direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C2×C4×D28, C42⋊38D14, C14⋊1(C4×D4), C28⋊11(C2×D4), (C2×C28)⋊32D4, (C2×C42)⋊7D7, C28⋊5(C22×C4), (C4×C28)⋊53C22, D14⋊1(C22×C4), C14.4(C23×C4), C14.2(C22×D4), C2.1(C22×D28), D14⋊C4⋊75C22, (C2×C14).17C24, C4⋊Dic7⋊81C22, C22.63(C2×D28), (C2×C28).875C23, (C22×D28).20C2, (C22×C4).468D14, C22.14(C23×D7), (C2×D28).284C22, C22.68(C4○D28), (C23×D7).92C22, C23.314(C22×D7), (C22×C28).503C22, (C22×C14).379C23, (C2×Dic7).173C23, (C22×D7).146C23, (C22×Dic7).201C22, C7⋊1(C2×C4×D4), C4⋊3(C2×C4×D7), (C2×C4×C28)⋊11C2, (C2×C4)⋊12(C4×D7), (C2×C28)⋊29(C2×C4), C2.6(D7×C22×C4), C14.5(C2×C4○D4), C2.3(C2×C4○D28), (C2×C4×D7)⋊62C22, (D7×C22×C4)⋊14C2, (C2×D14⋊C4)⋊45C2, C22.69(C2×C4×D7), (C2×C4⋊Dic7)⋊49C2, (C22×D7)⋊9(C2×C4), (C2×C14).169(C2×D4), (C2×C14).96(C4○D4), (C2×C4).817(C22×D7), (C2×C14).147(C22×C4), SmallGroup(448,926)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C2×C4×D28
G = < a,b,c,d | a2=b4=c28=d2=1, ab=ba, ac=ca, ad=da, bc=cb, bd=db, dcd=c-1 >
Subgroups: 1988 in 426 conjugacy classes, 183 normal (23 characteristic)
C1, C2, C2, C2, C4, C4, C22, C22, C22, C7, C2×C4, C2×C4, D4, C23, C23, D7, C14, C14, C42, C22⋊C4, C4⋊C4, C22×C4, C22×C4, C2×D4, C24, Dic7, C28, C28, D14, D14, C2×C14, C2×C14, C2×C42, 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, C4⋊Dic7, D14⋊C4, C4×C28, C2×C4×D7, C2×C4×D7, C2×D28, C22×Dic7, C22×C28, C23×D7, C4×D28, C2×C4⋊Dic7, C2×D14⋊C4, C2×C4×C28, D7×C22×C4, C22×D28, C2×C4×D28
Quotients: C1, C2, C4, C22, C2×C4, D4, C23, D7, C22×C4, C2×D4, C4○D4, C24, D14, C4×D4, C23×C4, C22×D4, C2×C4○D4, C4×D7, D28, C22×D7, C2×C4×D4, C2×C4×D7, C2×D28, C4○D28, C23×D7, C4×D28, D7×C22×C4, C22×D28, C2×C4○D28, C2×C4×D28
►On 224 points
Generators in S224
(1 123)(2 124)(3 125)(4 126)(5 127)(6 128)(7 129)(8 130)(9 131)(10 132)(11 133)(12 134)(13 135)(14 136)(15 137)(16 138)(17 139)(18 140)(19 113)(20 114)(21 115)(22 116)(23 117)(24 118)(25 119)(26 120)(27 121)(28 122)(29 111)(30 112)(31 85)(32 86)(33 87)(34 88)(35 89)(36 90)(37 91)(38 92)(39 93)(40 94)(41 95)(42 96)(43 97)(44 98)(45 99)(46 100)(47 101)(48 102)(49 103)(50 104)(51 105)(52 106)(53 107)(54 108)(55 109)(56 110)(57 197)(58 198)(59 199)(60 200)(61 201)(62 202)(63 203)(64 204)(65 205)(66 206)(67 207)(68 208)(69 209)(70 210)(71 211)(72 212)(73 213)(74 214)(75 215)(76 216)(77 217)(78 218)(79 219)(80 220)(81 221)(82 222)(83 223)(84 224)(141 186)(142 187)(143 188)(144 189)(145 190)(146 191)(147 192)(148 193)(149 194)(150 195)(151 196)(152 169)(153 170)(154 171)(155 172)(156 173)(157 174)(158 175)(159 176)(160 177)(161 178)(162 179)(163 180)(164 181)(165 182)(166 183)(167 184)(168 185)
(1 169 38 59)(2 170 39 60)(3 171 40 61)(4 172 41 62)(5 173 42 63)(6 174 43 64)(7 175 44 65)(8 176 45 66)(9 177 46 67)(10 178 47 68)(11 179 48 69)(12 180 49 70)(13 181 50 71)(14 182 51 72)(15 183 52 73)(16 184 53 74)(17 185 54 75)(18 186 55 76)(19 187 56 77)(20 188 29 78)(21 189 30 79)(22 190 31 80)(23 191 32 81)(24 192 33 82)(25 193 34 83)(26 194 35 84)(27 195 36 57)(28 196 37 58)(85 220 116 145)(86 221 117 146)(87 222 118 147)(88 223 119 148)(89 224 120 149)(90 197 121 150)(91 198 122 151)(92 199 123 152)(93 200 124 153)(94 201 125 154)(95 202 126 155)(96 203 127 156)(97 204 128 157)(98 205 129 158)(99 206 130 159)(100 207 131 160)(101 208 132 161)(102 209 133 162)(103 210 134 163)(104 211 135 164)(105 212 136 165)(106 213 137 166)(107 214 138 167)(108 215 139 168)(109 216 140 141)(110 217 113 142)(111 218 114 143)(112 219 115 144)
(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)
(1 105)(2 104)(3 103)(4 102)(5 101)(6 100)(7 99)(8 98)(9 97)(10 96)(11 95)(12 94)(13 93)(14 92)(15 91)(16 90)(17 89)(18 88)(19 87)(20 86)(21 85)(22 112)(23 111)(24 110)(25 109)(26 108)(27 107)(28 106)(29 117)(30 116)(31 115)(32 114)(33 113)(34 140)(35 139)(36 138)(37 137)(38 136)(39 135)(40 134)(41 133)(42 132)(43 131)(44 130)(45 129)(46 128)(47 127)(48 126)(49 125)(50 124)(51 123)(52 122)(53 121)(54 120)(55 119)(56 118)(57 167)(58 166)(59 165)(60 164)(61 163)(62 162)(63 161)(64 160)(65 159)(66 158)(67 157)(68 156)(69 155)(70 154)(71 153)(72 152)(73 151)(74 150)(75 149)(76 148)(77 147)(78 146)(79 145)(80 144)(81 143)(82 142)(83 141)(84 168)(169 212)(170 211)(171 210)(172 209)(173 208)(174 207)(175 206)(176 205)(177 204)(178 203)(179 202)(180 201)(181 200)(182 199)(183 198)(184 197)(185 224)(186 223)(187 222)(188 221)(189 220)(190 219)(191 218)(192 217)(193 216)(194 215)(195 214)(196 213)
G:=sub<Sym(224)| (1,123)(2,124)(3,125)(4,126)(5,127)(6,128)(7,129)(8,130)(9,131)(10,132)(11,133)(12,134)(13,135)(14,136)(15,137)(16,138)(17,139)(18,140)(19,113)(20,114)(21,115)(22,116)(23,117)(24,118)(25,119)(26,120)(27,121)(28,122)(29,111)(30,112)(31,85)(32,86)(33,87)(34,88)(35,89)(36,90)(37,91)(38,92)(39,93)(40,94)(41,95)(42,96)(43,97)(44,98)(45,99)(46,100)(47,101)(48,102)(49,103)(50,104)(51,105)(52,106)(53,107)(54,108)(55,109)(56,110)(57,197)(58,198)(59,199)(60,200)(61,201)(62,202)(63,203)(64,204)(65,205)(66,206)(67,207)(68,208)(69,209)(70,210)(71,211)(72,212)(73,213)(74,214)(75,215)(76,216)(77,217)(78,218)(79,219)(80,220)(81,221)(82,222)(83,223)(84,224)(141,186)(142,187)(143,188)(144,189)(145,190)(146,191)(147,192)(148,193)(149,194)(150,195)(151,196)(152,169)(153,170)(154,171)(155,172)(156,173)(157,174)(158,175)(159,176)(160,177)(161,178)(162,179)(163,180)(164,181)(165,182)(166,183)(167,184)(168,185), (1,169,38,59)(2,170,39,60)(3,171,40,61)(4,172,41,62)(5,173,42,63)(6,174,43,64)(7,175,44,65)(8,176,45,66)(9,177,46,67)(10,178,47,68)(11,179,48,69)(12,180,49,70)(13,181,50,71)(14,182,51,72)(15,183,52,73)(16,184,53,74)(17,185,54,75)(18,186,55,76)(19,187,56,77)(20,188,29,78)(21,189,30,79)(22,190,31,80)(23,191,32,81)(24,192,33,82)(25,193,34,83)(26,194,35,84)(27,195,36,57)(28,196,37,58)(85,220,116,145)(86,221,117,146)(87,222,118,147)(88,223,119,148)(89,224,120,149)(90,197,121,150)(91,198,122,151)(92,199,123,152)(93,200,124,153)(94,201,125,154)(95,202,126,155)(96,203,127,156)(97,204,128,157)(98,205,129,158)(99,206,130,159)(100,207,131,160)(101,208,132,161)(102,209,133,162)(103,210,134,163)(104,211,135,164)(105,212,136,165)(106,213,137,166)(107,214,138,167)(108,215,139,168)(109,216,140,141)(110,217,113,142)(111,218,114,143)(112,219,115,144), (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), (1,105)(2,104)(3,103)(4,102)(5,101)(6,100)(7,99)(8,98)(9,97)(10,96)(11,95)(12,94)(13,93)(14,92)(15,91)(16,90)(17,89)(18,88)(19,87)(20,86)(21,85)(22,112)(23,111)(24,110)(25,109)(26,108)(27,107)(28,106)(29,117)(30,116)(31,115)(32,114)(33,113)(34,140)(35,139)(36,138)(37,137)(38,136)(39,135)(40,134)(41,133)(42,132)(43,131)(44,130)(45,129)(46,128)(47,127)(48,126)(49,125)(50,124)(51,123)(52,122)(53,121)(54,120)(55,119)(56,118)(57,167)(58,166)(59,165)(60,164)(61,163)(62,162)(63,161)(64,160)(65,159)(66,158)(67,157)(68,156)(69,155)(70,154)(71,153)(72,152)(73,151)(74,150)(75,149)(76,148)(77,147)(78,146)(79,145)(80,144)(81,143)(82,142)(83,141)(84,168)(169,212)(170,211)(171,210)(172,209)(173,208)(174,207)(175,206)(176,205)(177,204)(178,203)(179,202)(180,201)(181,200)(182,199)(183,198)(184,197)(185,224)(186,223)(187,222)(188,221)(189,220)(190,219)(191,218)(192,217)(193,216)(194,215)(195,214)(196,213)>;
G:=Group( (1,123)(2,124)(3,125)(4,126)(5,127)(6,128)(7,129)(8,130)(9,131)(10,132)(11,133)(12,134)(13,135)(14,136)(15,137)(16,138)(17,139)(18,140)(19,113)(20,114)(21,115)(22,116)(23,117)(24,118)(25,119)(26,120)(27,121)(28,122)(29,111)(30,112)(31,85)(32,86)(33,87)(34,88)(35,89)(36,90)(37,91)(38,92)(39,93)(40,94)(41,95)(42,96)(43,97)(44,98)(45,99)(46,100)(47,101)(48,102)(49,103)(50,104)(51,105)(52,106)(53,107)(54,108)(55,109)(56,110)(57,197)(58,198)(59,199)(60,200)(61,201)(62,202)(63,203)(64,204)(65,205)(66,206)(67,207)(68,208)(69,209)(70,210)(71,211)(72,212)(73,213)(74,214)(75,215)(76,216)(77,217)(78,218)(79,219)(80,220)(81,221)(82,222)(83,223)(84,224)(141,186)(142,187)(143,188)(144,189)(145,190)(146,191)(147,192)(148,193)(149,194)(150,195)(151,196)(152,169)(153,170)(154,171)(155,172)(156,173)(157,174)(158,175)(159,176)(160,177)(161,178)(162,179)(163,180)(164,181)(165,182)(166,183)(167,184)(168,185), (1,169,38,59)(2,170,39,60)(3,171,40,61)(4,172,41,62)(5,173,42,63)(6,174,43,64)(7,175,44,65)(8,176,45,66)(9,177,46,67)(10,178,47,68)(11,179,48,69)(12,180,49,70)(13,181,50,71)(14,182,51,72)(15,183,52,73)(16,184,53,74)(17,185,54,75)(18,186,55,76)(19,187,56,77)(20,188,29,78)(21,189,30,79)(22,190,31,80)(23,191,32,81)(24,192,33,82)(25,193,34,83)(26,194,35,84)(27,195,36,57)(28,196,37,58)(85,220,116,145)(86,221,117,146)(87,222,118,147)(88,223,119,148)(89,224,120,149)(90,197,121,150)(91,198,122,151)(92,199,123,152)(93,200,124,153)(94,201,125,154)(95,202,126,155)(96,203,127,156)(97,204,128,157)(98,205,129,158)(99,206,130,159)(100,207,131,160)(101,208,132,161)(102,209,133,162)(103,210,134,163)(104,211,135,164)(105,212,136,165)(106,213,137,166)(107,214,138,167)(108,215,139,168)(109,216,140,141)(110,217,113,142)(111,218,114,143)(112,219,115,144), (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), (1,105)(2,104)(3,103)(4,102)(5,101)(6,100)(7,99)(8,98)(9,97)(10,96)(11,95)(12,94)(13,93)(14,92)(15,91)(16,90)(17,89)(18,88)(19,87)(20,86)(21,85)(22,112)(23,111)(24,110)(25,109)(26,108)(27,107)(28,106)(29,117)(30,116)(31,115)(32,114)(33,113)(34,140)(35,139)(36,138)(37,137)(38,136)(39,135)(40,134)(41,133)(42,132)(43,131)(44,130)(45,129)(46,128)(47,127)(48,126)(49,125)(50,124)(51,123)(52,122)(53,121)(54,120)(55,119)(56,118)(57,167)(58,166)(59,165)(60,164)(61,163)(62,162)(63,161)(64,160)(65,159)(66,158)(67,157)(68,156)(69,155)(70,154)(71,153)(72,152)(73,151)(74,150)(75,149)(76,148)(77,147)(78,146)(79,145)(80,144)(81,143)(82,142)(83,141)(84,168)(169,212)(170,211)(171,210)(172,209)(173,208)(174,207)(175,206)(176,205)(177,204)(178,203)(179,202)(180,201)(181,200)(182,199)(183,198)(184,197)(185,224)(186,223)(187,222)(188,221)(189,220)(190,219)(191,218)(192,217)(193,216)(194,215)(195,214)(196,213) );
G=PermutationGroup([[(1,123),(2,124),(3,125),(4,126),(5,127),(6,128),(7,129),(8,130),(9,131),(10,132),(11,133),(12,134),(13,135),(14,136),(15,137),(16,138),(17,139),(18,140),(19,113),(20,114),(21,115),(22,116),(23,117),(24,118),(25,119),(26,120),(27,121),(28,122),(29,111),(30,112),(31,85),(32,86),(33,87),(34,88),(35,89),(36,90),(37,91),(38,92),(39,93),(40,94),(41,95),(42,96),(43,97),(44,98),(45,99),(46,100),(47,101),(48,102),(49,103),(50,104),(51,105),(52,106),(53,107),(54,108),(55,109),(56,110),(57,197),(58,198),(59,199),(60,200),(61,201),(62,202),(63,203),(64,204),(65,205),(66,206),(67,207),(68,208),(69,209),(70,210),(71,211),(72,212),(73,213),(74,214),(75,215),(76,216),(77,217),(78,218),(79,219),(80,220),(81,221),(82,222),(83,223),(84,224),(141,186),(142,187),(143,188),(144,189),(145,190),(146,191),(147,192),(148,193),(149,194),(150,195),(151,196),(152,169),(153,170),(154,171),(155,172),(156,173),(157,174),(158,175),(159,176),(160,177),(161,178),(162,179),(163,180),(164,181),(165,182),(166,183),(167,184),(168,185)], [(1,169,38,59),(2,170,39,60),(3,171,40,61),(4,172,41,62),(5,173,42,63),(6,174,43,64),(7,175,44,65),(8,176,45,66),(9,177,46,67),(10,178,47,68),(11,179,48,69),(12,180,49,70),(13,181,50,71),(14,182,51,72),(15,183,52,73),(16,184,53,74),(17,185,54,75),(18,186,55,76),(19,187,56,77),(20,188,29,78),(21,189,30,79),(22,190,31,80),(23,191,32,81),(24,192,33,82),(25,193,34,83),(26,194,35,84),(27,195,36,57),(28,196,37,58),(85,220,116,145),(86,221,117,146),(87,222,118,147),(88,223,119,148),(89,224,120,149),(90,197,121,150),(91,198,122,151),(92,199,123,152),(93,200,124,153),(94,201,125,154),(95,202,126,155),(96,203,127,156),(97,204,128,157),(98,205,129,158),(99,206,130,159),(100,207,131,160),(101,208,132,161),(102,209,133,162),(103,210,134,163),(104,211,135,164),(105,212,136,165),(106,213,137,166),(107,214,138,167),(108,215,139,168),(109,216,140,141),(110,217,113,142),(111,218,114,143),(112,219,115,144)], [(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)], [(1,105),(2,104),(3,103),(4,102),(5,101),(6,100),(7,99),(8,98),(9,97),(10,96),(11,95),(12,94),(13,93),(14,92),(15,91),(16,90),(17,89),(18,88),(19,87),(20,86),(21,85),(22,112),(23,111),(24,110),(25,109),(26,108),(27,107),(28,106),(29,117),(30,116),(31,115),(32,114),(33,113),(34,140),(35,139),(36,138),(37,137),(38,136),(39,135),(40,134),(41,133),(42,132),(43,131),(44,130),(45,129),(46,128),(47,127),(48,126),(49,125),(50,124),(51,123),(52,122),(53,121),(54,120),(55,119),(56,118),(57,167),(58,166),(59,165),(60,164),(61,163),(62,162),(63,161),(64,160),(65,159),(66,158),(67,157),(68,156),(69,155),(70,154),(71,153),(72,152),(73,151),(74,150),(75,149),(76,148),(77,147),(78,146),(79,145),(80,144),(81,143),(82,142),(83,141),(84,168),(169,212),(170,211),(171,210),(172,209),(173,208),(174,207),(175,206),(176,205),(177,204),(178,203),(179,202),(180,201),(181,200),(182,199),(183,198),(184,197),(185,224),(186,223),(187,222),(188,221),(189,220),(190,219),(191,218),(192,217),(193,216),(194,215),(195,214),(196,213)]])
136 conjugacy classes
| class | 1 | 2A | ··· | 2G | 2H | ··· | 2O | 4A | ··· | 4H | 4I | ··· | 4P | 4Q | ··· | 4X | 7A | 7B | 7C | 14A | ··· | 14U | 28A | ··· | 28BT |
| order | 1 | 2 | ··· | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 | 4 | ··· | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 28 | ··· | 28 |
| size | 1 | 1 | ··· | 1 | 14 | ··· | 14 | 1 | ··· | 1 | 2 | ··· | 2 | 14 | ··· | 14 | 2 | 2 | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
136 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | ||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C4 | D4 | D7 | C4○D4 | D14 | D14 | C4×D7 | D28 | C4○D28 |
| kernel | C2×C4×D28 | C4×D28 | C2×C4⋊Dic7 | C2×D14⋊C4 | C2×C4×C28 | D7×C22×C4 | C22×D28 | C2×D28 | C2×C28 | C2×C42 | C2×C14 | C42 | C22×C4 | C2×C4 | C2×C4 | C22 |
| # reps | 1 | 8 | 1 | 2 | 1 | 2 | 1 | 16 | 4 | 3 | 4 | 12 | 9 | 24 | 24 | 24 |
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 |
| 17 | 0 | 0 | 0 | 0 | 0 |
| 0 | 17 | 0 | 0 | 0 | 0 |
| 0 | 0 | 17 | 0 | 0 | 0 |
| 0 | 0 | 0 | 17 | 0 | 0 |
| 0 | 0 | 0 | 0 | 17 | 0 |
| 0 | 0 | 0 | 0 | 0 | 17 |
| 19 | 18 | 0 | 0 | 0 | 0 |
| 17 | 7 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 22 | 0 | 0 |
| 0 | 0 | 7 | 19 | 0 | 0 |
| 0 | 0 | 0 | 0 | 7 | 7 |
| 0 | 0 | 0 | 0 | 26 | 22 |
| 10 | 28 | 0 | 0 | 0 | 0 |
| 12 | 19 | 0 | 0 | 0 | 0 |
| 0 | 0 | 10 | 19 | 0 | 0 |
| 0 | 0 | 7 | 19 | 0 | 0 |
| 0 | 0 | 0 | 0 | 22 | 22 |
| 0 | 0 | 0 | 0 | 11 | 7 |
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],[17,0,0,0,0,0,0,17,0,0,0,0,0,0,17,0,0,0,0,0,0,17,0,0,0,0,0,0,17,0,0,0,0,0,0,17],[19,17,0,0,0,0,18,7,0,0,0,0,0,0,28,7,0,0,0,0,22,19,0,0,0,0,0,0,7,26,0,0,0,0,7,22],[10,12,0,0,0,0,28,19,0,0,0,0,0,0,10,7,0,0,0,0,19,19,0,0,0,0,0,0,22,11,0,0,0,0,22,7] >;
C2×C4×D28 in GAP, Magma, Sage, TeX
C_2\times C_4\times D_{28} % in TeX
G:=Group("C2xC4xD28"); // GroupNames label
G:=SmallGroup(448,926);
// by ID
G=gap.SmallGroup(448,926);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,758,184,80,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^2=b^4=c^28=d^2=1,a*b=b*a,a*c=c*a,a*d=d*a,b*c=c*b,b*d=d*b,d*c*d=c^-1>;
// generators/relations