metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: D28⋊14D4, Dic14⋊13D4, C23.12D28, (C2×D56)⋊3C2, C22⋊C8⋊6D7, (C2×C8).3D14, C7⋊1(D4⋊D4), C4.122(D4×D7), C2.D56⋊9C2, C28⋊7D4⋊16C2, C14.9(C4○D8), C28.334(C2×D4), (C2×C4).119D28, (C2×C28).241D4, C14.10C22≀C2, C28.44D4⋊6C2, (C22×C14).54D4, (C22×C4).84D14, C2.13(C8⋊D14), C14.10(C8⋊C22), (C2×C28).744C23, (C2×C56).119C22, C22.107(C2×D28), C4⋊Dic7.13C22, C2.11(D56⋊7C2), C2.13(C22⋊D28), (C2×D28).193C22, (C22×C28).97C22, (C2×Dic14).211C22, (C2×C4○D28)⋊1C2, (C7×C22⋊C8)⋊8C2, (C2×C56⋊C2)⋊11C2, (C2×C14).127(C2×D4), (C2×C4).689(C22×D7), SmallGroup(448,268)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for D28⋊14D4
G = < a,b,c,d | a28=b2=c4=d2=1, bab=cac-1=a-1, ad=da, cbc-1=a5b, dbd=a14b, dcd=c-1 >
Subgroups: 1084 in 162 conjugacy classes, 43 normal (39 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C8, C2×C4, C2×C4, D4, Q8, C23, C23, D7, C14, C14, C22⋊C4, C4⋊C4, C2×C8, D8, SD16, C22×C4, C22×C4, C2×D4, C2×Q8, C4○D4, Dic7, C28, C28, D14, C2×C14, C2×C14, C22⋊C8, D4⋊C4, Q8⋊C4, C4⋊D4, C2×D8, C2×SD16, C2×C4○D4, C56, Dic14, Dic14, C4×D7, D28, D28, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C22×D7, C22×C14, D4⋊D4, C56⋊C2, D56, C4⋊Dic7, D14⋊C4, C2×C56, C2×Dic14, C2×C4×D7, C2×D28, C4○D28, C2×C7⋊D4, C22×C28, C28.44D4, C2.D56, C7×C22⋊C8, C2×C56⋊C2, C2×D56, C28⋊7D4, C2×C4○D28, D28⋊14D4
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⋊7C2, C8⋊D14, D28⋊14D4
►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 28)(2 27)(3 26)(4 25)(5 24)(6 23)(7 22)(8 21)(9 20)(10 19)(11 18)(12 17)(13 16)(14 15)(29 55)(30 54)(31 53)(32 52)(33 51)(34 50)(35 49)(36 48)(37 47)(38 46)(39 45)(40 44)(41 43)(57 77)(58 76)(59 75)(60 74)(61 73)(62 72)(63 71)(64 70)(65 69)(66 68)(78 84)(79 83)(80 82)(85 97)(86 96)(87 95)(88 94)(89 93)(90 92)(98 112)(99 111)(100 110)(101 109)(102 108)(103 107)(104 106)(113 122)(114 121)(115 120)(116 119)(117 118)(123 140)(124 139)(125 138)(126 137)(127 136)(128 135)(129 134)(130 133)(131 132)(141 156)(142 155)(143 154)(144 153)(145 152)(146 151)(147 150)(148 149)(157 168)(158 167)(159 166)(160 165)(161 164)(162 163)(169 181)(170 180)(171 179)(172 178)(173 177)(174 176)(182 196)(183 195)(184 194)(185 193)(186 192)(187 191)(188 190)(197 214)(198 213)(199 212)(200 211)(201 210)(202 209)(203 208)(204 207)(205 206)(215 224)(216 223)(217 222)(218 221)(219 220)
(1 39 132 88)(2 38 133 87)(3 37 134 86)(4 36 135 85)(5 35 136 112)(6 34 137 111)(7 33 138 110)(8 32 139 109)(9 31 140 108)(10 30 113 107)(11 29 114 106)(12 56 115 105)(13 55 116 104)(14 54 117 103)(15 53 118 102)(16 52 119 101)(17 51 120 100)(18 50 121 99)(19 49 122 98)(20 48 123 97)(21 47 124 96)(22 46 125 95)(23 45 126 94)(24 44 127 93)(25 43 128 92)(26 42 129 91)(27 41 130 90)(28 40 131 89)(57 142 193 199)(58 141 194 198)(59 168 195 197)(60 167 196 224)(61 166 169 223)(62 165 170 222)(63 164 171 221)(64 163 172 220)(65 162 173 219)(66 161 174 218)(67 160 175 217)(68 159 176 216)(69 158 177 215)(70 157 178 214)(71 156 179 213)(72 155 180 212)(73 154 181 211)(74 153 182 210)(75 152 183 209)(76 151 184 208)(77 150 185 207)(78 149 186 206)(79 148 187 205)(80 147 188 204)(81 146 189 203)(82 145 190 202)(83 144 191 201)(84 143 192 200)
(1 156)(2 157)(3 158)(4 159)(5 160)(6 161)(7 162)(8 163)(9 164)(10 165)(11 166)(12 167)(13 168)(14 141)(15 142)(16 143)(17 144)(18 145)(19 146)(20 147)(21 148)(22 149)(23 150)(24 151)(25 152)(26 153)(27 154)(28 155)(29 61)(30 62)(31 63)(32 64)(33 65)(34 66)(35 67)(36 68)(37 69)(38 70)(39 71)(40 72)(41 73)(42 74)(43 75)(44 76)(45 77)(46 78)(47 79)(48 80)(49 81)(50 82)(51 83)(52 84)(53 57)(54 58)(55 59)(56 60)(85 176)(86 177)(87 178)(88 179)(89 180)(90 181)(91 182)(92 183)(93 184)(94 185)(95 186)(96 187)(97 188)(98 189)(99 190)(100 191)(101 192)(102 193)(103 194)(104 195)(105 196)(106 169)(107 170)(108 171)(109 172)(110 173)(111 174)(112 175)(113 222)(114 223)(115 224)(116 197)(117 198)(118 199)(119 200)(120 201)(121 202)(122 203)(123 204)(124 205)(125 206)(126 207)(127 208)(128 209)(129 210)(130 211)(131 212)(132 213)(133 214)(134 215)(135 216)(136 217)(137 218)(138 219)(139 220)(140 221)
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), (1,28)(2,27)(3,26)(4,25)(5,24)(6,23)(7,22)(8,21)(9,20)(10,19)(11,18)(12,17)(13,16)(14,15)(29,55)(30,54)(31,53)(32,52)(33,51)(34,50)(35,49)(36,48)(37,47)(38,46)(39,45)(40,44)(41,43)(57,77)(58,76)(59,75)(60,74)(61,73)(62,72)(63,71)(64,70)(65,69)(66,68)(78,84)(79,83)(80,82)(85,97)(86,96)(87,95)(88,94)(89,93)(90,92)(98,112)(99,111)(100,110)(101,109)(102,108)(103,107)(104,106)(113,122)(114,121)(115,120)(116,119)(117,118)(123,140)(124,139)(125,138)(126,137)(127,136)(128,135)(129,134)(130,133)(131,132)(141,156)(142,155)(143,154)(144,153)(145,152)(146,151)(147,150)(148,149)(157,168)(158,167)(159,166)(160,165)(161,164)(162,163)(169,181)(170,180)(171,179)(172,178)(173,177)(174,176)(182,196)(183,195)(184,194)(185,193)(186,192)(187,191)(188,190)(197,214)(198,213)(199,212)(200,211)(201,210)(202,209)(203,208)(204,207)(205,206)(215,224)(216,223)(217,222)(218,221)(219,220), (1,39,132,88)(2,38,133,87)(3,37,134,86)(4,36,135,85)(5,35,136,112)(6,34,137,111)(7,33,138,110)(8,32,139,109)(9,31,140,108)(10,30,113,107)(11,29,114,106)(12,56,115,105)(13,55,116,104)(14,54,117,103)(15,53,118,102)(16,52,119,101)(17,51,120,100)(18,50,121,99)(19,49,122,98)(20,48,123,97)(21,47,124,96)(22,46,125,95)(23,45,126,94)(24,44,127,93)(25,43,128,92)(26,42,129,91)(27,41,130,90)(28,40,131,89)(57,142,193,199)(58,141,194,198)(59,168,195,197)(60,167,196,224)(61,166,169,223)(62,165,170,222)(63,164,171,221)(64,163,172,220)(65,162,173,219)(66,161,174,218)(67,160,175,217)(68,159,176,216)(69,158,177,215)(70,157,178,214)(71,156,179,213)(72,155,180,212)(73,154,181,211)(74,153,182,210)(75,152,183,209)(76,151,184,208)(77,150,185,207)(78,149,186,206)(79,148,187,205)(80,147,188,204)(81,146,189,203)(82,145,190,202)(83,144,191,201)(84,143,192,200), (1,156)(2,157)(3,158)(4,159)(5,160)(6,161)(7,162)(8,163)(9,164)(10,165)(11,166)(12,167)(13,168)(14,141)(15,142)(16,143)(17,144)(18,145)(19,146)(20,147)(21,148)(22,149)(23,150)(24,151)(25,152)(26,153)(27,154)(28,155)(29,61)(30,62)(31,63)(32,64)(33,65)(34,66)(35,67)(36,68)(37,69)(38,70)(39,71)(40,72)(41,73)(42,74)(43,75)(44,76)(45,77)(46,78)(47,79)(48,80)(49,81)(50,82)(51,83)(52,84)(53,57)(54,58)(55,59)(56,60)(85,176)(86,177)(87,178)(88,179)(89,180)(90,181)(91,182)(92,183)(93,184)(94,185)(95,186)(96,187)(97,188)(98,189)(99,190)(100,191)(101,192)(102,193)(103,194)(104,195)(105,196)(106,169)(107,170)(108,171)(109,172)(110,173)(111,174)(112,175)(113,222)(114,223)(115,224)(116,197)(117,198)(118,199)(119,200)(120,201)(121,202)(122,203)(123,204)(124,205)(125,206)(126,207)(127,208)(128,209)(129,210)(130,211)(131,212)(132,213)(133,214)(134,215)(135,216)(136,217)(137,218)(138,219)(139,220)(140,221)>;
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), (1,28)(2,27)(3,26)(4,25)(5,24)(6,23)(7,22)(8,21)(9,20)(10,19)(11,18)(12,17)(13,16)(14,15)(29,55)(30,54)(31,53)(32,52)(33,51)(34,50)(35,49)(36,48)(37,47)(38,46)(39,45)(40,44)(41,43)(57,77)(58,76)(59,75)(60,74)(61,73)(62,72)(63,71)(64,70)(65,69)(66,68)(78,84)(79,83)(80,82)(85,97)(86,96)(87,95)(88,94)(89,93)(90,92)(98,112)(99,111)(100,110)(101,109)(102,108)(103,107)(104,106)(113,122)(114,121)(115,120)(116,119)(117,118)(123,140)(124,139)(125,138)(126,137)(127,136)(128,135)(129,134)(130,133)(131,132)(141,156)(142,155)(143,154)(144,153)(145,152)(146,151)(147,150)(148,149)(157,168)(158,167)(159,166)(160,165)(161,164)(162,163)(169,181)(170,180)(171,179)(172,178)(173,177)(174,176)(182,196)(183,195)(184,194)(185,193)(186,192)(187,191)(188,190)(197,214)(198,213)(199,212)(200,211)(201,210)(202,209)(203,208)(204,207)(205,206)(215,224)(216,223)(217,222)(218,221)(219,220), (1,39,132,88)(2,38,133,87)(3,37,134,86)(4,36,135,85)(5,35,136,112)(6,34,137,111)(7,33,138,110)(8,32,139,109)(9,31,140,108)(10,30,113,107)(11,29,114,106)(12,56,115,105)(13,55,116,104)(14,54,117,103)(15,53,118,102)(16,52,119,101)(17,51,120,100)(18,50,121,99)(19,49,122,98)(20,48,123,97)(21,47,124,96)(22,46,125,95)(23,45,126,94)(24,44,127,93)(25,43,128,92)(26,42,129,91)(27,41,130,90)(28,40,131,89)(57,142,193,199)(58,141,194,198)(59,168,195,197)(60,167,196,224)(61,166,169,223)(62,165,170,222)(63,164,171,221)(64,163,172,220)(65,162,173,219)(66,161,174,218)(67,160,175,217)(68,159,176,216)(69,158,177,215)(70,157,178,214)(71,156,179,213)(72,155,180,212)(73,154,181,211)(74,153,182,210)(75,152,183,209)(76,151,184,208)(77,150,185,207)(78,149,186,206)(79,148,187,205)(80,147,188,204)(81,146,189,203)(82,145,190,202)(83,144,191,201)(84,143,192,200), (1,156)(2,157)(3,158)(4,159)(5,160)(6,161)(7,162)(8,163)(9,164)(10,165)(11,166)(12,167)(13,168)(14,141)(15,142)(16,143)(17,144)(18,145)(19,146)(20,147)(21,148)(22,149)(23,150)(24,151)(25,152)(26,153)(27,154)(28,155)(29,61)(30,62)(31,63)(32,64)(33,65)(34,66)(35,67)(36,68)(37,69)(38,70)(39,71)(40,72)(41,73)(42,74)(43,75)(44,76)(45,77)(46,78)(47,79)(48,80)(49,81)(50,82)(51,83)(52,84)(53,57)(54,58)(55,59)(56,60)(85,176)(86,177)(87,178)(88,179)(89,180)(90,181)(91,182)(92,183)(93,184)(94,185)(95,186)(96,187)(97,188)(98,189)(99,190)(100,191)(101,192)(102,193)(103,194)(104,195)(105,196)(106,169)(107,170)(108,171)(109,172)(110,173)(111,174)(112,175)(113,222)(114,223)(115,224)(116,197)(117,198)(118,199)(119,200)(120,201)(121,202)(122,203)(123,204)(124,205)(125,206)(126,207)(127,208)(128,209)(129,210)(130,211)(131,212)(132,213)(133,214)(134,215)(135,216)(136,217)(137,218)(138,219)(139,220)(140,221) );
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)], [(1,28),(2,27),(3,26),(4,25),(5,24),(6,23),(7,22),(8,21),(9,20),(10,19),(11,18),(12,17),(13,16),(14,15),(29,55),(30,54),(31,53),(32,52),(33,51),(34,50),(35,49),(36,48),(37,47),(38,46),(39,45),(40,44),(41,43),(57,77),(58,76),(59,75),(60,74),(61,73),(62,72),(63,71),(64,70),(65,69),(66,68),(78,84),(79,83),(80,82),(85,97),(86,96),(87,95),(88,94),(89,93),(90,92),(98,112),(99,111),(100,110),(101,109),(102,108),(103,107),(104,106),(113,122),(114,121),(115,120),(116,119),(117,118),(123,140),(124,139),(125,138),(126,137),(127,136),(128,135),(129,134),(130,133),(131,132),(141,156),(142,155),(143,154),(144,153),(145,152),(146,151),(147,150),(148,149),(157,168),(158,167),(159,166),(160,165),(161,164),(162,163),(169,181),(170,180),(171,179),(172,178),(173,177),(174,176),(182,196),(183,195),(184,194),(185,193),(186,192),(187,191),(188,190),(197,214),(198,213),(199,212),(200,211),(201,210),(202,209),(203,208),(204,207),(205,206),(215,224),(216,223),(217,222),(218,221),(219,220)], [(1,39,132,88),(2,38,133,87),(3,37,134,86),(4,36,135,85),(5,35,136,112),(6,34,137,111),(7,33,138,110),(8,32,139,109),(9,31,140,108),(10,30,113,107),(11,29,114,106),(12,56,115,105),(13,55,116,104),(14,54,117,103),(15,53,118,102),(16,52,119,101),(17,51,120,100),(18,50,121,99),(19,49,122,98),(20,48,123,97),(21,47,124,96),(22,46,125,95),(23,45,126,94),(24,44,127,93),(25,43,128,92),(26,42,129,91),(27,41,130,90),(28,40,131,89),(57,142,193,199),(58,141,194,198),(59,168,195,197),(60,167,196,224),(61,166,169,223),(62,165,170,222),(63,164,171,221),(64,163,172,220),(65,162,173,219),(66,161,174,218),(67,160,175,217),(68,159,176,216),(69,158,177,215),(70,157,178,214),(71,156,179,213),(72,155,180,212),(73,154,181,211),(74,153,182,210),(75,152,183,209),(76,151,184,208),(77,150,185,207),(78,149,186,206),(79,148,187,205),(80,147,188,204),(81,146,189,203),(82,145,190,202),(83,144,191,201),(84,143,192,200)], [(1,156),(2,157),(3,158),(4,159),(5,160),(6,161),(7,162),(8,163),(9,164),(10,165),(11,166),(12,167),(13,168),(14,141),(15,142),(16,143),(17,144),(18,145),(19,146),(20,147),(21,148),(22,149),(23,150),(24,151),(25,152),(26,153),(27,154),(28,155),(29,61),(30,62),(31,63),(32,64),(33,65),(34,66),(35,67),(36,68),(37,69),(38,70),(39,71),(40,72),(41,73),(42,74),(43,75),(44,76),(45,77),(46,78),(47,79),(48,80),(49,81),(50,82),(51,83),(52,84),(53,57),(54,58),(55,59),(56,60),(85,176),(86,177),(87,178),(88,179),(89,180),(90,181),(91,182),(92,183),(93,184),(94,185),(95,186),(96,187),(97,188),(98,189),(99,190),(100,191),(101,192),(102,193),(103,194),(104,195),(105,196),(106,169),(107,170),(108,171),(109,172),(110,173),(111,174),(112,175),(113,222),(114,223),(115,224),(116,197),(117,198),(118,199),(119,200),(120,201),(121,202),(122,203),(123,204),(124,205),(125,206),(126,207),(127,208),(128,209),(129,210),(130,211),(131,212),(132,213),(133,214),(134,215),(135,216),(136,217),(137,218),(138,219),(139,220),(140,221)]])
79 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 | ··· | 28L | 28M | ··· | 28R | 56A | ··· | 56X |
| 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 | 4 | 28 | 28 | 56 | 2 | 2 | 2 | 2 | 28 | 28 | 56 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 2 | ··· | 2 | 4 | ··· | 4 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 |
79 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 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | D4 | D4 | D4 | D7 | D14 | D14 | C4○D8 | D28 | D28 | D56⋊7C2 | C8⋊C22 | D4×D7 | C8⋊D14 |
| kernel | D28⋊14D4 | C28.44D4 | C2.D56 | C7×C22⋊C8 | C2×C56⋊C2 | C2×D56 | C28⋊7D4 | C2×C4○D28 | Dic14 | D28 | C2×C28 | C22×C14 | C22⋊C8 | C2×C8 | C22×C4 | C14 | C2×C4 | C23 | C2 | C14 | C4 | C2 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 1 | 1 | 3 | 6 | 3 | 4 | 6 | 6 | 24 | 1 | 6 | 6 |
Matrix representation of D28⋊14D4 ►in GL4(𝔽113) generated by
| 112 | 0 | 0 | 0 |
| 0 | 112 | 0 | 0 |
| 0 | 0 | 81 | 13 |
| 0 | 0 | 77 | 4 |
| 112 | 0 | 0 | 0 |
| 62 | 1 | 0 | 0 |
| 0 | 0 | 38 | 94 |
| 0 | 0 | 70 | 75 |
| 51 | 111 | 0 | 0 |
| 58 | 62 | 0 | 0 |
| 0 | 0 | 38 | 9 |
| 0 | 0 | 78 | 75 |
| 112 | 0 | 0 | 0 |
| 62 | 1 | 0 | 0 |
| 0 | 0 | 34 | 101 |
| 0 | 0 | 68 | 79 |
G:=sub<GL(4,GF(113))| [112,0,0,0,0,112,0,0,0,0,81,77,0,0,13,4],[112,62,0,0,0,1,0,0,0,0,38,70,0,0,94,75],[51,58,0,0,111,62,0,0,0,0,38,78,0,0,9,75],[112,62,0,0,0,1,0,0,0,0,34,68,0,0,101,79] >;
D28⋊14D4 in GAP, Magma, Sage, TeX
D_{28}\rtimes_{14}D_4 % in TeX
G:=Group("D28:14D4"); // GroupNames label
G:=SmallGroup(448,268);
// by ID
G=gap.SmallGroup(448,268);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,254,219,226,1123,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^28=b^2=c^4=d^2=1,b*a*b=c*a*c^-1=a^-1,a*d=d*a,c*b*c^-1=a^5*b,d*b*d=a^14*b,d*c*d=c^-1>;
// generators/relations