(15,179)(16,178)(17,177)(18,176)(19,175)(20,174)(21,173)(22,172)(23,171)(24,170)(25,169)(26,196)(27,195)(28,194)(29,156)(30,155)(31,154)(32,153)(33,152)(34,151)(35,150)(36,149)(37,148)(38,147)(39,146)(40,145)(41,144)(42,143)(43,142)(44,141)(45,168)(46,167)(47,166)(48,165)(49,164)(50,163)(51,162)(52,161)(53,160)(54,159)(55,158)(56,157)(57,203)(58,202)(59,201)(60,200)(61,199)(62,198)(63,197)(64,224)(65,223)(66,222)(67,221)(68,220)(69,219)(70,218)(71,217)(72,216)(73,215)(74,214)(75,213)(76,212)(77,211)(78,210)(79,209)(80,208)(81,207)(82,206)(83,205)(84,204)(85,121)(86,120)(87,119)(88,118)(89,117)(90,116)(91,115)(92,114)(93,113)(94,140)(95,139)(96,138)(97,137)(98,136)(99,135)(100,134)(101,133)(102,132)(103,131)(104,130)(105,129)(106,128)(107,127)(108,126)(109,125)(110,124)(111,123)(112,122), (1,45,74,108)(2,32,75,95)(3,47,76,110)(4,34,77,97)(5,49,78,112)(6,36,79,99)(7,51,80,86)(8,38,81,101)(9,53,82,88)(10,40,83,103)(11,55,84,90)(12,42,57,105)(13,29,58,92)(14,44,59,107)(15,31,60,94)(16,46,61,109)(17,33,62,96)(18,48,63,111)(19,35,64,98)(20,50,65,85)(21,37,66,100)(22,52,67,87)(23,39,68,102)(24,54,69,89)(25,41,70,104)(26,56,71,91)(27,43,72,106)(28,30,73,93)(113,173,155,222)(114,188,156,209)(115,175,157,224)(116,190,158,211)(117,177,159,198)(118,192,160,213)(119,179,161,200)(120,194,162,215)(121,181,163,202)(122,196,164,217)(123,183,165,204)(124,170,166,219)(125,185,167,206)(126,172,168,221)(127,187,141,208)(128,174,142,223)(129,189,143,210)(130,176,144,197)(131,191,145,212)(132,178,146,199)(133,193,147,214)(134,180,148,201)(135,195,149,216)(136,182,150,203)(137,169,151,218)(138,184,152,205)(139,171,153,220)(140,186,154,207), (1,45)(2,44)(3,43)(4,42)(5,41)(6,40)(7,39)(8,38)(9,37)(10,36)(11,35)(12,34)(13,33)(14,32)(15,31)(16,30)(17,29)(18,56)(19,55)(20,54)(21,53)(22,52)(23,51)(24,50)(25,49)(26,48)(27,47)(28,46)(57,97)(58,96)(59,95)(60,94)(61,93)(62,92)(63,91)(64,90)(65,89)(66,88)(67,87)(68,86)(69,85)(70,112)(71,111)(72,110)(73,109)(74,108)(75,107)(76,106)(77,105)(78,104)(79,103)(80,102)(81,101)(82,100)(83,99)(84,98)(113,208)(114,207)(115,206)(116,205)(117,204)(118,203)(119,202)(120,201)(121,200)(122,199)(123,198)(124,197)(125,224)(126,223)(127,222)(128,221)(129,220)(130,219)(131,218)(132,217)(133,216)(134,215)(135,214)(136,213)(137,212)(138,211)(139,210)(140,209)(141,173)(142,172)(143,171)(144,170)(145,169)(146,196)(147,195)(148,194)(149,193)(150,192)(151,191)(152,190)(153,189)(154,188)(155,187)(156,186)(157,185)(158,184)(159,183)(160,182)(161,181)(162,180)(163,179)(164,178)(165,177)(166,176)(167,175)(168,174) );
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)], [(1,193),(2,192),(3,191),(4,190),(5,189),(6,188),(7,187),(8,186),(9,185),(10,184),(11,183),(12,182),(13,181),(14,180),(15,179),(16,178),(17,177),(18,176),(19,175),(20,174),(21,173),(22,172),(23,171),(24,170),(25,169),(26,196),(27,195),(28,194),(29,156),(30,155),(31,154),(32,153),(33,152),(34,151),(35,150),(36,149),(37,148),(38,147),(39,146),(40,145),(41,144),(42,143),(43,142),(44,141),(45,168),(46,167),(47,166),(48,165),(49,164),(50,163),(51,162),(52,161),(53,160),(54,159),(55,158),(56,157),(57,203),(58,202),(59,201),(60,200),(61,199),(62,198),(63,197),(64,224),(65,223),(66,222),(67,221),(68,220),(69,219),(70,218),(71,217),(72,216),(73,215),(74,214),(75,213),(76,212),(77,211),(78,210),(79,209),(80,208),(81,207),(82,206),(83,205),(84,204),(85,121),(86,120),(87,119),(88,118),(89,117),(90,116),(91,115),(92,114),(93,113),(94,140),(95,139),(96,138),(97,137),(98,136),(99,135),(100,134),(101,133),(102,132),(103,131),(104,130),(105,129),(106,128),(107,127),(108,126),(109,125),(110,124),(111,123),(112,122)], [(1,45,74,108),(2,32,75,95),(3,47,76,110),(4,34,77,97),(5,49,78,112),(6,36,79,99),(7,51,80,86),(8,38,81,101),(9,53,82,88),(10,40,83,103),(11,55,84,90),(12,42,57,105),(13,29,58,92),(14,44,59,107),(15,31,60,94),(16,46,61,109),(17,33,62,96),(18,48,63,111),(19,35,64,98),(20,50,65,85),(21,37,66,100),(22,52,67,87),(23,39,68,102),(24,54,69,89),(25,41,70,104),(26,56,71,91),(27,43,72,106),(28,30,73,93),(113,173,155,222),(114,188,156,209),(115,175,157,224),(116,190,158,211),(117,177,159,198),(118,192,160,213),(119,179,161,200),(120,194,162,215),(121,181,163,202),(122,196,164,217),(123,183,165,204),(124,170,166,219),(125,185,167,206),(126,172,168,221),(127,187,141,208),(128,174,142,223),(129,189,143,210),(130,176,144,197),(131,191,145,212),(132,178,146,199),(133,193,147,214),(134,180,148,201),(135,195,149,216),(136,182,150,203),(137,169,151,218),(138,184,152,205),(139,171,153,220),(140,186,154,207)], [(1,45),(2,44),(3,43),(4,42),(5,41),(6,40),(7,39),(8,38),(9,37),(10,36),(11,35),(12,34),(13,33),(14,32),(15,31),(16,30),(17,29),(18,56),(19,55),(20,54),(21,53),(22,52),(23,51),(24,50),(25,49),(26,48),(27,47),(28,46),(57,97),(58,96),(59,95),(60,94),(61,93),(62,92),(63,91),(64,90),(65,89),(66,88),(67,87),(68,86),(69,85),(70,112),(71,111),(72,110),(73,109),(74,108),(75,107),(76,106),(77,105),(78,104),(79,103),(80,102),(81,101),(82,100),(83,99),(84,98),(113,208),(114,207),(115,206),(116,205),(117,204),(118,203),(119,202),(120,201),(121,200),(122,199),(123,198),(124,197),(125,224),(126,223),(127,222),(128,221),(129,220),(130,219),(131,218),(132,217),(133,216),(134,215),(135,214),(136,213),(137,212),(138,211),(139,210),(140,209),(141,173),(142,172),(143,171),(144,170),(145,169),(146,196),(147,195),(148,194),(149,193),(150,192),(151,191),(152,190),(153,189),(154,188),(155,187),(156,186),(157,185),(158,184),(159,183),(160,182),(161,181),(162,180),(163,179),(164,178),(165,177),(166,176),(167,175),(168,174)]])
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 | 28A | ··· | 28F | 28G | ··· | 28R | 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 | 28 | ··· | 28 | 28 | ··· | 28 | 56 | ··· | 56 |
| size | 1 | 1 | 1 | 1 | 28 | 28 | 28 | 56 | 2 | 2 | 4 | 4 | 8 | 14 | 14 | 2 | 2 | 2 | 4 | 4 | 28 | 28 | 2 | ··· | 2 | 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 | 2 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | |
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | D4 | D4 | D4 | D7 | D14 | D14 | D14 | C4○D8 | D28 | C8⋊C22 | D4×D7 | D4×D7 | D56⋊C2 | Q8.D14 |
| kernel | D28⋊4D4 | C14.D8 | D14⋊C8 | C7×Q8⋊C4 | C4⋊D28 | C2×D56 | C2×Q8⋊D7 | C2×Q8⋊2D7 | D28 | C2×Dic7 | C7×Q8 | C22×D7 | Q8⋊C4 | C4⋊C4 | C2×C8 | C2×Q8 | C14 | Q8 | C14 | C4 | C22 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 1 | 2 | 1 | 3 | 3 | 3 | 3 | 4 | 12 | 1 | 3 | 3 | 6 | 6 |
Matrix representation of D28⋊4D4 ►in GL4(𝔽113) generated by
| 43 | 9 | 0 | 0 |
| 95 | 104 | 0 | 0 |
| 0 | 0 | 98 | 0 |
| 0 | 0 | 98 | 15 |
| 8 | 33 | 0 | 0 |
| 70 | 105 | 0 | 0 |
| 0 | 0 | 15 | 83 |
| 0 | 0 | 15 | 98 |
| 47 | 38 | 0 | 0 |
| 37 | 66 | 0 | 0 |
| 0 | 0 | 44 | 25 |
| 0 | 0 | 31 | 69 |
| 94 | 81 | 0 | 0 |
| 96 | 19 | 0 | 0 |
| 0 | 0 | 69 | 88 |
| 0 | 0 | 100 | 44 |
G:=sub<GL(4,GF(113))| [43,95,0,0,9,104,0,0,0,0,98,98,0,0,0,15],[8,70,0,0,33,105,0,0,0,0,15,15,0,0,83,98],[47,37,0,0,38,66,0,0,0,0,44,31,0,0,25,69],[94,96,0,0,81,19,0,0,0,0,69,100,0,0,88,44] >;
D28⋊4D4 in GAP, Magma, Sage, TeX
D_{28}\rtimes_4D_4 % in TeX
G:=Group("D28:4D4"); // GroupNames label
G:=SmallGroup(448,345);
// by ID
G=gap.SmallGroup(448,345);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,253,120,758,135,184,570,297,136,18822]);
// 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^15,c*b*c^-1=a^21*b,d*b*d=a^19*b,d*c*d=c^-1>;
// generators/relations