direct product, metabelian, supersoluble, monomial, A-group, 2-hyperelementary
Aliases: C2×C4×Dic7, C14⋊C42, C23.28D14, (C2×C28)⋊7C4, C28⋊8(C2×C4), C7⋊2(C2×C42), (C2×C4).101D14, C22.15(C4×D7), (C22×C4).10D7, (C2×C14).40C23, (C22×C28).13C2, C14.22(C22×C4), C2.2(C22×Dic7), (C2×C28).113C22, (C22×Dic7).7C2, C22.13(C2×Dic7), C22.19(C22×D7), (C22×C14).32C22, (C2×Dic7).50C22, C2.3(C2×C4×D7), (C2×C14).33(C2×C4), SmallGroup(224,117)
Series: Derived ►Chief ►Lower central ►Upper central
| C7 — C2×C4×Dic7 |
Generators and relations for C2×C4×Dic7
G = < a,b,c,d | a2=b4=c14=1, d2=c7, ab=ba, ac=ca, ad=da, bc=cb, bd=db, dcd-1=c-1 >
Subgroups: 270 in 108 conjugacy classes, 81 normal (11 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C2×C4, C2×C4, C23, C14, C14, C42, C22×C4, C22×C4, Dic7, C28, C2×C14, C2×C14, C2×C42, C2×Dic7, C2×C28, C22×C14, C4×Dic7, C22×Dic7, C22×C28, C2×C4×Dic7
Quotients: C1, C2, C4, C22, C2×C4, C23, D7, C42, C22×C4, Dic7, D14, C2×C42, C4×D7, C2×Dic7, C22×D7, C4×Dic7, C2×C4×D7, C22×Dic7, C2×C4×Dic7
►Regular action on 224 points
Generators in S224
(1 204)(2 205)(3 206)(4 207)(5 208)(6 209)(7 210)(8 197)(9 198)(10 199)(11 200)(12 201)(13 202)(14 203)(15 145)(16 146)(17 147)(18 148)(19 149)(20 150)(21 151)(22 152)(23 153)(24 154)(25 141)(26 142)(27 143)(28 144)(29 215)(30 216)(31 217)(32 218)(33 219)(34 220)(35 221)(36 222)(37 223)(38 224)(39 211)(40 212)(41 213)(42 214)(43 182)(44 169)(45 170)(46 171)(47 172)(48 173)(49 174)(50 175)(51 176)(52 177)(53 178)(54 179)(55 180)(56 181)(57 97)(58 98)(59 85)(60 86)(61 87)(62 88)(63 89)(64 90)(65 91)(66 92)(67 93)(68 94)(69 95)(70 96)(71 160)(72 161)(73 162)(74 163)(75 164)(76 165)(77 166)(78 167)(79 168)(80 155)(81 156)(82 157)(83 158)(84 159)(99 138)(100 139)(101 140)(102 127)(103 128)(104 129)(105 130)(106 131)(107 132)(108 133)(109 134)(110 135)(111 136)(112 137)(113 188)(114 189)(115 190)(116 191)(117 192)(118 193)(119 194)(120 195)(121 196)(122 183)(123 184)(124 185)(125 186)(126 187)
(1 75 109 90)(2 76 110 91)(3 77 111 92)(4 78 112 93)(5 79 99 94)(6 80 100 95)(7 81 101 96)(8 82 102 97)(9 83 103 98)(10 84 104 85)(11 71 105 86)(12 72 106 87)(13 73 107 88)(14 74 108 89)(15 181 29 188)(16 182 30 189)(17 169 31 190)(18 170 32 191)(19 171 33 192)(20 172 34 193)(21 173 35 194)(22 174 36 195)(23 175 37 196)(24 176 38 183)(25 177 39 184)(26 178 40 185)(27 179 41 186)(28 180 42 187)(43 216 114 146)(44 217 115 147)(45 218 116 148)(46 219 117 149)(47 220 118 150)(48 221 119 151)(49 222 120 152)(50 223 121 153)(51 224 122 154)(52 211 123 141)(53 212 124 142)(54 213 125 143)(55 214 126 144)(56 215 113 145)(57 197 157 127)(58 198 158 128)(59 199 159 129)(60 200 160 130)(61 201 161 131)(62 202 162 132)(63 203 163 133)(64 204 164 134)(65 205 165 135)(66 206 166 136)(67 207 167 137)(68 208 168 138)(69 209 155 139)(70 210 156 140)
(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)
(1 170 8 177)(2 169 9 176)(3 182 10 175)(4 181 11 174)(5 180 12 173)(6 179 13 172)(7 178 14 171)(15 86 22 93)(16 85 23 92)(17 98 24 91)(18 97 25 90)(19 96 26 89)(20 95 27 88)(21 94 28 87)(29 71 36 78)(30 84 37 77)(31 83 38 76)(32 82 39 75)(33 81 40 74)(34 80 41 73)(35 79 42 72)(43 199 50 206)(44 198 51 205)(45 197 52 204)(46 210 53 203)(47 209 54 202)(48 208 55 201)(49 207 56 200)(57 141 64 148)(58 154 65 147)(59 153 66 146)(60 152 67 145)(61 151 68 144)(62 150 69 143)(63 149 70 142)(99 187 106 194)(100 186 107 193)(101 185 108 192)(102 184 109 191)(103 183 110 190)(104 196 111 189)(105 195 112 188)(113 130 120 137)(114 129 121 136)(115 128 122 135)(116 127 123 134)(117 140 124 133)(118 139 125 132)(119 138 126 131)(155 213 162 220)(156 212 163 219)(157 211 164 218)(158 224 165 217)(159 223 166 216)(160 222 167 215)(161 221 168 214)
G:=sub<Sym(224)| (1,204)(2,205)(3,206)(4,207)(5,208)(6,209)(7,210)(8,197)(9,198)(10,199)(11,200)(12,201)(13,202)(14,203)(15,145)(16,146)(17,147)(18,148)(19,149)(20,150)(21,151)(22,152)(23,153)(24,154)(25,141)(26,142)(27,143)(28,144)(29,215)(30,216)(31,217)(32,218)(33,219)(34,220)(35,221)(36,222)(37,223)(38,224)(39,211)(40,212)(41,213)(42,214)(43,182)(44,169)(45,170)(46,171)(47,172)(48,173)(49,174)(50,175)(51,176)(52,177)(53,178)(54,179)(55,180)(56,181)(57,97)(58,98)(59,85)(60,86)(61,87)(62,88)(63,89)(64,90)(65,91)(66,92)(67,93)(68,94)(69,95)(70,96)(71,160)(72,161)(73,162)(74,163)(75,164)(76,165)(77,166)(78,167)(79,168)(80,155)(81,156)(82,157)(83,158)(84,159)(99,138)(100,139)(101,140)(102,127)(103,128)(104,129)(105,130)(106,131)(107,132)(108,133)(109,134)(110,135)(111,136)(112,137)(113,188)(114,189)(115,190)(116,191)(117,192)(118,193)(119,194)(120,195)(121,196)(122,183)(123,184)(124,185)(125,186)(126,187), (1,75,109,90)(2,76,110,91)(3,77,111,92)(4,78,112,93)(5,79,99,94)(6,80,100,95)(7,81,101,96)(8,82,102,97)(9,83,103,98)(10,84,104,85)(11,71,105,86)(12,72,106,87)(13,73,107,88)(14,74,108,89)(15,181,29,188)(16,182,30,189)(17,169,31,190)(18,170,32,191)(19,171,33,192)(20,172,34,193)(21,173,35,194)(22,174,36,195)(23,175,37,196)(24,176,38,183)(25,177,39,184)(26,178,40,185)(27,179,41,186)(28,180,42,187)(43,216,114,146)(44,217,115,147)(45,218,116,148)(46,219,117,149)(47,220,118,150)(48,221,119,151)(49,222,120,152)(50,223,121,153)(51,224,122,154)(52,211,123,141)(53,212,124,142)(54,213,125,143)(55,214,126,144)(56,215,113,145)(57,197,157,127)(58,198,158,128)(59,199,159,129)(60,200,160,130)(61,201,161,131)(62,202,162,132)(63,203,163,133)(64,204,164,134)(65,205,165,135)(66,206,166,136)(67,207,167,137)(68,208,168,138)(69,209,155,139)(70,210,156,140), (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), (1,170,8,177)(2,169,9,176)(3,182,10,175)(4,181,11,174)(5,180,12,173)(6,179,13,172)(7,178,14,171)(15,86,22,93)(16,85,23,92)(17,98,24,91)(18,97,25,90)(19,96,26,89)(20,95,27,88)(21,94,28,87)(29,71,36,78)(30,84,37,77)(31,83,38,76)(32,82,39,75)(33,81,40,74)(34,80,41,73)(35,79,42,72)(43,199,50,206)(44,198,51,205)(45,197,52,204)(46,210,53,203)(47,209,54,202)(48,208,55,201)(49,207,56,200)(57,141,64,148)(58,154,65,147)(59,153,66,146)(60,152,67,145)(61,151,68,144)(62,150,69,143)(63,149,70,142)(99,187,106,194)(100,186,107,193)(101,185,108,192)(102,184,109,191)(103,183,110,190)(104,196,111,189)(105,195,112,188)(113,130,120,137)(114,129,121,136)(115,128,122,135)(116,127,123,134)(117,140,124,133)(118,139,125,132)(119,138,126,131)(155,213,162,220)(156,212,163,219)(157,211,164,218)(158,224,165,217)(159,223,166,216)(160,222,167,215)(161,221,168,214)>;
G:=Group( (1,204)(2,205)(3,206)(4,207)(5,208)(6,209)(7,210)(8,197)(9,198)(10,199)(11,200)(12,201)(13,202)(14,203)(15,145)(16,146)(17,147)(18,148)(19,149)(20,150)(21,151)(22,152)(23,153)(24,154)(25,141)(26,142)(27,143)(28,144)(29,215)(30,216)(31,217)(32,218)(33,219)(34,220)(35,221)(36,222)(37,223)(38,224)(39,211)(40,212)(41,213)(42,214)(43,182)(44,169)(45,170)(46,171)(47,172)(48,173)(49,174)(50,175)(51,176)(52,177)(53,178)(54,179)(55,180)(56,181)(57,97)(58,98)(59,85)(60,86)(61,87)(62,88)(63,89)(64,90)(65,91)(66,92)(67,93)(68,94)(69,95)(70,96)(71,160)(72,161)(73,162)(74,163)(75,164)(76,165)(77,166)(78,167)(79,168)(80,155)(81,156)(82,157)(83,158)(84,159)(99,138)(100,139)(101,140)(102,127)(103,128)(104,129)(105,130)(106,131)(107,132)(108,133)(109,134)(110,135)(111,136)(112,137)(113,188)(114,189)(115,190)(116,191)(117,192)(118,193)(119,194)(120,195)(121,196)(122,183)(123,184)(124,185)(125,186)(126,187), (1,75,109,90)(2,76,110,91)(3,77,111,92)(4,78,112,93)(5,79,99,94)(6,80,100,95)(7,81,101,96)(8,82,102,97)(9,83,103,98)(10,84,104,85)(11,71,105,86)(12,72,106,87)(13,73,107,88)(14,74,108,89)(15,181,29,188)(16,182,30,189)(17,169,31,190)(18,170,32,191)(19,171,33,192)(20,172,34,193)(21,173,35,194)(22,174,36,195)(23,175,37,196)(24,176,38,183)(25,177,39,184)(26,178,40,185)(27,179,41,186)(28,180,42,187)(43,216,114,146)(44,217,115,147)(45,218,116,148)(46,219,117,149)(47,220,118,150)(48,221,119,151)(49,222,120,152)(50,223,121,153)(51,224,122,154)(52,211,123,141)(53,212,124,142)(54,213,125,143)(55,214,126,144)(56,215,113,145)(57,197,157,127)(58,198,158,128)(59,199,159,129)(60,200,160,130)(61,201,161,131)(62,202,162,132)(63,203,163,133)(64,204,164,134)(65,205,165,135)(66,206,166,136)(67,207,167,137)(68,208,168,138)(69,209,155,139)(70,210,156,140), (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), (1,170,8,177)(2,169,9,176)(3,182,10,175)(4,181,11,174)(5,180,12,173)(6,179,13,172)(7,178,14,171)(15,86,22,93)(16,85,23,92)(17,98,24,91)(18,97,25,90)(19,96,26,89)(20,95,27,88)(21,94,28,87)(29,71,36,78)(30,84,37,77)(31,83,38,76)(32,82,39,75)(33,81,40,74)(34,80,41,73)(35,79,42,72)(43,199,50,206)(44,198,51,205)(45,197,52,204)(46,210,53,203)(47,209,54,202)(48,208,55,201)(49,207,56,200)(57,141,64,148)(58,154,65,147)(59,153,66,146)(60,152,67,145)(61,151,68,144)(62,150,69,143)(63,149,70,142)(99,187,106,194)(100,186,107,193)(101,185,108,192)(102,184,109,191)(103,183,110,190)(104,196,111,189)(105,195,112,188)(113,130,120,137)(114,129,121,136)(115,128,122,135)(116,127,123,134)(117,140,124,133)(118,139,125,132)(119,138,126,131)(155,213,162,220)(156,212,163,219)(157,211,164,218)(158,224,165,217)(159,223,166,216)(160,222,167,215)(161,221,168,214) );
G=PermutationGroup([[(1,204),(2,205),(3,206),(4,207),(5,208),(6,209),(7,210),(8,197),(9,198),(10,199),(11,200),(12,201),(13,202),(14,203),(15,145),(16,146),(17,147),(18,148),(19,149),(20,150),(21,151),(22,152),(23,153),(24,154),(25,141),(26,142),(27,143),(28,144),(29,215),(30,216),(31,217),(32,218),(33,219),(34,220),(35,221),(36,222),(37,223),(38,224),(39,211),(40,212),(41,213),(42,214),(43,182),(44,169),(45,170),(46,171),(47,172),(48,173),(49,174),(50,175),(51,176),(52,177),(53,178),(54,179),(55,180),(56,181),(57,97),(58,98),(59,85),(60,86),(61,87),(62,88),(63,89),(64,90),(65,91),(66,92),(67,93),(68,94),(69,95),(70,96),(71,160),(72,161),(73,162),(74,163),(75,164),(76,165),(77,166),(78,167),(79,168),(80,155),(81,156),(82,157),(83,158),(84,159),(99,138),(100,139),(101,140),(102,127),(103,128),(104,129),(105,130),(106,131),(107,132),(108,133),(109,134),(110,135),(111,136),(112,137),(113,188),(114,189),(115,190),(116,191),(117,192),(118,193),(119,194),(120,195),(121,196),(122,183),(123,184),(124,185),(125,186),(126,187)], [(1,75,109,90),(2,76,110,91),(3,77,111,92),(4,78,112,93),(5,79,99,94),(6,80,100,95),(7,81,101,96),(8,82,102,97),(9,83,103,98),(10,84,104,85),(11,71,105,86),(12,72,106,87),(13,73,107,88),(14,74,108,89),(15,181,29,188),(16,182,30,189),(17,169,31,190),(18,170,32,191),(19,171,33,192),(20,172,34,193),(21,173,35,194),(22,174,36,195),(23,175,37,196),(24,176,38,183),(25,177,39,184),(26,178,40,185),(27,179,41,186),(28,180,42,187),(43,216,114,146),(44,217,115,147),(45,218,116,148),(46,219,117,149),(47,220,118,150),(48,221,119,151),(49,222,120,152),(50,223,121,153),(51,224,122,154),(52,211,123,141),(53,212,124,142),(54,213,125,143),(55,214,126,144),(56,215,113,145),(57,197,157,127),(58,198,158,128),(59,199,159,129),(60,200,160,130),(61,201,161,131),(62,202,162,132),(63,203,163,133),(64,204,164,134),(65,205,165,135),(66,206,166,136),(67,207,167,137),(68,208,168,138),(69,209,155,139),(70,210,156,140)], [(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)], [(1,170,8,177),(2,169,9,176),(3,182,10,175),(4,181,11,174),(5,180,12,173),(6,179,13,172),(7,178,14,171),(15,86,22,93),(16,85,23,92),(17,98,24,91),(18,97,25,90),(19,96,26,89),(20,95,27,88),(21,94,28,87),(29,71,36,78),(30,84,37,77),(31,83,38,76),(32,82,39,75),(33,81,40,74),(34,80,41,73),(35,79,42,72),(43,199,50,206),(44,198,51,205),(45,197,52,204),(46,210,53,203),(47,209,54,202),(48,208,55,201),(49,207,56,200),(57,141,64,148),(58,154,65,147),(59,153,66,146),(60,152,67,145),(61,151,68,144),(62,150,69,143),(63,149,70,142),(99,187,106,194),(100,186,107,193),(101,185,108,192),(102,184,109,191),(103,183,110,190),(104,196,111,189),(105,195,112,188),(113,130,120,137),(114,129,121,136),(115,128,122,135),(116,127,123,134),(117,140,124,133),(118,139,125,132),(119,138,126,131),(155,213,162,220),(156,212,163,219),(157,211,164,218),(158,224,165,217),(159,223,166,216),(160,222,167,215),(161,221,168,214)]])
C2×C4×Dic7 is a maximal subgroup of
C28.2C42 (C2×C56)⋊5C4 C28.3C42 (C2×C28)⋊Q8 C14.(C4×Q8) Dic7.5C42 Dic7⋊C42 C7⋊(C42⋊8C4) C7⋊(C42⋊5C4) Dic7⋊C4⋊C4 C4⋊Dic7⋊7C4 C4⋊Dic7⋊8C4 C14.(C4×D4) D14⋊C42 D14⋊C4⋊5C4 C2.(C4×D28) Dic7.5M4(2) Dic7.M4(2) C42⋊4Dic7 C24.3D14 C24.4D14 C24.8D14 C24.13D14 Dic7⋊(C4⋊C4) C28⋊(C4⋊C4) (C2×Dic7)⋊6Q8 (C4×Dic7)⋊8C4 (C4×Dic7)⋊9C4 C22.23(Q8×D7) C4⋊C4⋊5Dic7 C4⋊(C4⋊Dic7) (C2×D28)⋊10C4 D14⋊C4⋊7C4 Dic7⋊4M4(2) C24.19D14 (Q8×C14)⋊7C4 D7×C2×C42 C42.88D14 C42.188D14 C42.102D14 C28⋊(C4○D4) C4⋊C4.178D14 (Q8×Dic7)⋊C2 C22⋊Q8⋊25D7 C4⋊C4.197D14 (C2×C28)⋊17D4
C2×C4×Dic7 is a maximal quotient of
C42⋊4Dic7 C28.5C42 C28.12C42 C28.7C42
80 conjugacy classes
| class | 1 | 2A | ··· | 2G | 4A | ··· | 4H | 4I | ··· | 4X | 7A | 7B | 7C | 14A | ··· | 14U | 28A | ··· | 28X |
| order | 1 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 28 | ··· | 28 |
| size | 1 | 1 | ··· | 1 | 1 | ··· | 1 | 7 | ··· | 7 | 2 | 2 | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
80 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | - | + | + | |||
| image | C1 | C2 | C2 | C2 | C4 | C4 | D7 | Dic7 | D14 | D14 | C4×D7 |
| kernel | C2×C4×Dic7 | C4×Dic7 | C22×Dic7 | C22×C28 | C2×Dic7 | C2×C28 | C22×C4 | C2×C4 | C2×C4 | C23 | C22 |
| # reps | 1 | 4 | 2 | 1 | 16 | 8 | 3 | 12 | 6 | 3 | 24 |
Matrix representation of C2×C4×Dic7 ►in GL4(𝔽29) generated by
| 28 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 17 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 |
| 0 | 0 | 12 | 0 |
| 0 | 0 | 0 | 12 |
| 28 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 28 | 1 |
| 0 | 0 | 20 | 8 |
| 17 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 |
| 0 | 0 | 26 | 10 |
| 0 | 0 | 5 | 3 |
G:=sub<GL(4,GF(29))| [28,0,0,0,0,28,0,0,0,0,1,0,0,0,0,1],[17,0,0,0,0,28,0,0,0,0,12,0,0,0,0,12],[28,0,0,0,0,1,0,0,0,0,28,20,0,0,1,8],[17,0,0,0,0,28,0,0,0,0,26,5,0,0,10,3] >;
C2×C4×Dic7 in GAP, Magma, Sage, TeX
C_2\times C_4\times {\rm Dic}_7 % in TeX
G:=Group("C2xC4xDic7"); // GroupNames label
G:=SmallGroup(224,117);
// by ID
G=gap.SmallGroup(224,117);
# by ID
G:=PCGroup([6,-2,-2,-2,-2,-2,-7,48,86,6917]);
// Polycyclic
G:=Group<a,b,c,d|a^2=b^4=c^14=1,d^2=c^7,a*b=b*a,a*c=c*a,a*d=d*a,b*c=c*b,b*d=d*b,d*c*d^-1=c^-1>;
// generators/relations