direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C2×C4⋊Dic7, C22.15D28, C23.30D14, C22.5Dic14, C28⋊7(C2×C4), (C2×C28)⋊5C4, C14⋊2(C4⋊C4), (C2×C4)⋊3Dic7, C4⋊2(C2×Dic7), C2.2(C2×D28), C14.9(C2×Q8), (C2×C14).6Q8, C14.15(C2×D4), (C2×C14).20D4, (C2×C4).84D14, (C22×C4).6D7, (C22×C28).7C2, C2.3(C2×Dic14), (C2×C14).43C23, (C2×C28).92C22, C14.23(C22×C4), C2.4(C22×Dic7), (C22×Dic7).5C2, C22.14(C2×Dic7), C22.21(C22×D7), (C22×C14).35C22, (C2×Dic7).34C22, C7⋊3(C2×C4⋊C4), (C2×C14).34(C2×C4), SmallGroup(224,120)
Series: Derived ►Chief ►Lower central ►Upper central
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, dbd-1=b-1, dcd-1=c-1 >
Subgroups: 270 in 92 conjugacy classes, 65 normal (15 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C2×C4, C2×C4, C23, C14, C14, C4⋊C4, C22×C4, C22×C4, Dic7, C28, C2×C14, C2×C14, C2×C4⋊C4, C2×Dic7, C2×Dic7, C2×C28, C22×C14, C4⋊Dic7, C22×Dic7, C22×C28, C2×C4⋊Dic7
Quotients: C1, C2, C4, C22, C2×C4, D4, Q8, C23, D7, C4⋊C4, C22×C4, C2×D4, C2×Q8, Dic7, D14, C2×C4⋊C4, Dic14, D28, C2×Dic7, C22×D7, C4⋊Dic7, C2×Dic14, C2×D28, C22×Dic7, C2×C4⋊Dic7
►Regular action on 224 points
Generators in S224
(1 158)(2 159)(3 160)(4 161)(5 162)(6 163)(7 164)(8 165)(9 166)(10 167)(11 168)(12 155)(13 156)(14 157)(15 31)(16 32)(17 33)(18 34)(19 35)(20 36)(21 37)(22 38)(23 39)(24 40)(25 41)(26 42)(27 29)(28 30)(43 129)(44 130)(45 131)(46 132)(47 133)(48 134)(49 135)(50 136)(51 137)(52 138)(53 139)(54 140)(55 127)(56 128)(57 147)(58 148)(59 149)(60 150)(61 151)(62 152)(63 153)(64 154)(65 141)(66 142)(67 143)(68 144)(69 145)(70 146)(71 207)(72 208)(73 209)(74 210)(75 197)(76 198)(77 199)(78 200)(79 201)(80 202)(81 203)(82 204)(83 205)(84 206)(85 196)(86 183)(87 184)(88 185)(89 186)(90 187)(91 188)(92 189)(93 190)(94 191)(95 192)(96 193)(97 194)(98 195)(99 181)(100 182)(101 169)(102 170)(103 171)(104 172)(105 173)(106 174)(107 175)(108 176)(109 177)(110 178)(111 179)(112 180)(113 212)(114 213)(115 214)(116 215)(117 216)(118 217)(119 218)(120 219)(121 220)(122 221)(123 222)(124 223)(125 224)(126 211)
(1 54 66 85)(2 55 67 86)(3 56 68 87)(4 43 69 88)(5 44 70 89)(6 45 57 90)(7 46 58 91)(8 47 59 92)(9 48 60 93)(10 49 61 94)(11 50 62 95)(12 51 63 96)(13 52 64 97)(14 53 65 98)(15 202 112 126)(16 203 99 113)(17 204 100 114)(18 205 101 115)(19 206 102 116)(20 207 103 117)(21 208 104 118)(22 209 105 119)(23 210 106 120)(24 197 107 121)(25 198 108 122)(26 199 109 123)(27 200 110 124)(28 201 111 125)(29 78 178 223)(30 79 179 224)(31 80 180 211)(32 81 181 212)(33 82 182 213)(34 83 169 214)(35 84 170 215)(36 71 171 216)(37 72 172 217)(38 73 173 218)(39 74 174 219)(40 75 175 220)(41 76 176 221)(42 77 177 222)(127 143 183 159)(128 144 184 160)(129 145 185 161)(130 146 186 162)(131 147 187 163)(132 148 188 164)(133 149 189 165)(134 150 190 166)(135 151 191 167)(136 152 192 168)(137 153 193 155)(138 154 194 156)(139 141 195 157)(140 142 196 158)
(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 39 8 32)(2 38 9 31)(3 37 10 30)(4 36 11 29)(5 35 12 42)(6 34 13 41)(7 33 14 40)(15 159 22 166)(16 158 23 165)(17 157 24 164)(18 156 25 163)(19 155 26 162)(20 168 27 161)(21 167 28 160)(43 216 50 223)(44 215 51 222)(45 214 52 221)(46 213 53 220)(47 212 54 219)(48 211 55 218)(49 224 56 217)(57 169 64 176)(58 182 65 175)(59 181 66 174)(60 180 67 173)(61 179 68 172)(62 178 69 171)(63 177 70 170)(71 95 78 88)(72 94 79 87)(73 93 80 86)(74 92 81 85)(75 91 82 98)(76 90 83 97)(77 89 84 96)(99 142 106 149)(100 141 107 148)(101 154 108 147)(102 153 109 146)(103 152 110 145)(104 151 111 144)(105 150 112 143)(113 140 120 133)(114 139 121 132)(115 138 122 131)(116 137 123 130)(117 136 124 129)(118 135 125 128)(119 134 126 127)(183 209 190 202)(184 208 191 201)(185 207 192 200)(186 206 193 199)(187 205 194 198)(188 204 195 197)(189 203 196 210)
G:=sub<Sym(224)| (1,158)(2,159)(3,160)(4,161)(5,162)(6,163)(7,164)(8,165)(9,166)(10,167)(11,168)(12,155)(13,156)(14,157)(15,31)(16,32)(17,33)(18,34)(19,35)(20,36)(21,37)(22,38)(23,39)(24,40)(25,41)(26,42)(27,29)(28,30)(43,129)(44,130)(45,131)(46,132)(47,133)(48,134)(49,135)(50,136)(51,137)(52,138)(53,139)(54,140)(55,127)(56,128)(57,147)(58,148)(59,149)(60,150)(61,151)(62,152)(63,153)(64,154)(65,141)(66,142)(67,143)(68,144)(69,145)(70,146)(71,207)(72,208)(73,209)(74,210)(75,197)(76,198)(77,199)(78,200)(79,201)(80,202)(81,203)(82,204)(83,205)(84,206)(85,196)(86,183)(87,184)(88,185)(89,186)(90,187)(91,188)(92,189)(93,190)(94,191)(95,192)(96,193)(97,194)(98,195)(99,181)(100,182)(101,169)(102,170)(103,171)(104,172)(105,173)(106,174)(107,175)(108,176)(109,177)(110,178)(111,179)(112,180)(113,212)(114,213)(115,214)(116,215)(117,216)(118,217)(119,218)(120,219)(121,220)(122,221)(123,222)(124,223)(125,224)(126,211), (1,54,66,85)(2,55,67,86)(3,56,68,87)(4,43,69,88)(5,44,70,89)(6,45,57,90)(7,46,58,91)(8,47,59,92)(9,48,60,93)(10,49,61,94)(11,50,62,95)(12,51,63,96)(13,52,64,97)(14,53,65,98)(15,202,112,126)(16,203,99,113)(17,204,100,114)(18,205,101,115)(19,206,102,116)(20,207,103,117)(21,208,104,118)(22,209,105,119)(23,210,106,120)(24,197,107,121)(25,198,108,122)(26,199,109,123)(27,200,110,124)(28,201,111,125)(29,78,178,223)(30,79,179,224)(31,80,180,211)(32,81,181,212)(33,82,182,213)(34,83,169,214)(35,84,170,215)(36,71,171,216)(37,72,172,217)(38,73,173,218)(39,74,174,219)(40,75,175,220)(41,76,176,221)(42,77,177,222)(127,143,183,159)(128,144,184,160)(129,145,185,161)(130,146,186,162)(131,147,187,163)(132,148,188,164)(133,149,189,165)(134,150,190,166)(135,151,191,167)(136,152,192,168)(137,153,193,155)(138,154,194,156)(139,141,195,157)(140,142,196,158), (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), (1,39,8,32)(2,38,9,31)(3,37,10,30)(4,36,11,29)(5,35,12,42)(6,34,13,41)(7,33,14,40)(15,159,22,166)(16,158,23,165)(17,157,24,164)(18,156,25,163)(19,155,26,162)(20,168,27,161)(21,167,28,160)(43,216,50,223)(44,215,51,222)(45,214,52,221)(46,213,53,220)(47,212,54,219)(48,211,55,218)(49,224,56,217)(57,169,64,176)(58,182,65,175)(59,181,66,174)(60,180,67,173)(61,179,68,172)(62,178,69,171)(63,177,70,170)(71,95,78,88)(72,94,79,87)(73,93,80,86)(74,92,81,85)(75,91,82,98)(76,90,83,97)(77,89,84,96)(99,142,106,149)(100,141,107,148)(101,154,108,147)(102,153,109,146)(103,152,110,145)(104,151,111,144)(105,150,112,143)(113,140,120,133)(114,139,121,132)(115,138,122,131)(116,137,123,130)(117,136,124,129)(118,135,125,128)(119,134,126,127)(183,209,190,202)(184,208,191,201)(185,207,192,200)(186,206,193,199)(187,205,194,198)(188,204,195,197)(189,203,196,210)>;
G:=Group( (1,158)(2,159)(3,160)(4,161)(5,162)(6,163)(7,164)(8,165)(9,166)(10,167)(11,168)(12,155)(13,156)(14,157)(15,31)(16,32)(17,33)(18,34)(19,35)(20,36)(21,37)(22,38)(23,39)(24,40)(25,41)(26,42)(27,29)(28,30)(43,129)(44,130)(45,131)(46,132)(47,133)(48,134)(49,135)(50,136)(51,137)(52,138)(53,139)(54,140)(55,127)(56,128)(57,147)(58,148)(59,149)(60,150)(61,151)(62,152)(63,153)(64,154)(65,141)(66,142)(67,143)(68,144)(69,145)(70,146)(71,207)(72,208)(73,209)(74,210)(75,197)(76,198)(77,199)(78,200)(79,201)(80,202)(81,203)(82,204)(83,205)(84,206)(85,196)(86,183)(87,184)(88,185)(89,186)(90,187)(91,188)(92,189)(93,190)(94,191)(95,192)(96,193)(97,194)(98,195)(99,181)(100,182)(101,169)(102,170)(103,171)(104,172)(105,173)(106,174)(107,175)(108,176)(109,177)(110,178)(111,179)(112,180)(113,212)(114,213)(115,214)(116,215)(117,216)(118,217)(119,218)(120,219)(121,220)(122,221)(123,222)(124,223)(125,224)(126,211), (1,54,66,85)(2,55,67,86)(3,56,68,87)(4,43,69,88)(5,44,70,89)(6,45,57,90)(7,46,58,91)(8,47,59,92)(9,48,60,93)(10,49,61,94)(11,50,62,95)(12,51,63,96)(13,52,64,97)(14,53,65,98)(15,202,112,126)(16,203,99,113)(17,204,100,114)(18,205,101,115)(19,206,102,116)(20,207,103,117)(21,208,104,118)(22,209,105,119)(23,210,106,120)(24,197,107,121)(25,198,108,122)(26,199,109,123)(27,200,110,124)(28,201,111,125)(29,78,178,223)(30,79,179,224)(31,80,180,211)(32,81,181,212)(33,82,182,213)(34,83,169,214)(35,84,170,215)(36,71,171,216)(37,72,172,217)(38,73,173,218)(39,74,174,219)(40,75,175,220)(41,76,176,221)(42,77,177,222)(127,143,183,159)(128,144,184,160)(129,145,185,161)(130,146,186,162)(131,147,187,163)(132,148,188,164)(133,149,189,165)(134,150,190,166)(135,151,191,167)(136,152,192,168)(137,153,193,155)(138,154,194,156)(139,141,195,157)(140,142,196,158), (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), (1,39,8,32)(2,38,9,31)(3,37,10,30)(4,36,11,29)(5,35,12,42)(6,34,13,41)(7,33,14,40)(15,159,22,166)(16,158,23,165)(17,157,24,164)(18,156,25,163)(19,155,26,162)(20,168,27,161)(21,167,28,160)(43,216,50,223)(44,215,51,222)(45,214,52,221)(46,213,53,220)(47,212,54,219)(48,211,55,218)(49,224,56,217)(57,169,64,176)(58,182,65,175)(59,181,66,174)(60,180,67,173)(61,179,68,172)(62,178,69,171)(63,177,70,170)(71,95,78,88)(72,94,79,87)(73,93,80,86)(74,92,81,85)(75,91,82,98)(76,90,83,97)(77,89,84,96)(99,142,106,149)(100,141,107,148)(101,154,108,147)(102,153,109,146)(103,152,110,145)(104,151,111,144)(105,150,112,143)(113,140,120,133)(114,139,121,132)(115,138,122,131)(116,137,123,130)(117,136,124,129)(118,135,125,128)(119,134,126,127)(183,209,190,202)(184,208,191,201)(185,207,192,200)(186,206,193,199)(187,205,194,198)(188,204,195,197)(189,203,196,210) );
G=PermutationGroup([[(1,158),(2,159),(3,160),(4,161),(5,162),(6,163),(7,164),(8,165),(9,166),(10,167),(11,168),(12,155),(13,156),(14,157),(15,31),(16,32),(17,33),(18,34),(19,35),(20,36),(21,37),(22,38),(23,39),(24,40),(25,41),(26,42),(27,29),(28,30),(43,129),(44,130),(45,131),(46,132),(47,133),(48,134),(49,135),(50,136),(51,137),(52,138),(53,139),(54,140),(55,127),(56,128),(57,147),(58,148),(59,149),(60,150),(61,151),(62,152),(63,153),(64,154),(65,141),(66,142),(67,143),(68,144),(69,145),(70,146),(71,207),(72,208),(73,209),(74,210),(75,197),(76,198),(77,199),(78,200),(79,201),(80,202),(81,203),(82,204),(83,205),(84,206),(85,196),(86,183),(87,184),(88,185),(89,186),(90,187),(91,188),(92,189),(93,190),(94,191),(95,192),(96,193),(97,194),(98,195),(99,181),(100,182),(101,169),(102,170),(103,171),(104,172),(105,173),(106,174),(107,175),(108,176),(109,177),(110,178),(111,179),(112,180),(113,212),(114,213),(115,214),(116,215),(117,216),(118,217),(119,218),(120,219),(121,220),(122,221),(123,222),(124,223),(125,224),(126,211)], [(1,54,66,85),(2,55,67,86),(3,56,68,87),(4,43,69,88),(5,44,70,89),(6,45,57,90),(7,46,58,91),(8,47,59,92),(9,48,60,93),(10,49,61,94),(11,50,62,95),(12,51,63,96),(13,52,64,97),(14,53,65,98),(15,202,112,126),(16,203,99,113),(17,204,100,114),(18,205,101,115),(19,206,102,116),(20,207,103,117),(21,208,104,118),(22,209,105,119),(23,210,106,120),(24,197,107,121),(25,198,108,122),(26,199,109,123),(27,200,110,124),(28,201,111,125),(29,78,178,223),(30,79,179,224),(31,80,180,211),(32,81,181,212),(33,82,182,213),(34,83,169,214),(35,84,170,215),(36,71,171,216),(37,72,172,217),(38,73,173,218),(39,74,174,219),(40,75,175,220),(41,76,176,221),(42,77,177,222),(127,143,183,159),(128,144,184,160),(129,145,185,161),(130,146,186,162),(131,147,187,163),(132,148,188,164),(133,149,189,165),(134,150,190,166),(135,151,191,167),(136,152,192,168),(137,153,193,155),(138,154,194,156),(139,141,195,157),(140,142,196,158)], [(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)], [(1,39,8,32),(2,38,9,31),(3,37,10,30),(4,36,11,29),(5,35,12,42),(6,34,13,41),(7,33,14,40),(15,159,22,166),(16,158,23,165),(17,157,24,164),(18,156,25,163),(19,155,26,162),(20,168,27,161),(21,167,28,160),(43,216,50,223),(44,215,51,222),(45,214,52,221),(46,213,53,220),(47,212,54,219),(48,211,55,218),(49,224,56,217),(57,169,64,176),(58,182,65,175),(59,181,66,174),(60,180,67,173),(61,179,68,172),(62,178,69,171),(63,177,70,170),(71,95,78,88),(72,94,79,87),(73,93,80,86),(74,92,81,85),(75,91,82,98),(76,90,83,97),(77,89,84,96),(99,142,106,149),(100,141,107,148),(101,154,108,147),(102,153,109,146),(103,152,110,145),(104,151,111,144),(105,150,112,143),(113,140,120,133),(114,139,121,132),(115,138,122,131),(116,137,123,130),(117,136,124,129),(118,135,125,128),(119,134,126,127),(183,209,190,202),(184,208,191,201),(185,207,192,200),(186,206,193,199),(187,205,194,198),(188,204,195,197),(189,203,196,210)]])
C2×C4⋊Dic7 is a maximal subgroup of
C28.C42 C28.9C42 M4(2)⋊Dic7 C14.(C4×Q8) C4⋊Dic7⋊7C4 C4⋊Dic7⋊8C4 C14.(C4×D4) (C2×Dic7)⋊Q8 C2.(C28⋊Q8) (C2×C28).28D4 (C2×C4).Dic14 C14.(C4⋊Q8) D14⋊C4⋊C4 C2.(C4×D28) (C2×C4).21D28 (C2×C28).33D4 C23.34D28 C23.35D28 C23.38D28 C22.D56 C28⋊4(C4⋊C4) (C2×C28)⋊10Q8 C42⋊8Dic7 C42⋊9Dic7 (C2×C4)⋊6D28 C24.6D14 C24.7D14 C24.47D14 C24.8D14 C24.10D14 C23.16D28 C28⋊(C4⋊C4) C4⋊C4×Dic7 (C4×Dic7)⋊8C4 (C4×Dic7)⋊9C4 C4⋊C4⋊5Dic7 (C2×C4).44D28 (C2×C28).54D4 C4⋊(C4⋊Dic7) (C2×C28).55D4 C4⋊(D14⋊C4) (C2×C4).45D28 C28.(C2×Q8) (C2×C14).D8 C4⋊D4.D7 C22⋊Q8.D7 (C2×C14).Q16 C23.47D28 C23.49D28 C23.27D28 C24.19D14 (Q8×C14)⋊7C4 C4○D4⋊Dic7 C2×C4×Dic14 C2×C4×D28 C2×D7×C4⋊C4 C42.90D14 C42.91D14 C42.105D14 D4⋊6Dic14 D4⋊6D28 C42.119D14 C14.732- 1+4 C14.1152+ 1+4 C14.1182+ 1+4 C14.772- 1+4 C14.852- 1+4 C2×D4×Dic7 C2×Q8×Dic7 C14.1062- 1+4 C14.1082- 1+4
C2×C4⋊Dic7 is a maximal quotient of
C28⋊7M4(2) C42⋊8Dic7 C42⋊9Dic7 C24.47D14 C4⋊(C4⋊Dic7) C42.43D14 C23.22D28 C23.47D28 M4(2).Dic7 C23.27D28
68 conjugacy classes
| class | 1 | 2A | ··· | 2G | 4A | 4B | 4C | 4D | 4E | ··· | 4L | 7A | 7B | 7C | 14A | ··· | 14U | 28A | ··· | 28X |
| order | 1 | 2 | ··· | 2 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 28 | ··· | 28 |
| size | 1 | 1 | ··· | 1 | 2 | 2 | 2 | 2 | 14 | ··· | 14 | 2 | 2 | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
68 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | - | + | - | + | + | - | + | |
| image | C1 | C2 | C2 | C2 | C4 | D4 | Q8 | D7 | Dic7 | D14 | D14 | Dic14 | D28 |
| kernel | C2×C4⋊Dic7 | C4⋊Dic7 | C22×Dic7 | C22×C28 | C2×C28 | C2×C14 | C2×C14 | C22×C4 | C2×C4 | C2×C4 | C23 | C22 | C22 |
| # reps | 1 | 4 | 2 | 1 | 8 | 2 | 2 | 3 | 12 | 6 | 3 | 12 | 12 |
Matrix representation of C2×C4⋊Dic7 ►in GL5(𝔽29)
| 28 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 28 |
| 28 | 0 | 0 | 0 | 0 |
| 0 | 17 | 0 | 0 | 0 |
| 0 | 0 | 12 | 0 | 0 |
| 0 | 0 | 0 | 16 | 11 |
| 0 | 0 | 0 | 3 | 13 |
| 28 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 25 | 1 |
| 0 | 0 | 0 | 24 | 1 |
| 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 12 | 17 |
| 0 | 0 | 0 | 0 | 17 |
G:=sub<GL(5,GF(29))| [28,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,28,0,0,0,0,0,28],[28,0,0,0,0,0,17,0,0,0,0,0,12,0,0,0,0,0,16,3,0,0,0,11,13],[28,0,0,0,0,0,28,0,0,0,0,0,28,0,0,0,0,0,25,24,0,0,0,1,1],[12,0,0,0,0,0,0,28,0,0,0,1,0,0,0,0,0,0,12,0,0,0,0,17,17] >;
C2×C4⋊Dic7 in GAP, Magma, Sage, TeX
C_2\times C_4\rtimes {\rm Dic}_7 % in TeX
G:=Group("C2xC4:Dic7"); // GroupNames label
G:=SmallGroup(224,120);
// by ID
G=gap.SmallGroup(224,120);
# by ID
G:=PCGroup([6,-2,-2,-2,-2,-2,-7,48,362,86,6917]);
// 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,d*b*d^-1=b^-1,d*c*d^-1=c^-1>;
// generators/relations