direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C2×C4⋊D28, C4⋊3(C2×D28), C28⋊4(C2×D4), (C2×C28)⋊8D4, C4⋊C4⋊38D14, D14⋊2(C2×D4), (C2×C4)⋊10D28, C14⋊2(C4⋊D4), (C22×D7)⋊10D4, (C22×D28)⋊7C2, C14.9(C22×D4), D14⋊C4⋊50C22, (C2×D28)⋊45C22, (C2×C14).50C24, C22.67(C2×D28), C2.11(C22×D28), C22.133(D4×D7), (C2×C28).487C23, (C22×C4).360D14, C22.84(C23×D7), C23.328(C22×D7), (C22×C14).399C23, (C22×C28).217C22, C22.36(Q8⋊2D7), (C2×Dic7).188C23, (C23×D7).100C22, (C22×D7).156C23, (C22×Dic7).213C22, C7⋊2(C2×C4⋊D4), C2.15(C2×D4×D7), (C2×C4⋊C4)⋊15D7, (C14×C4⋊C4)⋊12C2, (D7×C22×C4)⋊1C2, (C2×C4×D7)⋊55C22, (C2×D14⋊C4)⋊20C2, (C7×C4⋊C4)⋊46C22, C2.7(C2×Q8⋊2D7), C14.109(C2×C4○D4), (C2×C14).174(C2×D4), (C2×C4).141(C22×D7), (C2×C14).197(C4○D4), SmallGroup(448,959)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C2×C4⋊D28
G = < a,b,c,d | a2=b28=c4=d2=1, ab=ba, ac=ca, ad=da, cbc-1=b15, dbd=b-1, dcd=c-1 >
Subgroups: 2500 in 426 conjugacy classes, 135 normal (21 characteristic)
C1, C2, C2, C2, C4, C4, C22, C22, C22, C7, C2×C4, C2×C4, D4, C23, C23, D7, C14, C14, C22⋊C4, C4⋊C4, C22×C4, C22×C4, C22×C4, C2×D4, C24, Dic7, C28, C28, D14, D14, C2×C14, C2×C14, C2×C22⋊C4, C2×C4⋊C4, C4⋊D4, C23×C4, C22×D4, C4×D7, D28, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C22×D7, C22×D7, C22×C14, C2×C4⋊D4, D14⋊C4, C7×C4⋊C4, C2×C4×D7, C2×C4×D7, C2×D28, C2×D28, C22×Dic7, C22×C28, C22×C28, C23×D7, C23×D7, C4⋊D28, C2×D14⋊C4, C14×C4⋊C4, D7×C22×C4, C22×D28, C22×D28, C2×C4⋊D28
Quotients: C1, C2, C22, D4, C23, D7, C2×D4, C4○D4, C24, D14, C4⋊D4, C22×D4, C2×C4○D4, D28, C22×D7, C2×C4⋊D4, C2×D28, D4×D7, Q8⋊2D7, C23×D7, C4⋊D28, C22×D28, C2×D4×D7, C2×Q8⋊2D7, C2×C4⋊D28
►On 224 points
Generators in S224
(1 223)(2 224)(3 197)(4 198)(5 199)(6 200)(7 201)(8 202)(9 203)(10 204)(11 205)(12 206)(13 207)(14 208)(15 209)(16 210)(17 211)(18 212)(19 213)(20 214)(21 215)(22 216)(23 217)(24 218)(25 219)(26 220)(27 221)(28 222)(29 194)(30 195)(31 196)(32 169)(33 170)(34 171)(35 172)(36 173)(37 174)(38 175)(39 176)(40 177)(41 178)(42 179)(43 180)(44 181)(45 182)(46 183)(47 184)(48 185)(49 186)(50 187)(51 188)(52 189)(53 190)(54 191)(55 192)(56 193)(57 125)(58 126)(59 127)(60 128)(61 129)(62 130)(63 131)(64 132)(65 133)(66 134)(67 135)(68 136)(69 137)(70 138)(71 139)(72 140)(73 113)(74 114)(75 115)(76 116)(77 117)(78 118)(79 119)(80 120)(81 121)(82 122)(83 123)(84 124)(85 159)(86 160)(87 161)(88 162)(89 163)(90 164)(91 165)(92 166)(93 167)(94 168)(95 141)(96 142)(97 143)(98 144)(99 145)(100 146)(101 147)(102 148)(103 149)(104 150)(105 151)(106 152)(107 153)(108 154)(109 155)(110 156)(111 157)(112 158)
(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)
(1 185 153 132)(2 172 154 119)(3 187 155 134)(4 174 156 121)(5 189 157 136)(6 176 158 123)(7 191 159 138)(8 178 160 125)(9 193 161 140)(10 180 162 127)(11 195 163 114)(12 182 164 129)(13 169 165 116)(14 184 166 131)(15 171 167 118)(16 186 168 133)(17 173 141 120)(18 188 142 135)(19 175 143 122)(20 190 144 137)(21 177 145 124)(22 192 146 139)(23 179 147 126)(24 194 148 113)(25 181 149 128)(26 196 150 115)(27 183 151 130)(28 170 152 117)(29 102 73 218)(30 89 74 205)(31 104 75 220)(32 91 76 207)(33 106 77 222)(34 93 78 209)(35 108 79 224)(36 95 80 211)(37 110 81 198)(38 97 82 213)(39 112 83 200)(40 99 84 215)(41 86 57 202)(42 101 58 217)(43 88 59 204)(44 103 60 219)(45 90 61 206)(46 105 62 221)(47 92 63 208)(48 107 64 223)(49 94 65 210)(50 109 66 197)(51 96 67 212)(52 111 68 199)(53 98 69 214)(54 85 70 201)(55 100 71 216)(56 87 72 203)
(1 132)(2 131)(3 130)(4 129)(5 128)(6 127)(7 126)(8 125)(9 124)(10 123)(11 122)(12 121)(13 120)(14 119)(15 118)(16 117)(17 116)(18 115)(19 114)(20 113)(21 140)(22 139)(23 138)(24 137)(25 136)(26 135)(27 134)(28 133)(29 98)(30 97)(31 96)(32 95)(33 94)(34 93)(35 92)(36 91)(37 90)(38 89)(39 88)(40 87)(41 86)(42 85)(43 112)(44 111)(45 110)(46 109)(47 108)(48 107)(49 106)(50 105)(51 104)(52 103)(53 102)(54 101)(55 100)(56 99)(57 202)(58 201)(59 200)(60 199)(61 198)(62 197)(63 224)(64 223)(65 222)(66 221)(67 220)(68 219)(69 218)(70 217)(71 216)(72 215)(73 214)(74 213)(75 212)(76 211)(77 210)(78 209)(79 208)(80 207)(81 206)(82 205)(83 204)(84 203)(141 169)(142 196)(143 195)(144 194)(145 193)(146 192)(147 191)(148 190)(149 189)(150 188)(151 187)(152 186)(153 185)(154 184)(155 183)(156 182)(157 181)(158 180)(159 179)(160 178)(161 177)(162 176)(163 175)(164 174)(165 173)(166 172)(167 171)(168 170)
G:=sub<Sym(224)| (1,223)(2,224)(3,197)(4,198)(5,199)(6,200)(7,201)(8,202)(9,203)(10,204)(11,205)(12,206)(13,207)(14,208)(15,209)(16,210)(17,211)(18,212)(19,213)(20,214)(21,215)(22,216)(23,217)(24,218)(25,219)(26,220)(27,221)(28,222)(29,194)(30,195)(31,196)(32,169)(33,170)(34,171)(35,172)(36,173)(37,174)(38,175)(39,176)(40,177)(41,178)(42,179)(43,180)(44,181)(45,182)(46,183)(47,184)(48,185)(49,186)(50,187)(51,188)(52,189)(53,190)(54,191)(55,192)(56,193)(57,125)(58,126)(59,127)(60,128)(61,129)(62,130)(63,131)(64,132)(65,133)(66,134)(67,135)(68,136)(69,137)(70,138)(71,139)(72,140)(73,113)(74,114)(75,115)(76,116)(77,117)(78,118)(79,119)(80,120)(81,121)(82,122)(83,123)(84,124)(85,159)(86,160)(87,161)(88,162)(89,163)(90,164)(91,165)(92,166)(93,167)(94,168)(95,141)(96,142)(97,143)(98,144)(99,145)(100,146)(101,147)(102,148)(103,149)(104,150)(105,151)(106,152)(107,153)(108,154)(109,155)(110,156)(111,157)(112,158), (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), (1,185,153,132)(2,172,154,119)(3,187,155,134)(4,174,156,121)(5,189,157,136)(6,176,158,123)(7,191,159,138)(8,178,160,125)(9,193,161,140)(10,180,162,127)(11,195,163,114)(12,182,164,129)(13,169,165,116)(14,184,166,131)(15,171,167,118)(16,186,168,133)(17,173,141,120)(18,188,142,135)(19,175,143,122)(20,190,144,137)(21,177,145,124)(22,192,146,139)(23,179,147,126)(24,194,148,113)(25,181,149,128)(26,196,150,115)(27,183,151,130)(28,170,152,117)(29,102,73,218)(30,89,74,205)(31,104,75,220)(32,91,76,207)(33,106,77,222)(34,93,78,209)(35,108,79,224)(36,95,80,211)(37,110,81,198)(38,97,82,213)(39,112,83,200)(40,99,84,215)(41,86,57,202)(42,101,58,217)(43,88,59,204)(44,103,60,219)(45,90,61,206)(46,105,62,221)(47,92,63,208)(48,107,64,223)(49,94,65,210)(50,109,66,197)(51,96,67,212)(52,111,68,199)(53,98,69,214)(54,85,70,201)(55,100,71,216)(56,87,72,203), (1,132)(2,131)(3,130)(4,129)(5,128)(6,127)(7,126)(8,125)(9,124)(10,123)(11,122)(12,121)(13,120)(14,119)(15,118)(16,117)(17,116)(18,115)(19,114)(20,113)(21,140)(22,139)(23,138)(24,137)(25,136)(26,135)(27,134)(28,133)(29,98)(30,97)(31,96)(32,95)(33,94)(34,93)(35,92)(36,91)(37,90)(38,89)(39,88)(40,87)(41,86)(42,85)(43,112)(44,111)(45,110)(46,109)(47,108)(48,107)(49,106)(50,105)(51,104)(52,103)(53,102)(54,101)(55,100)(56,99)(57,202)(58,201)(59,200)(60,199)(61,198)(62,197)(63,224)(64,223)(65,222)(66,221)(67,220)(68,219)(69,218)(70,217)(71,216)(72,215)(73,214)(74,213)(75,212)(76,211)(77,210)(78,209)(79,208)(80,207)(81,206)(82,205)(83,204)(84,203)(141,169)(142,196)(143,195)(144,194)(145,193)(146,192)(147,191)(148,190)(149,189)(150,188)(151,187)(152,186)(153,185)(154,184)(155,183)(156,182)(157,181)(158,180)(159,179)(160,178)(161,177)(162,176)(163,175)(164,174)(165,173)(166,172)(167,171)(168,170)>;
G:=Group( (1,223)(2,224)(3,197)(4,198)(5,199)(6,200)(7,201)(8,202)(9,203)(10,204)(11,205)(12,206)(13,207)(14,208)(15,209)(16,210)(17,211)(18,212)(19,213)(20,214)(21,215)(22,216)(23,217)(24,218)(25,219)(26,220)(27,221)(28,222)(29,194)(30,195)(31,196)(32,169)(33,170)(34,171)(35,172)(36,173)(37,174)(38,175)(39,176)(40,177)(41,178)(42,179)(43,180)(44,181)(45,182)(46,183)(47,184)(48,185)(49,186)(50,187)(51,188)(52,189)(53,190)(54,191)(55,192)(56,193)(57,125)(58,126)(59,127)(60,128)(61,129)(62,130)(63,131)(64,132)(65,133)(66,134)(67,135)(68,136)(69,137)(70,138)(71,139)(72,140)(73,113)(74,114)(75,115)(76,116)(77,117)(78,118)(79,119)(80,120)(81,121)(82,122)(83,123)(84,124)(85,159)(86,160)(87,161)(88,162)(89,163)(90,164)(91,165)(92,166)(93,167)(94,168)(95,141)(96,142)(97,143)(98,144)(99,145)(100,146)(101,147)(102,148)(103,149)(104,150)(105,151)(106,152)(107,153)(108,154)(109,155)(110,156)(111,157)(112,158), (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), (1,185,153,132)(2,172,154,119)(3,187,155,134)(4,174,156,121)(5,189,157,136)(6,176,158,123)(7,191,159,138)(8,178,160,125)(9,193,161,140)(10,180,162,127)(11,195,163,114)(12,182,164,129)(13,169,165,116)(14,184,166,131)(15,171,167,118)(16,186,168,133)(17,173,141,120)(18,188,142,135)(19,175,143,122)(20,190,144,137)(21,177,145,124)(22,192,146,139)(23,179,147,126)(24,194,148,113)(25,181,149,128)(26,196,150,115)(27,183,151,130)(28,170,152,117)(29,102,73,218)(30,89,74,205)(31,104,75,220)(32,91,76,207)(33,106,77,222)(34,93,78,209)(35,108,79,224)(36,95,80,211)(37,110,81,198)(38,97,82,213)(39,112,83,200)(40,99,84,215)(41,86,57,202)(42,101,58,217)(43,88,59,204)(44,103,60,219)(45,90,61,206)(46,105,62,221)(47,92,63,208)(48,107,64,223)(49,94,65,210)(50,109,66,197)(51,96,67,212)(52,111,68,199)(53,98,69,214)(54,85,70,201)(55,100,71,216)(56,87,72,203), (1,132)(2,131)(3,130)(4,129)(5,128)(6,127)(7,126)(8,125)(9,124)(10,123)(11,122)(12,121)(13,120)(14,119)(15,118)(16,117)(17,116)(18,115)(19,114)(20,113)(21,140)(22,139)(23,138)(24,137)(25,136)(26,135)(27,134)(28,133)(29,98)(30,97)(31,96)(32,95)(33,94)(34,93)(35,92)(36,91)(37,90)(38,89)(39,88)(40,87)(41,86)(42,85)(43,112)(44,111)(45,110)(46,109)(47,108)(48,107)(49,106)(50,105)(51,104)(52,103)(53,102)(54,101)(55,100)(56,99)(57,202)(58,201)(59,200)(60,199)(61,198)(62,197)(63,224)(64,223)(65,222)(66,221)(67,220)(68,219)(69,218)(70,217)(71,216)(72,215)(73,214)(74,213)(75,212)(76,211)(77,210)(78,209)(79,208)(80,207)(81,206)(82,205)(83,204)(84,203)(141,169)(142,196)(143,195)(144,194)(145,193)(146,192)(147,191)(148,190)(149,189)(150,188)(151,187)(152,186)(153,185)(154,184)(155,183)(156,182)(157,181)(158,180)(159,179)(160,178)(161,177)(162,176)(163,175)(164,174)(165,173)(166,172)(167,171)(168,170) );
G=PermutationGroup([[(1,223),(2,224),(3,197),(4,198),(5,199),(6,200),(7,201),(8,202),(9,203),(10,204),(11,205),(12,206),(13,207),(14,208),(15,209),(16,210),(17,211),(18,212),(19,213),(20,214),(21,215),(22,216),(23,217),(24,218),(25,219),(26,220),(27,221),(28,222),(29,194),(30,195),(31,196),(32,169),(33,170),(34,171),(35,172),(36,173),(37,174),(38,175),(39,176),(40,177),(41,178),(42,179),(43,180),(44,181),(45,182),(46,183),(47,184),(48,185),(49,186),(50,187),(51,188),(52,189),(53,190),(54,191),(55,192),(56,193),(57,125),(58,126),(59,127),(60,128),(61,129),(62,130),(63,131),(64,132),(65,133),(66,134),(67,135),(68,136),(69,137),(70,138),(71,139),(72,140),(73,113),(74,114),(75,115),(76,116),(77,117),(78,118),(79,119),(80,120),(81,121),(82,122),(83,123),(84,124),(85,159),(86,160),(87,161),(88,162),(89,163),(90,164),(91,165),(92,166),(93,167),(94,168),(95,141),(96,142),(97,143),(98,144),(99,145),(100,146),(101,147),(102,148),(103,149),(104,150),(105,151),(106,152),(107,153),(108,154),(109,155),(110,156),(111,157),(112,158)], [(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)], [(1,185,153,132),(2,172,154,119),(3,187,155,134),(4,174,156,121),(5,189,157,136),(6,176,158,123),(7,191,159,138),(8,178,160,125),(9,193,161,140),(10,180,162,127),(11,195,163,114),(12,182,164,129),(13,169,165,116),(14,184,166,131),(15,171,167,118),(16,186,168,133),(17,173,141,120),(18,188,142,135),(19,175,143,122),(20,190,144,137),(21,177,145,124),(22,192,146,139),(23,179,147,126),(24,194,148,113),(25,181,149,128),(26,196,150,115),(27,183,151,130),(28,170,152,117),(29,102,73,218),(30,89,74,205),(31,104,75,220),(32,91,76,207),(33,106,77,222),(34,93,78,209),(35,108,79,224),(36,95,80,211),(37,110,81,198),(38,97,82,213),(39,112,83,200),(40,99,84,215),(41,86,57,202),(42,101,58,217),(43,88,59,204),(44,103,60,219),(45,90,61,206),(46,105,62,221),(47,92,63,208),(48,107,64,223),(49,94,65,210),(50,109,66,197),(51,96,67,212),(52,111,68,199),(53,98,69,214),(54,85,70,201),(55,100,71,216),(56,87,72,203)], [(1,132),(2,131),(3,130),(4,129),(5,128),(6,127),(7,126),(8,125),(9,124),(10,123),(11,122),(12,121),(13,120),(14,119),(15,118),(16,117),(17,116),(18,115),(19,114),(20,113),(21,140),(22,139),(23,138),(24,137),(25,136),(26,135),(27,134),(28,133),(29,98),(30,97),(31,96),(32,95),(33,94),(34,93),(35,92),(36,91),(37,90),(38,89),(39,88),(40,87),(41,86),(42,85),(43,112),(44,111),(45,110),(46,109),(47,108),(48,107),(49,106),(50,105),(51,104),(52,103),(53,102),(54,101),(55,100),(56,99),(57,202),(58,201),(59,200),(60,199),(61,198),(62,197),(63,224),(64,223),(65,222),(66,221),(67,220),(68,219),(69,218),(70,217),(71,216),(72,215),(73,214),(74,213),(75,212),(76,211),(77,210),(78,209),(79,208),(80,207),(81,206),(82,205),(83,204),(84,203),(141,169),(142,196),(143,195),(144,194),(145,193),(146,192),(147,191),(148,190),(149,189),(150,188),(151,187),(152,186),(153,185),(154,184),(155,183),(156,182),(157,181),(158,180),(159,179),(160,178),(161,177),(162,176),(163,175),(164,174),(165,173),(166,172),(167,171),(168,170)]])
88 conjugacy classes
| class | 1 | 2A | ··· | 2G | 2H | 2I | 2J | 2K | 2L | 2M | 2N | 2O | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 4K | 4L | 7A | 7B | 7C | 14A | ··· | 14U | 28A | ··· | 28AJ |
| order | 1 | 2 | ··· | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 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 | 28 | 28 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 14 | 14 | 14 | 14 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 |
88 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | |
| image | C1 | C2 | C2 | C2 | C2 | C2 | D4 | D4 | D7 | C4○D4 | D14 | D14 | D28 | D4×D7 | Q8⋊2D7 |
| kernel | C2×C4⋊D28 | C4⋊D28 | C2×D14⋊C4 | C14×C4⋊C4 | D7×C22×C4 | C22×D28 | C2×C28 | C22×D7 | C2×C4⋊C4 | C2×C14 | C4⋊C4 | C22×C4 | C2×C4 | C22 | C22 |
| # reps | 1 | 8 | 2 | 1 | 1 | 3 | 4 | 4 | 3 | 4 | 12 | 9 | 24 | 6 | 6 |
Matrix representation of C2×C4⋊D28 ►in GL6(𝔽29)
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 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 |
| 21 | 3 | 0 | 0 | 0 | 0 |
| 26 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 27 | 18 | 0 | 0 |
| 0 | 0 | 11 | 2 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 0 |
| 0 | 0 | 0 | 0 | 0 | 17 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 3 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 1 | 0 |
G:=sub<GL(6,GF(29))| [28,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[21,26,0,0,0,0,3,1,0,0,0,0,0,0,27,11,0,0,0,0,18,2,0,0,0,0,0,0,12,0,0,0,0,0,0,17],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,28,0,0,0,0,1,0],[1,3,0,0,0,0,0,28,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0] >;
C2×C4⋊D28 in GAP, Magma, Sage, TeX
C_2\times C_4\rtimes D_{28} % in TeX
G:=Group("C2xC4:D28"); // GroupNames label
G:=SmallGroup(448,959);
// by ID
G=gap.SmallGroup(448,959);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,184,675,297,80,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^2=b^28=c^4=d^2=1,a*b=b*a,a*c=c*a,a*d=d*a,c*b*c^-1=b^15,d*b*d=b^-1,d*c*d=c^-1>;
// generators/relations