metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: (C2×C4)⋊9D28, (C2×D28)⋊5C4, (C2×C28)⋊19D4, C14.2(C4×D4), C2.5(C4×D28), C14.2C22≀C2, (C2×Dic7)⋊15D4, C22.59(D4×D7), D14⋊1(C22⋊C4), C2.1(C4⋊D28), C14.3(C4⋊D4), (C22×D28).1C2, (C22×D7).66D4, (C22×C4).15D14, C22.24(C2×D28), C2.C42⋊7D7, C2.5(D28⋊C4), C2.1(C22⋊D28), C2.2(D14⋊D4), C7⋊1(C23.23D4), C14.C42⋊27C2, C2.3(D14.5D4), C22.34(C4○D28), (C23×D7).82C22, C23.255(C22×D7), (C22×C14).290C23, (C22×C28).331C22, C22.17(Q8⋊2D7), C14.38(C22.D4), (C22×Dic7).14C22, (C2×C4)⋊2(C4×D7), (C2×C28)⋊4(C2×C4), (D7×C22×C4)⋊12C2, (C2×D14⋊C4)⋊28C2, C2.7(D7×C22⋊C4), C22.89(C2×C4×D7), (C22×D7)⋊3(C2×C4), C14.4(C2×C22⋊C4), (C2×C14).199(C2×D4), (C2×C14).49(C22×C4), (C2×C14).183(C4○D4), (C7×C2.C42)⋊14C2, SmallGroup(448,199)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for (C2×C4)⋊9D28
G = < a,b,c,d | a2=b4=c28=d2=1, cbc-1=dbd=ab=ba, ac=ca, ad=da, dcd=c-1 >
Subgroups: 1692 in 286 conjugacy classes, 77 normal (51 characteristic)
C1, C2, C2, C4, C22, C22, C7, C2×C4, C2×C4, D4, C23, C23, D7, C14, C22⋊C4, C22×C4, C22×C4, C2×D4, C24, Dic7, C28, D14, D14, C2×C14, C2.C42, C2.C42, C2×C22⋊C4, C23×C4, C22×D4, C4×D7, D28, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C22×D7, C22×D7, C22×C14, C23.23D4, D14⋊C4, C2×C4×D7, C2×D28, C2×D28, C22×Dic7, C22×C28, C23×D7, C14.C42, C7×C2.C42, C2×D14⋊C4, D7×C22×C4, C22×D28, (C2×C4)⋊9D28
Quotients: C1, C2, C4, C22, C2×C4, D4, C23, D7, C22⋊C4, C22×C4, C2×D4, C4○D4, D14, C2×C22⋊C4, C4×D4, C22≀C2, C4⋊D4, C22.D4, C4×D7, D28, C22×D7, C23.23D4, C2×C4×D7, C2×D28, C4○D28, D4×D7, Q8⋊2D7, C4×D28, D7×C22⋊C4, C22⋊D28, D14⋊D4, D28⋊C4, D14.5D4, C4⋊D28, (C2×C4)⋊9D28
►On 224 points
Generators in S224
(1 218)(2 219)(3 220)(4 221)(5 222)(6 223)(7 224)(8 197)(9 198)(10 199)(11 200)(12 201)(13 202)(14 203)(15 204)(16 205)(17 206)(18 207)(19 208)(20 209)(21 210)(22 211)(23 212)(24 213)(25 214)(26 215)(27 216)(28 217)(29 178)(30 179)(31 180)(32 181)(33 182)(34 183)(35 184)(36 185)(37 186)(38 187)(39 188)(40 189)(41 190)(42 191)(43 192)(44 193)(45 194)(46 195)(47 196)(48 169)(49 170)(50 171)(51 172)(52 173)(53 174)(54 175)(55 176)(56 177)(57 94)(58 95)(59 96)(60 97)(61 98)(62 99)(63 100)(64 101)(65 102)(66 103)(67 104)(68 105)(69 106)(70 107)(71 108)(72 109)(73 110)(74 111)(75 112)(76 85)(77 86)(78 87)(79 88)(80 89)(81 90)(82 91)(83 92)(84 93)(113 163)(114 164)(115 165)(116 166)(117 167)(118 168)(119 141)(120 142)(121 143)(122 144)(123 145)(124 146)(125 147)(126 148)(127 149)(128 150)(129 151)(130 152)(131 153)(132 154)(133 155)(134 156)(135 157)(136 158)(137 159)(138 160)(139 161)(140 162)
(1 171 58 166)(2 51 59 117)(3 173 60 168)(4 53 61 119)(5 175 62 142)(6 55 63 121)(7 177 64 144)(8 29 65 123)(9 179 66 146)(10 31 67 125)(11 181 68 148)(12 33 69 127)(13 183 70 150)(14 35 71 129)(15 185 72 152)(16 37 73 131)(17 187 74 154)(18 39 75 133)(19 189 76 156)(20 41 77 135)(21 191 78 158)(22 43 79 137)(23 193 80 160)(24 45 81 139)(25 195 82 162)(26 47 83 113)(27 169 84 164)(28 49 57 115)(30 103 124 198)(32 105 126 200)(34 107 128 202)(36 109 130 204)(38 111 132 206)(40 85 134 208)(42 87 136 210)(44 89 138 212)(46 91 140 214)(48 93 114 216)(50 95 116 218)(52 97 118 220)(54 99 120 222)(56 101 122 224)(86 157 209 190)(88 159 211 192)(90 161 213 194)(92 163 215 196)(94 165 217 170)(96 167 219 172)(98 141 221 174)(100 143 223 176)(102 145 197 178)(104 147 199 180)(106 149 201 182)(108 151 203 184)(110 153 205 186)(112 155 207 188)
(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 94)(2 93)(3 92)(4 91)(5 90)(6 89)(7 88)(8 87)(9 86)(10 85)(11 112)(12 111)(13 110)(14 109)(15 108)(16 107)(17 106)(18 105)(19 104)(20 103)(21 102)(22 101)(23 100)(24 99)(25 98)(26 97)(27 96)(28 95)(29 158)(30 157)(31 156)(32 155)(33 154)(34 153)(35 152)(36 151)(37 150)(38 149)(39 148)(40 147)(41 146)(42 145)(43 144)(44 143)(45 142)(46 141)(47 168)(48 167)(49 166)(50 165)(51 164)(52 163)(53 162)(54 161)(55 160)(56 159)(57 218)(58 217)(59 216)(60 215)(61 214)(62 213)(63 212)(64 211)(65 210)(66 209)(67 208)(68 207)(69 206)(70 205)(71 204)(72 203)(73 202)(74 201)(75 200)(76 199)(77 198)(78 197)(79 224)(80 223)(81 222)(82 221)(83 220)(84 219)(113 173)(114 172)(115 171)(116 170)(117 169)(118 196)(119 195)(120 194)(121 193)(122 192)(123 191)(124 190)(125 189)(126 188)(127 187)(128 186)(129 185)(130 184)(131 183)(132 182)(133 181)(134 180)(135 179)(136 178)(137 177)(138 176)(139 175)(140 174)
G:=sub<Sym(224)| (1,218)(2,219)(3,220)(4,221)(5,222)(6,223)(7,224)(8,197)(9,198)(10,199)(11,200)(12,201)(13,202)(14,203)(15,204)(16,205)(17,206)(18,207)(19,208)(20,209)(21,210)(22,211)(23,212)(24,213)(25,214)(26,215)(27,216)(28,217)(29,178)(30,179)(31,180)(32,181)(33,182)(34,183)(35,184)(36,185)(37,186)(38,187)(39,188)(40,189)(41,190)(42,191)(43,192)(44,193)(45,194)(46,195)(47,196)(48,169)(49,170)(50,171)(51,172)(52,173)(53,174)(54,175)(55,176)(56,177)(57,94)(58,95)(59,96)(60,97)(61,98)(62,99)(63,100)(64,101)(65,102)(66,103)(67,104)(68,105)(69,106)(70,107)(71,108)(72,109)(73,110)(74,111)(75,112)(76,85)(77,86)(78,87)(79,88)(80,89)(81,90)(82,91)(83,92)(84,93)(113,163)(114,164)(115,165)(116,166)(117,167)(118,168)(119,141)(120,142)(121,143)(122,144)(123,145)(124,146)(125,147)(126,148)(127,149)(128,150)(129,151)(130,152)(131,153)(132,154)(133,155)(134,156)(135,157)(136,158)(137,159)(138,160)(139,161)(140,162), (1,171,58,166)(2,51,59,117)(3,173,60,168)(4,53,61,119)(5,175,62,142)(6,55,63,121)(7,177,64,144)(8,29,65,123)(9,179,66,146)(10,31,67,125)(11,181,68,148)(12,33,69,127)(13,183,70,150)(14,35,71,129)(15,185,72,152)(16,37,73,131)(17,187,74,154)(18,39,75,133)(19,189,76,156)(20,41,77,135)(21,191,78,158)(22,43,79,137)(23,193,80,160)(24,45,81,139)(25,195,82,162)(26,47,83,113)(27,169,84,164)(28,49,57,115)(30,103,124,198)(32,105,126,200)(34,107,128,202)(36,109,130,204)(38,111,132,206)(40,85,134,208)(42,87,136,210)(44,89,138,212)(46,91,140,214)(48,93,114,216)(50,95,116,218)(52,97,118,220)(54,99,120,222)(56,101,122,224)(86,157,209,190)(88,159,211,192)(90,161,213,194)(92,163,215,196)(94,165,217,170)(96,167,219,172)(98,141,221,174)(100,143,223,176)(102,145,197,178)(104,147,199,180)(106,149,201,182)(108,151,203,184)(110,153,205,186)(112,155,207,188), (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), (1,94)(2,93)(3,92)(4,91)(5,90)(6,89)(7,88)(8,87)(9,86)(10,85)(11,112)(12,111)(13,110)(14,109)(15,108)(16,107)(17,106)(18,105)(19,104)(20,103)(21,102)(22,101)(23,100)(24,99)(25,98)(26,97)(27,96)(28,95)(29,158)(30,157)(31,156)(32,155)(33,154)(34,153)(35,152)(36,151)(37,150)(38,149)(39,148)(40,147)(41,146)(42,145)(43,144)(44,143)(45,142)(46,141)(47,168)(48,167)(49,166)(50,165)(51,164)(52,163)(53,162)(54,161)(55,160)(56,159)(57,218)(58,217)(59,216)(60,215)(61,214)(62,213)(63,212)(64,211)(65,210)(66,209)(67,208)(68,207)(69,206)(70,205)(71,204)(72,203)(73,202)(74,201)(75,200)(76,199)(77,198)(78,197)(79,224)(80,223)(81,222)(82,221)(83,220)(84,219)(113,173)(114,172)(115,171)(116,170)(117,169)(118,196)(119,195)(120,194)(121,193)(122,192)(123,191)(124,190)(125,189)(126,188)(127,187)(128,186)(129,185)(130,184)(131,183)(132,182)(133,181)(134,180)(135,179)(136,178)(137,177)(138,176)(139,175)(140,174)>;
G:=Group( (1,218)(2,219)(3,220)(4,221)(5,222)(6,223)(7,224)(8,197)(9,198)(10,199)(11,200)(12,201)(13,202)(14,203)(15,204)(16,205)(17,206)(18,207)(19,208)(20,209)(21,210)(22,211)(23,212)(24,213)(25,214)(26,215)(27,216)(28,217)(29,178)(30,179)(31,180)(32,181)(33,182)(34,183)(35,184)(36,185)(37,186)(38,187)(39,188)(40,189)(41,190)(42,191)(43,192)(44,193)(45,194)(46,195)(47,196)(48,169)(49,170)(50,171)(51,172)(52,173)(53,174)(54,175)(55,176)(56,177)(57,94)(58,95)(59,96)(60,97)(61,98)(62,99)(63,100)(64,101)(65,102)(66,103)(67,104)(68,105)(69,106)(70,107)(71,108)(72,109)(73,110)(74,111)(75,112)(76,85)(77,86)(78,87)(79,88)(80,89)(81,90)(82,91)(83,92)(84,93)(113,163)(114,164)(115,165)(116,166)(117,167)(118,168)(119,141)(120,142)(121,143)(122,144)(123,145)(124,146)(125,147)(126,148)(127,149)(128,150)(129,151)(130,152)(131,153)(132,154)(133,155)(134,156)(135,157)(136,158)(137,159)(138,160)(139,161)(140,162), (1,171,58,166)(2,51,59,117)(3,173,60,168)(4,53,61,119)(5,175,62,142)(6,55,63,121)(7,177,64,144)(8,29,65,123)(9,179,66,146)(10,31,67,125)(11,181,68,148)(12,33,69,127)(13,183,70,150)(14,35,71,129)(15,185,72,152)(16,37,73,131)(17,187,74,154)(18,39,75,133)(19,189,76,156)(20,41,77,135)(21,191,78,158)(22,43,79,137)(23,193,80,160)(24,45,81,139)(25,195,82,162)(26,47,83,113)(27,169,84,164)(28,49,57,115)(30,103,124,198)(32,105,126,200)(34,107,128,202)(36,109,130,204)(38,111,132,206)(40,85,134,208)(42,87,136,210)(44,89,138,212)(46,91,140,214)(48,93,114,216)(50,95,116,218)(52,97,118,220)(54,99,120,222)(56,101,122,224)(86,157,209,190)(88,159,211,192)(90,161,213,194)(92,163,215,196)(94,165,217,170)(96,167,219,172)(98,141,221,174)(100,143,223,176)(102,145,197,178)(104,147,199,180)(106,149,201,182)(108,151,203,184)(110,153,205,186)(112,155,207,188), (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), (1,94)(2,93)(3,92)(4,91)(5,90)(6,89)(7,88)(8,87)(9,86)(10,85)(11,112)(12,111)(13,110)(14,109)(15,108)(16,107)(17,106)(18,105)(19,104)(20,103)(21,102)(22,101)(23,100)(24,99)(25,98)(26,97)(27,96)(28,95)(29,158)(30,157)(31,156)(32,155)(33,154)(34,153)(35,152)(36,151)(37,150)(38,149)(39,148)(40,147)(41,146)(42,145)(43,144)(44,143)(45,142)(46,141)(47,168)(48,167)(49,166)(50,165)(51,164)(52,163)(53,162)(54,161)(55,160)(56,159)(57,218)(58,217)(59,216)(60,215)(61,214)(62,213)(63,212)(64,211)(65,210)(66,209)(67,208)(68,207)(69,206)(70,205)(71,204)(72,203)(73,202)(74,201)(75,200)(76,199)(77,198)(78,197)(79,224)(80,223)(81,222)(82,221)(83,220)(84,219)(113,173)(114,172)(115,171)(116,170)(117,169)(118,196)(119,195)(120,194)(121,193)(122,192)(123,191)(124,190)(125,189)(126,188)(127,187)(128,186)(129,185)(130,184)(131,183)(132,182)(133,181)(134,180)(135,179)(136,178)(137,177)(138,176)(139,175)(140,174) );
G=PermutationGroup([[(1,218),(2,219),(3,220),(4,221),(5,222),(6,223),(7,224),(8,197),(9,198),(10,199),(11,200),(12,201),(13,202),(14,203),(15,204),(16,205),(17,206),(18,207),(19,208),(20,209),(21,210),(22,211),(23,212),(24,213),(25,214),(26,215),(27,216),(28,217),(29,178),(30,179),(31,180),(32,181),(33,182),(34,183),(35,184),(36,185),(37,186),(38,187),(39,188),(40,189),(41,190),(42,191),(43,192),(44,193),(45,194),(46,195),(47,196),(48,169),(49,170),(50,171),(51,172),(52,173),(53,174),(54,175),(55,176),(56,177),(57,94),(58,95),(59,96),(60,97),(61,98),(62,99),(63,100),(64,101),(65,102),(66,103),(67,104),(68,105),(69,106),(70,107),(71,108),(72,109),(73,110),(74,111),(75,112),(76,85),(77,86),(78,87),(79,88),(80,89),(81,90),(82,91),(83,92),(84,93),(113,163),(114,164),(115,165),(116,166),(117,167),(118,168),(119,141),(120,142),(121,143),(122,144),(123,145),(124,146),(125,147),(126,148),(127,149),(128,150),(129,151),(130,152),(131,153),(132,154),(133,155),(134,156),(135,157),(136,158),(137,159),(138,160),(139,161),(140,162)], [(1,171,58,166),(2,51,59,117),(3,173,60,168),(4,53,61,119),(5,175,62,142),(6,55,63,121),(7,177,64,144),(8,29,65,123),(9,179,66,146),(10,31,67,125),(11,181,68,148),(12,33,69,127),(13,183,70,150),(14,35,71,129),(15,185,72,152),(16,37,73,131),(17,187,74,154),(18,39,75,133),(19,189,76,156),(20,41,77,135),(21,191,78,158),(22,43,79,137),(23,193,80,160),(24,45,81,139),(25,195,82,162),(26,47,83,113),(27,169,84,164),(28,49,57,115),(30,103,124,198),(32,105,126,200),(34,107,128,202),(36,109,130,204),(38,111,132,206),(40,85,134,208),(42,87,136,210),(44,89,138,212),(46,91,140,214),(48,93,114,216),(50,95,116,218),(52,97,118,220),(54,99,120,222),(56,101,122,224),(86,157,209,190),(88,159,211,192),(90,161,213,194),(92,163,215,196),(94,165,217,170),(96,167,219,172),(98,141,221,174),(100,143,223,176),(102,145,197,178),(104,147,199,180),(106,149,201,182),(108,151,203,184),(110,153,205,186),(112,155,207,188)], [(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)], [(1,94),(2,93),(3,92),(4,91),(5,90),(6,89),(7,88),(8,87),(9,86),(10,85),(11,112),(12,111),(13,110),(14,109),(15,108),(16,107),(17,106),(18,105),(19,104),(20,103),(21,102),(22,101),(23,100),(24,99),(25,98),(26,97),(27,96),(28,95),(29,158),(30,157),(31,156),(32,155),(33,154),(34,153),(35,152),(36,151),(37,150),(38,149),(39,148),(40,147),(41,146),(42,145),(43,144),(44,143),(45,142),(46,141),(47,168),(48,167),(49,166),(50,165),(51,164),(52,163),(53,162),(54,161),(55,160),(56,159),(57,218),(58,217),(59,216),(60,215),(61,214),(62,213),(63,212),(64,211),(65,210),(66,209),(67,208),(68,207),(69,206),(70,205),(71,204),(72,203),(73,202),(74,201),(75,200),(76,199),(77,198),(78,197),(79,224),(80,223),(81,222),(82,221),(83,220),(84,219),(113,173),(114,172),(115,171),(116,170),(117,169),(118,196),(119,195),(120,194),(121,193),(122,192),(123,191),(124,190),(125,189),(126,188),(127,187),(128,186),(129,185),(130,184),(131,183),(132,182),(133,181),(134,180),(135,179),(136,178),(137,177),(138,176),(139,175),(140,174)]])
88 conjugacy classes
| class | 1 | 2A | ··· | 2G | 2H | 2I | 2J | 2K | 2L | 2M | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 4K | 4L | 4M | 4N | 7A | 7B | 7C | 14A | ··· | 14U | 28A | ··· | 28AJ |
| order | 1 | 2 | ··· | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 28 | ··· | 28 |
| size | 1 | 1 | ··· | 1 | 14 | 14 | 14 | 14 | 28 | 28 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 14 | 14 | 14 | 14 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 |
88 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | ||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C4 | D4 | D4 | D4 | D7 | C4○D4 | D14 | C4×D7 | D28 | C4○D28 | D4×D7 | Q8⋊2D7 |
| kernel | (C2×C4)⋊9D28 | C14.C42 | C7×C2.C42 | C2×D14⋊C4 | D7×C22×C4 | C22×D28 | C2×D28 | C2×Dic7 | C2×C28 | C22×D7 | C2.C42 | C2×C14 | C22×C4 | C2×C4 | C2×C4 | C22 | C22 | C22 |
| # reps | 1 | 1 | 1 | 3 | 1 | 1 | 8 | 2 | 2 | 4 | 3 | 4 | 9 | 12 | 12 | 12 | 9 | 3 |
Matrix representation of (C2×C4)⋊9D28 ►in GL6(𝔽29)
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 |
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 17 | 0 | 0 | 0 |
| 0 | 0 | 0 | 17 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 24 |
| 0 | 0 | 0 | 0 | 0 | 28 |
| 9 | 4 | 0 | 0 | 0 | 0 |
| 25 | 8 | 0 | 0 | 0 | 0 |
| 0 | 0 | 19 | 22 | 0 | 0 |
| 0 | 0 | 7 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 16 | 10 |
| 0 | 0 | 0 | 0 | 18 | 13 |
| 9 | 4 | 0 | 0 | 0 | 0 |
| 9 | 20 | 0 | 0 | 0 | 0 |
| 0 | 0 | 10 | 7 | 0 | 0 |
| 0 | 0 | 19 | 19 | 0 | 0 |
| 0 | 0 | 0 | 0 | 13 | 19 |
| 0 | 0 | 0 | 0 | 11 | 16 |
G:=sub<GL(6,GF(29))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[28,0,0,0,0,0,0,28,0,0,0,0,0,0,17,0,0,0,0,0,0,17,0,0,0,0,0,0,1,0,0,0,0,0,24,28],[9,25,0,0,0,0,4,8,0,0,0,0,0,0,19,7,0,0,0,0,22,28,0,0,0,0,0,0,16,18,0,0,0,0,10,13],[9,9,0,0,0,0,4,20,0,0,0,0,0,0,10,19,0,0,0,0,7,19,0,0,0,0,0,0,13,11,0,0,0,0,19,16] >;
(C2×C4)⋊9D28 in GAP, Magma, Sage, TeX
(C_2\times C_4)\rtimes_9D_{28} % in TeX
G:=Group("(C2xC4):9D28"); // GroupNames label
G:=SmallGroup(448,199);
// by ID
G=gap.SmallGroup(448,199);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,253,120,387,58,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^2=b^4=c^28=d^2=1,c*b*c^-1=d*b*d=a*b=b*a,a*c=c*a,a*d=d*a,d*c*d=c^-1>;
// generators/relations