direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C2×D28⋊C4, C14⋊3(C4×D4), C4⋊C4⋊52D14, (C2×D28)⋊17C4, D28⋊22(C2×C4), C28⋊3(C22×C4), (C2×Dic7)⋊24D4, Dic7⋊10(C2×D4), D14⋊3(C22×C4), D14⋊C4⋊59C22, (C2×C14).47C24, C14.13(C23×C4), C22.131(D4×D7), C14.41(C22×D4), (C2×C28).579C23, (C4×Dic7)⋊64C22, (C22×D28).16C2, (C22×C4).317D14, C22.23(C23×D7), (C2×D28).252C22, (C23×D7).98C22, C23.326(C22×D7), (C22×C14).396C23, (C22×C28).215C22, C22.34(Q8⋊2D7), (C2×Dic7).305C23, (C22×D7).154C23, (C22×Dic7).211C22, C7⋊3(C2×C4×D4), C4⋊2(C2×C4×D7), C2.4(C2×D4×D7), (C2×C4)⋊9(C4×D7), (C14×C4⋊C4)⋊9C2, (C2×C28)⋊8(C2×C4), (C2×C4⋊C4)⋊26D7, (C2×C4×Dic7)⋊5C2, (D7×C22×C4)⋊19C2, (C2×C4×D7)⋊67C22, (C2×D14⋊C4)⋊32C2, (C7×C4⋊C4)⋊44C22, C2.15(D7×C22×C4), C22.73(C2×C4×D7), C2.2(C2×Q8⋊2D7), C14.108(C2×C4○D4), (C2×C14).387(C2×D4), (C22×D7)⋊11(C2×C4), (C2×C4).266(C22×D7), (C2×C14).196(C4○D4), (C2×C14).152(C22×C4), SmallGroup(448,956)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C2×D28⋊C4
G = < a,b,c,d | a2=b28=c2=d4=1, ab=ba, ac=ca, ad=da, cbc=b-1, dbd-1=b15, dcd-1=b14c >
Subgroups: 1988 in 426 conjugacy classes, 175 normal (21 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, C22×C4, C2×D4, C24, Dic7, 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, C7×C4⋊C4, C2×C4×D7, C2×C4×D7, C2×D28, C22×Dic7, C22×C28, C22×C28, C23×D7, D28⋊C4, C2×C4×Dic7, C2×D14⋊C4, C14×C4⋊C4, D7×C22×C4, C22×D28, C2×D28⋊C4
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, C22×D7, C2×C4×D4, C2×C4×D7, D4×D7, Q8⋊2D7, C23×D7, D28⋊C4, D7×C22×C4, C2×D4×D7, C2×Q8⋊2D7, C2×D28⋊C4
►On 224 points
Generators in S224
(1 79)(2 80)(3 81)(4 82)(5 83)(6 84)(7 57)(8 58)(9 59)(10 60)(11 61)(12 62)(13 63)(14 64)(15 65)(16 66)(17 67)(18 68)(19 69)(20 70)(21 71)(22 72)(23 73)(24 74)(25 75)(26 76)(27 77)(28 78)(29 153)(30 154)(31 155)(32 156)(33 157)(34 158)(35 159)(36 160)(37 161)(38 162)(39 163)(40 164)(41 165)(42 166)(43 167)(44 168)(45 141)(46 142)(47 143)(48 144)(49 145)(50 146)(51 147)(52 148)(53 149)(54 150)(55 151)(56 152)(85 199)(86 200)(87 201)(88 202)(89 203)(90 204)(91 205)(92 206)(93 207)(94 208)(95 209)(96 210)(97 211)(98 212)(99 213)(100 214)(101 215)(102 216)(103 217)(104 218)(105 219)(106 220)(107 221)(108 222)(109 223)(110 224)(111 197)(112 198)(113 196)(114 169)(115 170)(116 171)(117 172)(118 173)(119 174)(120 175)(121 176)(122 177)(123 178)(124 179)(125 180)(126 181)(127 182)(128 183)(129 184)(130 185)(131 186)(132 187)(133 188)(134 189)(135 190)(136 191)(137 192)(138 193)(139 194)(140 195)
(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 64)(2 63)(3 62)(4 61)(5 60)(6 59)(7 58)(8 57)(9 84)(10 83)(11 82)(12 81)(13 80)(14 79)(15 78)(16 77)(17 76)(18 75)(19 74)(20 73)(21 72)(22 71)(23 70)(24 69)(25 68)(26 67)(27 66)(28 65)(29 168)(30 167)(31 166)(32 165)(33 164)(34 163)(35 162)(36 161)(37 160)(38 159)(39 158)(40 157)(41 156)(42 155)(43 154)(44 153)(45 152)(46 151)(47 150)(48 149)(49 148)(50 147)(51 146)(52 145)(53 144)(54 143)(55 142)(56 141)(85 216)(86 215)(87 214)(88 213)(89 212)(90 211)(91 210)(92 209)(93 208)(94 207)(95 206)(96 205)(97 204)(98 203)(99 202)(100 201)(101 200)(102 199)(103 198)(104 197)(105 224)(106 223)(107 222)(108 221)(109 220)(110 219)(111 218)(112 217)(113 181)(114 180)(115 179)(116 178)(117 177)(118 176)(119 175)(120 174)(121 173)(122 172)(123 171)(124 170)(125 169)(126 196)(127 195)(128 194)(129 193)(130 192)(131 191)(132 190)(133 189)(134 188)(135 187)(136 186)(137 185)(138 184)(139 183)(140 182)
(1 182 87 154)(2 169 88 141)(3 184 89 156)(4 171 90 143)(5 186 91 158)(6 173 92 145)(7 188 93 160)(8 175 94 147)(9 190 95 162)(10 177 96 149)(11 192 97 164)(12 179 98 151)(13 194 99 166)(14 181 100 153)(15 196 101 168)(16 183 102 155)(17 170 103 142)(18 185 104 157)(19 172 105 144)(20 187 106 159)(21 174 107 146)(22 189 108 161)(23 176 109 148)(24 191 110 163)(25 178 111 150)(26 193 112 165)(27 180 85 152)(28 195 86 167)(29 64 126 214)(30 79 127 201)(31 66 128 216)(32 81 129 203)(33 68 130 218)(34 83 131 205)(35 70 132 220)(36 57 133 207)(37 72 134 222)(38 59 135 209)(39 74 136 224)(40 61 137 211)(41 76 138 198)(42 63 139 213)(43 78 140 200)(44 65 113 215)(45 80 114 202)(46 67 115 217)(47 82 116 204)(48 69 117 219)(49 84 118 206)(50 71 119 221)(51 58 120 208)(52 73 121 223)(53 60 122 210)(54 75 123 197)(55 62 124 212)(56 77 125 199)
G:=sub<Sym(224)| (1,79)(2,80)(3,81)(4,82)(5,83)(6,84)(7,57)(8,58)(9,59)(10,60)(11,61)(12,62)(13,63)(14,64)(15,65)(16,66)(17,67)(18,68)(19,69)(20,70)(21,71)(22,72)(23,73)(24,74)(25,75)(26,76)(27,77)(28,78)(29,153)(30,154)(31,155)(32,156)(33,157)(34,158)(35,159)(36,160)(37,161)(38,162)(39,163)(40,164)(41,165)(42,166)(43,167)(44,168)(45,141)(46,142)(47,143)(48,144)(49,145)(50,146)(51,147)(52,148)(53,149)(54,150)(55,151)(56,152)(85,199)(86,200)(87,201)(88,202)(89,203)(90,204)(91,205)(92,206)(93,207)(94,208)(95,209)(96,210)(97,211)(98,212)(99,213)(100,214)(101,215)(102,216)(103,217)(104,218)(105,219)(106,220)(107,221)(108,222)(109,223)(110,224)(111,197)(112,198)(113,196)(114,169)(115,170)(116,171)(117,172)(118,173)(119,174)(120,175)(121,176)(122,177)(123,178)(124,179)(125,180)(126,181)(127,182)(128,183)(129,184)(130,185)(131,186)(132,187)(133,188)(134,189)(135,190)(136,191)(137,192)(138,193)(139,194)(140,195), (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), (1,64)(2,63)(3,62)(4,61)(5,60)(6,59)(7,58)(8,57)(9,84)(10,83)(11,82)(12,81)(13,80)(14,79)(15,78)(16,77)(17,76)(18,75)(19,74)(20,73)(21,72)(22,71)(23,70)(24,69)(25,68)(26,67)(27,66)(28,65)(29,168)(30,167)(31,166)(32,165)(33,164)(34,163)(35,162)(36,161)(37,160)(38,159)(39,158)(40,157)(41,156)(42,155)(43,154)(44,153)(45,152)(46,151)(47,150)(48,149)(49,148)(50,147)(51,146)(52,145)(53,144)(54,143)(55,142)(56,141)(85,216)(86,215)(87,214)(88,213)(89,212)(90,211)(91,210)(92,209)(93,208)(94,207)(95,206)(96,205)(97,204)(98,203)(99,202)(100,201)(101,200)(102,199)(103,198)(104,197)(105,224)(106,223)(107,222)(108,221)(109,220)(110,219)(111,218)(112,217)(113,181)(114,180)(115,179)(116,178)(117,177)(118,176)(119,175)(120,174)(121,173)(122,172)(123,171)(124,170)(125,169)(126,196)(127,195)(128,194)(129,193)(130,192)(131,191)(132,190)(133,189)(134,188)(135,187)(136,186)(137,185)(138,184)(139,183)(140,182), (1,182,87,154)(2,169,88,141)(3,184,89,156)(4,171,90,143)(5,186,91,158)(6,173,92,145)(7,188,93,160)(8,175,94,147)(9,190,95,162)(10,177,96,149)(11,192,97,164)(12,179,98,151)(13,194,99,166)(14,181,100,153)(15,196,101,168)(16,183,102,155)(17,170,103,142)(18,185,104,157)(19,172,105,144)(20,187,106,159)(21,174,107,146)(22,189,108,161)(23,176,109,148)(24,191,110,163)(25,178,111,150)(26,193,112,165)(27,180,85,152)(28,195,86,167)(29,64,126,214)(30,79,127,201)(31,66,128,216)(32,81,129,203)(33,68,130,218)(34,83,131,205)(35,70,132,220)(36,57,133,207)(37,72,134,222)(38,59,135,209)(39,74,136,224)(40,61,137,211)(41,76,138,198)(42,63,139,213)(43,78,140,200)(44,65,113,215)(45,80,114,202)(46,67,115,217)(47,82,116,204)(48,69,117,219)(49,84,118,206)(50,71,119,221)(51,58,120,208)(52,73,121,223)(53,60,122,210)(54,75,123,197)(55,62,124,212)(56,77,125,199)>;
G:=Group( (1,79)(2,80)(3,81)(4,82)(5,83)(6,84)(7,57)(8,58)(9,59)(10,60)(11,61)(12,62)(13,63)(14,64)(15,65)(16,66)(17,67)(18,68)(19,69)(20,70)(21,71)(22,72)(23,73)(24,74)(25,75)(26,76)(27,77)(28,78)(29,153)(30,154)(31,155)(32,156)(33,157)(34,158)(35,159)(36,160)(37,161)(38,162)(39,163)(40,164)(41,165)(42,166)(43,167)(44,168)(45,141)(46,142)(47,143)(48,144)(49,145)(50,146)(51,147)(52,148)(53,149)(54,150)(55,151)(56,152)(85,199)(86,200)(87,201)(88,202)(89,203)(90,204)(91,205)(92,206)(93,207)(94,208)(95,209)(96,210)(97,211)(98,212)(99,213)(100,214)(101,215)(102,216)(103,217)(104,218)(105,219)(106,220)(107,221)(108,222)(109,223)(110,224)(111,197)(112,198)(113,196)(114,169)(115,170)(116,171)(117,172)(118,173)(119,174)(120,175)(121,176)(122,177)(123,178)(124,179)(125,180)(126,181)(127,182)(128,183)(129,184)(130,185)(131,186)(132,187)(133,188)(134,189)(135,190)(136,191)(137,192)(138,193)(139,194)(140,195), (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), (1,64)(2,63)(3,62)(4,61)(5,60)(6,59)(7,58)(8,57)(9,84)(10,83)(11,82)(12,81)(13,80)(14,79)(15,78)(16,77)(17,76)(18,75)(19,74)(20,73)(21,72)(22,71)(23,70)(24,69)(25,68)(26,67)(27,66)(28,65)(29,168)(30,167)(31,166)(32,165)(33,164)(34,163)(35,162)(36,161)(37,160)(38,159)(39,158)(40,157)(41,156)(42,155)(43,154)(44,153)(45,152)(46,151)(47,150)(48,149)(49,148)(50,147)(51,146)(52,145)(53,144)(54,143)(55,142)(56,141)(85,216)(86,215)(87,214)(88,213)(89,212)(90,211)(91,210)(92,209)(93,208)(94,207)(95,206)(96,205)(97,204)(98,203)(99,202)(100,201)(101,200)(102,199)(103,198)(104,197)(105,224)(106,223)(107,222)(108,221)(109,220)(110,219)(111,218)(112,217)(113,181)(114,180)(115,179)(116,178)(117,177)(118,176)(119,175)(120,174)(121,173)(122,172)(123,171)(124,170)(125,169)(126,196)(127,195)(128,194)(129,193)(130,192)(131,191)(132,190)(133,189)(134,188)(135,187)(136,186)(137,185)(138,184)(139,183)(140,182), (1,182,87,154)(2,169,88,141)(3,184,89,156)(4,171,90,143)(5,186,91,158)(6,173,92,145)(7,188,93,160)(8,175,94,147)(9,190,95,162)(10,177,96,149)(11,192,97,164)(12,179,98,151)(13,194,99,166)(14,181,100,153)(15,196,101,168)(16,183,102,155)(17,170,103,142)(18,185,104,157)(19,172,105,144)(20,187,106,159)(21,174,107,146)(22,189,108,161)(23,176,109,148)(24,191,110,163)(25,178,111,150)(26,193,112,165)(27,180,85,152)(28,195,86,167)(29,64,126,214)(30,79,127,201)(31,66,128,216)(32,81,129,203)(33,68,130,218)(34,83,131,205)(35,70,132,220)(36,57,133,207)(37,72,134,222)(38,59,135,209)(39,74,136,224)(40,61,137,211)(41,76,138,198)(42,63,139,213)(43,78,140,200)(44,65,113,215)(45,80,114,202)(46,67,115,217)(47,82,116,204)(48,69,117,219)(49,84,118,206)(50,71,119,221)(51,58,120,208)(52,73,121,223)(53,60,122,210)(54,75,123,197)(55,62,124,212)(56,77,125,199) );
G=PermutationGroup([[(1,79),(2,80),(3,81),(4,82),(5,83),(6,84),(7,57),(8,58),(9,59),(10,60),(11,61),(12,62),(13,63),(14,64),(15,65),(16,66),(17,67),(18,68),(19,69),(20,70),(21,71),(22,72),(23,73),(24,74),(25,75),(26,76),(27,77),(28,78),(29,153),(30,154),(31,155),(32,156),(33,157),(34,158),(35,159),(36,160),(37,161),(38,162),(39,163),(40,164),(41,165),(42,166),(43,167),(44,168),(45,141),(46,142),(47,143),(48,144),(49,145),(50,146),(51,147),(52,148),(53,149),(54,150),(55,151),(56,152),(85,199),(86,200),(87,201),(88,202),(89,203),(90,204),(91,205),(92,206),(93,207),(94,208),(95,209),(96,210),(97,211),(98,212),(99,213),(100,214),(101,215),(102,216),(103,217),(104,218),(105,219),(106,220),(107,221),(108,222),(109,223),(110,224),(111,197),(112,198),(113,196),(114,169),(115,170),(116,171),(117,172),(118,173),(119,174),(120,175),(121,176),(122,177),(123,178),(124,179),(125,180),(126,181),(127,182),(128,183),(129,184),(130,185),(131,186),(132,187),(133,188),(134,189),(135,190),(136,191),(137,192),(138,193),(139,194),(140,195)], [(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)], [(1,64),(2,63),(3,62),(4,61),(5,60),(6,59),(7,58),(8,57),(9,84),(10,83),(11,82),(12,81),(13,80),(14,79),(15,78),(16,77),(17,76),(18,75),(19,74),(20,73),(21,72),(22,71),(23,70),(24,69),(25,68),(26,67),(27,66),(28,65),(29,168),(30,167),(31,166),(32,165),(33,164),(34,163),(35,162),(36,161),(37,160),(38,159),(39,158),(40,157),(41,156),(42,155),(43,154),(44,153),(45,152),(46,151),(47,150),(48,149),(49,148),(50,147),(51,146),(52,145),(53,144),(54,143),(55,142),(56,141),(85,216),(86,215),(87,214),(88,213),(89,212),(90,211),(91,210),(92,209),(93,208),(94,207),(95,206),(96,205),(97,204),(98,203),(99,202),(100,201),(101,200),(102,199),(103,198),(104,197),(105,224),(106,223),(107,222),(108,221),(109,220),(110,219),(111,218),(112,217),(113,181),(114,180),(115,179),(116,178),(117,177),(118,176),(119,175),(120,174),(121,173),(122,172),(123,171),(124,170),(125,169),(126,196),(127,195),(128,194),(129,193),(130,192),(131,191),(132,190),(133,189),(134,188),(135,187),(136,186),(137,185),(138,184),(139,183),(140,182)], [(1,182,87,154),(2,169,88,141),(3,184,89,156),(4,171,90,143),(5,186,91,158),(6,173,92,145),(7,188,93,160),(8,175,94,147),(9,190,95,162),(10,177,96,149),(11,192,97,164),(12,179,98,151),(13,194,99,166),(14,181,100,153),(15,196,101,168),(16,183,102,155),(17,170,103,142),(18,185,104,157),(19,172,105,144),(20,187,106,159),(21,174,107,146),(22,189,108,161),(23,176,109,148),(24,191,110,163),(25,178,111,150),(26,193,112,165),(27,180,85,152),(28,195,86,167),(29,64,126,214),(30,79,127,201),(31,66,128,216),(32,81,129,203),(33,68,130,218),(34,83,131,205),(35,70,132,220),(36,57,133,207),(37,72,134,222),(38,59,135,209),(39,74,136,224),(40,61,137,211),(41,76,138,198),(42,63,139,213),(43,78,140,200),(44,65,113,215),(45,80,114,202),(46,67,115,217),(47,82,116,204),(48,69,117,219),(49,84,118,206),(50,71,119,221),(51,58,120,208),(52,73,121,223),(53,60,122,210),(54,75,123,197),(55,62,124,212),(56,77,125,199)]])
100 conjugacy classes
| class | 1 | 2A | ··· | 2G | 2H | ··· | 2O | 4A | ··· | 4L | 4M | ··· | 4T | 4U | 4V | 4W | 4X | 7A | 7B | 7C | 14A | ··· | 14U | 28A | ··· | 28AJ |
| order | 1 | 2 | ··· | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 28 | ··· | 28 |
| size | 1 | 1 | ··· | 1 | 14 | ··· | 14 | 2 | ··· | 2 | 7 | ··· | 7 | 14 | 14 | 14 | 14 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 |
100 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | |||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C4 | D4 | D7 | C4○D4 | D14 | D14 | C4×D7 | D4×D7 | Q8⋊2D7 |
| kernel | C2×D28⋊C4 | D28⋊C4 | C2×C4×Dic7 | C2×D14⋊C4 | C14×C4⋊C4 | D7×C22×C4 | C22×D28 | C2×D28 | C2×Dic7 | C2×C4⋊C4 | C2×C14 | C4⋊C4 | C22×C4 | C2×C4 | C22 | C22 |
| # reps | 1 | 8 | 1 | 2 | 1 | 2 | 1 | 16 | 4 | 3 | 4 | 12 | 9 | 24 | 6 | 6 |
Matrix representation of C2×D28⋊C4 ►in GL6(𝔽29)
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 19 | 7 | 0 | 0 | 0 | 0 |
| 22 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 11 | 22 | 0 | 0 |
| 0 | 0 | 25 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 18 | 28 |
| 0 | 0 | 0 | 0 | 6 | 11 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 22 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 14 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 11 | 1 |
| 0 | 0 | 0 | 0 | 25 | 18 |
| 17 | 0 | 0 | 0 | 0 | 0 |
| 0 | 17 | 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 | 7 | 28 |
G:=sub<GL(6,GF(29))| [28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[19,22,0,0,0,0,7,28,0,0,0,0,0,0,11,25,0,0,0,0,22,0,0,0,0,0,0,0,18,6,0,0,0,0,28,11],[1,22,0,0,0,0,0,28,0,0,0,0,0,0,1,14,0,0,0,0,0,28,0,0,0,0,0,0,11,25,0,0,0,0,1,18],[17,0,0,0,0,0,0,17,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,7,0,0,0,0,0,28] >;
C2×D28⋊C4 in GAP, Magma, Sage, TeX
C_2\times D_{28}\rtimes C_4 % in TeX
G:=Group("C2xD28:C4"); // GroupNames label
G:=SmallGroup(448,956);
// by ID
G=gap.SmallGroup(448,956);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,758,184,297,80,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^2=b^28=c^2=d^4=1,a*b=b*a,a*c=c*a,a*d=d*a,c*b*c=b^-1,d*b*d^-1=b^15,d*c*d^-1=b^14*c>;
// generators/relations