direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C2×C4.D28, C42⋊40D14, (C2×C4).98D28, C4.43(C2×D28), (C2×C42)⋊10D7, (C4×C28)⋊51C22, (C2×C28).389D4, C28.286(C2×D4), C14.4(C22×D4), C2.6(C22×D28), D14⋊C4⋊39C22, C14⋊1(C4.4D4), (C2×C14).20C24, (C22×D28).7C2, C22.65(C2×D28), (C2×C28).781C23, (C22×Dic14)⋊4C2, (C22×C4).439D14, (C2×Dic7).4C23, (C22×D7).2C23, C22.63(C23×D7), (C2×Dic14)⋊46C22, (C2×D28).202C22, C22.69(C4○D28), (C23×D7).28C22, C23.316(C22×D7), (C22×C28).504C22, (C22×C14).382C23, (C22×Dic7).74C22, (C2×C4×C28)⋊9C2, C7⋊1(C2×C4.4D4), C2.9(C2×C4○D28), C14.7(C2×C4○D4), (C2×D14⋊C4)⋊12C2, (C2×C14).171(C2×D4), (C2×C14).97(C4○D4), (C2×C4).649(C22×D7), SmallGroup(448,929)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C2×C4.D28
G = < a,b,c,d | a2=b4=c28=1, d2=b2, ab=ba, ac=ca, ad=da, bc=cb, dbd-1=b-1, dcd-1=b2c-1 >
Subgroups: 1796 in 330 conjugacy classes, 127 normal (15 characteristic)
C1, C2, C2, C2, C4, C4, C22, C22, C22, C7, C2×C4, C2×C4, D4, Q8, C23, C23, D7, C14, C14, C42, C22⋊C4, C22×C4, C22×C4, C22×C4, C2×D4, C2×Q8, C24, Dic7, C28, C28, D14, C2×C14, C2×C14, C2×C42, C2×C22⋊C4, C4.4D4, C22×D4, C22×Q8, Dic14, D28, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C22×D7, C22×D7, C22×C14, C2×C4.4D4, D14⋊C4, C4×C28, C2×Dic14, C2×Dic14, C2×D28, C2×D28, C22×Dic7, C22×C28, C22×C28, C23×D7, C4.D28, C2×D14⋊C4, C2×C4×C28, C22×Dic14, C22×D28, C2×C4.D28
Quotients: C1, C2, C22, D4, C23, D7, C2×D4, C4○D4, C24, D14, C4.4D4, C22×D4, C2×C4○D4, D28, C22×D7, C2×C4.4D4, C2×D28, C4○D28, C23×D7, C4.D28, C22×D28, C2×C4○D28, C2×C4.D28
►On 224 points
Generators in S224
(1 170)(2 171)(3 172)(4 173)(5 174)(6 175)(7 176)(8 177)(9 178)(10 179)(11 180)(12 181)(13 182)(14 183)(15 184)(16 185)(17 186)(18 187)(19 188)(20 189)(21 190)(22 191)(23 192)(24 193)(25 194)(26 195)(27 196)(28 169)(29 213)(30 214)(31 215)(32 216)(33 217)(34 218)(35 219)(36 220)(37 221)(38 222)(39 223)(40 224)(41 197)(42 198)(43 199)(44 200)(45 201)(46 202)(47 203)(48 204)(49 205)(50 206)(51 207)(52 208)(53 209)(54 210)(55 211)(56 212)(57 86)(58 87)(59 88)(60 89)(61 90)(62 91)(63 92)(64 93)(65 94)(66 95)(67 96)(68 97)(69 98)(70 99)(71 100)(72 101)(73 102)(74 103)(75 104)(76 105)(77 106)(78 107)(79 108)(80 109)(81 110)(82 111)(83 112)(84 85)(113 147)(114 148)(115 149)(116 150)(117 151)(118 152)(119 153)(120 154)(121 155)(122 156)(123 157)(124 158)(125 159)(126 160)(127 161)(128 162)(129 163)(130 164)(131 165)(132 166)(133 167)(134 168)(135 141)(136 142)(137 143)(138 144)(139 145)(140 146)
(1 61 141 199)(2 62 142 200)(3 63 143 201)(4 64 144 202)(5 65 145 203)(6 66 146 204)(7 67 147 205)(8 68 148 206)(9 69 149 207)(10 70 150 208)(11 71 151 209)(12 72 152 210)(13 73 153 211)(14 74 154 212)(15 75 155 213)(16 76 156 214)(17 77 157 215)(18 78 158 216)(19 79 159 217)(20 80 160 218)(21 81 161 219)(22 82 162 220)(23 83 163 221)(24 84 164 222)(25 57 165 223)(26 58 166 224)(27 59 167 197)(28 60 168 198)(29 184 104 121)(30 185 105 122)(31 186 106 123)(32 187 107 124)(33 188 108 125)(34 189 109 126)(35 190 110 127)(36 191 111 128)(37 192 112 129)(38 193 85 130)(39 194 86 131)(40 195 87 132)(41 196 88 133)(42 169 89 134)(43 170 90 135)(44 171 91 136)(45 172 92 137)(46 173 93 138)(47 174 94 139)(48 175 95 140)(49 176 96 113)(50 177 97 114)(51 178 98 115)(52 179 99 116)(53 180 100 117)(54 181 101 118)(55 182 102 119)(56 183 103 120)
(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)
(1 168 141 28)(2 27 142 167)(3 166 143 26)(4 25 144 165)(5 164 145 24)(6 23 146 163)(7 162 147 22)(8 21 148 161)(9 160 149 20)(10 19 150 159)(11 158 151 18)(12 17 152 157)(13 156 153 16)(14 15 154 155)(29 56 104 103)(30 102 105 55)(31 54 106 101)(32 100 107 53)(33 52 108 99)(34 98 109 51)(35 50 110 97)(36 96 111 49)(37 48 112 95)(38 94 85 47)(39 46 86 93)(40 92 87 45)(41 44 88 91)(42 90 89 43)(57 64 223 202)(58 201 224 63)(59 62 197 200)(60 199 198 61)(65 84 203 222)(66 221 204 83)(67 82 205 220)(68 219 206 81)(69 80 207 218)(70 217 208 79)(71 78 209 216)(72 215 210 77)(73 76 211 214)(74 213 212 75)(113 191 176 128)(114 127 177 190)(115 189 178 126)(116 125 179 188)(117 187 180 124)(118 123 181 186)(119 185 182 122)(120 121 183 184)(129 175 192 140)(130 139 193 174)(131 173 194 138)(132 137 195 172)(133 171 196 136)(134 135 169 170)
G:=sub<Sym(224)| (1,170)(2,171)(3,172)(4,173)(5,174)(6,175)(7,176)(8,177)(9,178)(10,179)(11,180)(12,181)(13,182)(14,183)(15,184)(16,185)(17,186)(18,187)(19,188)(20,189)(21,190)(22,191)(23,192)(24,193)(25,194)(26,195)(27,196)(28,169)(29,213)(30,214)(31,215)(32,216)(33,217)(34,218)(35,219)(36,220)(37,221)(38,222)(39,223)(40,224)(41,197)(42,198)(43,199)(44,200)(45,201)(46,202)(47,203)(48,204)(49,205)(50,206)(51,207)(52,208)(53,209)(54,210)(55,211)(56,212)(57,86)(58,87)(59,88)(60,89)(61,90)(62,91)(63,92)(64,93)(65,94)(66,95)(67,96)(68,97)(69,98)(70,99)(71,100)(72,101)(73,102)(74,103)(75,104)(76,105)(77,106)(78,107)(79,108)(80,109)(81,110)(82,111)(83,112)(84,85)(113,147)(114,148)(115,149)(116,150)(117,151)(118,152)(119,153)(120,154)(121,155)(122,156)(123,157)(124,158)(125,159)(126,160)(127,161)(128,162)(129,163)(130,164)(131,165)(132,166)(133,167)(134,168)(135,141)(136,142)(137,143)(138,144)(139,145)(140,146), (1,61,141,199)(2,62,142,200)(3,63,143,201)(4,64,144,202)(5,65,145,203)(6,66,146,204)(7,67,147,205)(8,68,148,206)(9,69,149,207)(10,70,150,208)(11,71,151,209)(12,72,152,210)(13,73,153,211)(14,74,154,212)(15,75,155,213)(16,76,156,214)(17,77,157,215)(18,78,158,216)(19,79,159,217)(20,80,160,218)(21,81,161,219)(22,82,162,220)(23,83,163,221)(24,84,164,222)(25,57,165,223)(26,58,166,224)(27,59,167,197)(28,60,168,198)(29,184,104,121)(30,185,105,122)(31,186,106,123)(32,187,107,124)(33,188,108,125)(34,189,109,126)(35,190,110,127)(36,191,111,128)(37,192,112,129)(38,193,85,130)(39,194,86,131)(40,195,87,132)(41,196,88,133)(42,169,89,134)(43,170,90,135)(44,171,91,136)(45,172,92,137)(46,173,93,138)(47,174,94,139)(48,175,95,140)(49,176,96,113)(50,177,97,114)(51,178,98,115)(52,179,99,116)(53,180,100,117)(54,181,101,118)(55,182,102,119)(56,183,103,120), (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), (1,168,141,28)(2,27,142,167)(3,166,143,26)(4,25,144,165)(5,164,145,24)(6,23,146,163)(7,162,147,22)(8,21,148,161)(9,160,149,20)(10,19,150,159)(11,158,151,18)(12,17,152,157)(13,156,153,16)(14,15,154,155)(29,56,104,103)(30,102,105,55)(31,54,106,101)(32,100,107,53)(33,52,108,99)(34,98,109,51)(35,50,110,97)(36,96,111,49)(37,48,112,95)(38,94,85,47)(39,46,86,93)(40,92,87,45)(41,44,88,91)(42,90,89,43)(57,64,223,202)(58,201,224,63)(59,62,197,200)(60,199,198,61)(65,84,203,222)(66,221,204,83)(67,82,205,220)(68,219,206,81)(69,80,207,218)(70,217,208,79)(71,78,209,216)(72,215,210,77)(73,76,211,214)(74,213,212,75)(113,191,176,128)(114,127,177,190)(115,189,178,126)(116,125,179,188)(117,187,180,124)(118,123,181,186)(119,185,182,122)(120,121,183,184)(129,175,192,140)(130,139,193,174)(131,173,194,138)(132,137,195,172)(133,171,196,136)(134,135,169,170)>;
G:=Group( (1,170)(2,171)(3,172)(4,173)(5,174)(6,175)(7,176)(8,177)(9,178)(10,179)(11,180)(12,181)(13,182)(14,183)(15,184)(16,185)(17,186)(18,187)(19,188)(20,189)(21,190)(22,191)(23,192)(24,193)(25,194)(26,195)(27,196)(28,169)(29,213)(30,214)(31,215)(32,216)(33,217)(34,218)(35,219)(36,220)(37,221)(38,222)(39,223)(40,224)(41,197)(42,198)(43,199)(44,200)(45,201)(46,202)(47,203)(48,204)(49,205)(50,206)(51,207)(52,208)(53,209)(54,210)(55,211)(56,212)(57,86)(58,87)(59,88)(60,89)(61,90)(62,91)(63,92)(64,93)(65,94)(66,95)(67,96)(68,97)(69,98)(70,99)(71,100)(72,101)(73,102)(74,103)(75,104)(76,105)(77,106)(78,107)(79,108)(80,109)(81,110)(82,111)(83,112)(84,85)(113,147)(114,148)(115,149)(116,150)(117,151)(118,152)(119,153)(120,154)(121,155)(122,156)(123,157)(124,158)(125,159)(126,160)(127,161)(128,162)(129,163)(130,164)(131,165)(132,166)(133,167)(134,168)(135,141)(136,142)(137,143)(138,144)(139,145)(140,146), (1,61,141,199)(2,62,142,200)(3,63,143,201)(4,64,144,202)(5,65,145,203)(6,66,146,204)(7,67,147,205)(8,68,148,206)(9,69,149,207)(10,70,150,208)(11,71,151,209)(12,72,152,210)(13,73,153,211)(14,74,154,212)(15,75,155,213)(16,76,156,214)(17,77,157,215)(18,78,158,216)(19,79,159,217)(20,80,160,218)(21,81,161,219)(22,82,162,220)(23,83,163,221)(24,84,164,222)(25,57,165,223)(26,58,166,224)(27,59,167,197)(28,60,168,198)(29,184,104,121)(30,185,105,122)(31,186,106,123)(32,187,107,124)(33,188,108,125)(34,189,109,126)(35,190,110,127)(36,191,111,128)(37,192,112,129)(38,193,85,130)(39,194,86,131)(40,195,87,132)(41,196,88,133)(42,169,89,134)(43,170,90,135)(44,171,91,136)(45,172,92,137)(46,173,93,138)(47,174,94,139)(48,175,95,140)(49,176,96,113)(50,177,97,114)(51,178,98,115)(52,179,99,116)(53,180,100,117)(54,181,101,118)(55,182,102,119)(56,183,103,120), (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), (1,168,141,28)(2,27,142,167)(3,166,143,26)(4,25,144,165)(5,164,145,24)(6,23,146,163)(7,162,147,22)(8,21,148,161)(9,160,149,20)(10,19,150,159)(11,158,151,18)(12,17,152,157)(13,156,153,16)(14,15,154,155)(29,56,104,103)(30,102,105,55)(31,54,106,101)(32,100,107,53)(33,52,108,99)(34,98,109,51)(35,50,110,97)(36,96,111,49)(37,48,112,95)(38,94,85,47)(39,46,86,93)(40,92,87,45)(41,44,88,91)(42,90,89,43)(57,64,223,202)(58,201,224,63)(59,62,197,200)(60,199,198,61)(65,84,203,222)(66,221,204,83)(67,82,205,220)(68,219,206,81)(69,80,207,218)(70,217,208,79)(71,78,209,216)(72,215,210,77)(73,76,211,214)(74,213,212,75)(113,191,176,128)(114,127,177,190)(115,189,178,126)(116,125,179,188)(117,187,180,124)(118,123,181,186)(119,185,182,122)(120,121,183,184)(129,175,192,140)(130,139,193,174)(131,173,194,138)(132,137,195,172)(133,171,196,136)(134,135,169,170) );
G=PermutationGroup([[(1,170),(2,171),(3,172),(4,173),(5,174),(6,175),(7,176),(8,177),(9,178),(10,179),(11,180),(12,181),(13,182),(14,183),(15,184),(16,185),(17,186),(18,187),(19,188),(20,189),(21,190),(22,191),(23,192),(24,193),(25,194),(26,195),(27,196),(28,169),(29,213),(30,214),(31,215),(32,216),(33,217),(34,218),(35,219),(36,220),(37,221),(38,222),(39,223),(40,224),(41,197),(42,198),(43,199),(44,200),(45,201),(46,202),(47,203),(48,204),(49,205),(50,206),(51,207),(52,208),(53,209),(54,210),(55,211),(56,212),(57,86),(58,87),(59,88),(60,89),(61,90),(62,91),(63,92),(64,93),(65,94),(66,95),(67,96),(68,97),(69,98),(70,99),(71,100),(72,101),(73,102),(74,103),(75,104),(76,105),(77,106),(78,107),(79,108),(80,109),(81,110),(82,111),(83,112),(84,85),(113,147),(114,148),(115,149),(116,150),(117,151),(118,152),(119,153),(120,154),(121,155),(122,156),(123,157),(124,158),(125,159),(126,160),(127,161),(128,162),(129,163),(130,164),(131,165),(132,166),(133,167),(134,168),(135,141),(136,142),(137,143),(138,144),(139,145),(140,146)], [(1,61,141,199),(2,62,142,200),(3,63,143,201),(4,64,144,202),(5,65,145,203),(6,66,146,204),(7,67,147,205),(8,68,148,206),(9,69,149,207),(10,70,150,208),(11,71,151,209),(12,72,152,210),(13,73,153,211),(14,74,154,212),(15,75,155,213),(16,76,156,214),(17,77,157,215),(18,78,158,216),(19,79,159,217),(20,80,160,218),(21,81,161,219),(22,82,162,220),(23,83,163,221),(24,84,164,222),(25,57,165,223),(26,58,166,224),(27,59,167,197),(28,60,168,198),(29,184,104,121),(30,185,105,122),(31,186,106,123),(32,187,107,124),(33,188,108,125),(34,189,109,126),(35,190,110,127),(36,191,111,128),(37,192,112,129),(38,193,85,130),(39,194,86,131),(40,195,87,132),(41,196,88,133),(42,169,89,134),(43,170,90,135),(44,171,91,136),(45,172,92,137),(46,173,93,138),(47,174,94,139),(48,175,95,140),(49,176,96,113),(50,177,97,114),(51,178,98,115),(52,179,99,116),(53,180,100,117),(54,181,101,118),(55,182,102,119),(56,183,103,120)], [(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)], [(1,168,141,28),(2,27,142,167),(3,166,143,26),(4,25,144,165),(5,164,145,24),(6,23,146,163),(7,162,147,22),(8,21,148,161),(9,160,149,20),(10,19,150,159),(11,158,151,18),(12,17,152,157),(13,156,153,16),(14,15,154,155),(29,56,104,103),(30,102,105,55),(31,54,106,101),(32,100,107,53),(33,52,108,99),(34,98,109,51),(35,50,110,97),(36,96,111,49),(37,48,112,95),(38,94,85,47),(39,46,86,93),(40,92,87,45),(41,44,88,91),(42,90,89,43),(57,64,223,202),(58,201,224,63),(59,62,197,200),(60,199,198,61),(65,84,203,222),(66,221,204,83),(67,82,205,220),(68,219,206,81),(69,80,207,218),(70,217,208,79),(71,78,209,216),(72,215,210,77),(73,76,211,214),(74,213,212,75),(113,191,176,128),(114,127,177,190),(115,189,178,126),(116,125,179,188),(117,187,180,124),(118,123,181,186),(119,185,182,122),(120,121,183,184),(129,175,192,140),(130,139,193,174),(131,173,194,138),(132,137,195,172),(133,171,196,136),(134,135,169,170)]])
124 conjugacy classes
| class | 1 | 2A | ··· | 2G | 2H | 2I | 2J | 2K | 4A | ··· | 4L | 4M | 4N | 4O | 4P | 7A | 7B | 7C | 14A | ··· | 14U | 28A | ··· | 28BT |
| order | 1 | 2 | ··· | 2 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 28 | ··· | 28 |
| size | 1 | 1 | ··· | 1 | 28 | 28 | 28 | 28 | 2 | ··· | 2 | 28 | 28 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
124 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | + | + | + | + | + | + | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | D4 | D7 | C4○D4 | D14 | D14 | D28 | C4○D28 |
| kernel | C2×C4.D28 | C4.D28 | C2×D14⋊C4 | C2×C4×C28 | C22×Dic14 | C22×D28 | C2×C28 | C2×C42 | C2×C14 | C42 | C22×C4 | C2×C4 | C22 |
| # reps | 1 | 8 | 4 | 1 | 1 | 1 | 4 | 3 | 8 | 12 | 9 | 24 | 48 |
Matrix representation of C2×C4.D28 ►in GL6(𝔽29)
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 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 |
| 13 | 20 | 0 | 0 | 0 | 0 |
| 6 | 16 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 2 | 18 |
| 0 | 0 | 0 | 0 | 11 | 27 |
| 26 | 14 | 0 | 0 | 0 | 0 |
| 10 | 2 | 0 | 0 | 0 | 0 |
| 0 | 0 | 7 | 7 | 0 | 0 |
| 0 | 0 | 15 | 11 | 0 | 0 |
| 0 | 0 | 0 | 0 | 17 | 7 |
| 0 | 0 | 0 | 0 | 22 | 9 |
| 26 | 14 | 0 | 0 | 0 | 0 |
| 20 | 3 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 13 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 17 | 7 |
| 0 | 0 | 0 | 0 | 0 | 12 |
G:=sub<GL(6,GF(29))| [1,0,0,0,0,0,0,1,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[13,6,0,0,0,0,20,16,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,2,11,0,0,0,0,18,27],[26,10,0,0,0,0,14,2,0,0,0,0,0,0,7,15,0,0,0,0,7,11,0,0,0,0,0,0,17,22,0,0,0,0,7,9],[26,20,0,0,0,0,14,3,0,0,0,0,0,0,1,13,0,0,0,0,0,28,0,0,0,0,0,0,17,0,0,0,0,0,7,12] >;
C2×C4.D28 in GAP, Magma, Sage, TeX
C_2\times C_4.D_{28} % in TeX
G:=Group("C2xC4.D28"); // GroupNames label
G:=SmallGroup(448,929);
// by ID
G=gap.SmallGroup(448,929);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,758,100,675,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^2=b^4=c^28=1,d^2=b^2,a*b=b*a,a*c=c*a,a*d=d*a,b*c=c*b,d*b*d^-1=b^-1,d*c*d^-1=b^2*c^-1>;
// generators/relations