direct product, metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C2×Dic7⋊C4, C23.29D14, C22.4Dic14, C14⋊1(C4⋊C4), C14.7(C2×Q8), (C2×C14).5Q8, Dic7⋊4(C2×C4), (C2×Dic7)⋊4C4, (C2×C14).35D4, C14.38(C2×D4), (C2×C4).64D14, (C22×C4).3D7, (C22×C28).4C2, C2.2(C2×Dic14), C22.16(C4×D7), (C2×C14).41C23, C14.17(C22×C4), (C2×C28).76C22, C22.19(C7⋊D4), (C22×Dic7).4C2, C22.20(C22×D7), (C22×C14).33C22, (C2×Dic7).33C22, C7⋊2(C2×C4⋊C4), C2.18(C2×C4×D7), C2.1(C2×C7⋊D4), (C2×C14).17(C2×C4), SmallGroup(224,118)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C2×Dic7⋊C4
G = < a,b,c,d | a2=b14=d4=1, c2=b7, ab=ba, ac=ca, ad=da, cbc-1=b-1, bd=db, dcd-1=b7c >
Subgroups: 270 in 92 conjugacy classes, 57 normal (17 characteristic)
C1, C2, C2, C4, C22, C22, C7, C2×C4, C2×C4, C23, C14, C14, C4⋊C4, C22×C4, C22×C4, Dic7, Dic7, C28, C2×C14, C2×C14, C2×C4⋊C4, C2×Dic7, C2×Dic7, C2×C28, C2×C28, C22×C14, Dic7⋊C4, C22×Dic7, C22×C28, C2×Dic7⋊C4
Quotients: C1, C2, C4, C22, C2×C4, D4, Q8, C23, D7, C4⋊C4, C22×C4, C2×D4, C2×Q8, D14, C2×C4⋊C4, Dic14, C4×D7, C7⋊D4, C22×D7, Dic7⋊C4, C2×Dic14, C2×C4×D7, C2×C7⋊D4, C2×Dic7⋊C4
►Regular action on 224 points
Generators in S224
(1 78)(2 79)(3 80)(4 81)(5 82)(6 83)(7 84)(8 71)(9 72)(10 73)(11 74)(12 75)(13 76)(14 77)(15 57)(16 58)(17 59)(18 60)(19 61)(20 62)(21 63)(22 64)(23 65)(24 66)(25 67)(26 68)(27 69)(28 70)(29 106)(30 107)(31 108)(32 109)(33 110)(34 111)(35 112)(36 99)(37 100)(38 101)(39 102)(40 103)(41 104)(42 105)(43 92)(44 93)(45 94)(46 95)(47 96)(48 97)(49 98)(50 85)(51 86)(52 87)(53 88)(54 89)(55 90)(56 91)(113 195)(114 196)(115 183)(116 184)(117 185)(118 186)(119 187)(120 188)(121 189)(122 190)(123 191)(124 192)(125 193)(126 194)(127 181)(128 182)(129 169)(130 170)(131 171)(132 172)(133 173)(134 174)(135 175)(136 176)(137 177)(138 178)(139 179)(140 180)(141 218)(142 219)(143 220)(144 221)(145 222)(146 223)(147 224)(148 211)(149 212)(150 213)(151 214)(152 215)(153 216)(154 217)(155 209)(156 210)(157 197)(158 198)(159 199)(160 200)(161 201)(162 202)(163 203)(164 204)(165 205)(166 206)(167 207)(168 208)
(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)
(1 133 8 140)(2 132 9 139)(3 131 10 138)(4 130 11 137)(5 129 12 136)(6 128 13 135)(7 127 14 134)(15 125 22 118)(16 124 23 117)(17 123 24 116)(18 122 25 115)(19 121 26 114)(20 120 27 113)(21 119 28 126)(29 168 36 161)(30 167 37 160)(31 166 38 159)(32 165 39 158)(33 164 40 157)(34 163 41 156)(35 162 42 155)(43 151 50 144)(44 150 51 143)(45 149 52 142)(46 148 53 141)(47 147 54 154)(48 146 55 153)(49 145 56 152)(57 193 64 186)(58 192 65 185)(59 191 66 184)(60 190 67 183)(61 189 68 196)(62 188 69 195)(63 187 70 194)(71 180 78 173)(72 179 79 172)(73 178 80 171)(74 177 81 170)(75 176 82 169)(76 175 83 182)(77 174 84 181)(85 221 92 214)(86 220 93 213)(87 219 94 212)(88 218 95 211)(89 217 96 224)(90 216 97 223)(91 215 98 222)(99 201 106 208)(100 200 107 207)(101 199 108 206)(102 198 109 205)(103 197 110 204)(104 210 111 203)(105 209 112 202)
(1 43 22 36)(2 44 23 37)(3 45 24 38)(4 46 25 39)(5 47 26 40)(6 48 27 41)(7 49 28 42)(8 50 15 29)(9 51 16 30)(10 52 17 31)(11 53 18 32)(12 54 19 33)(13 55 20 34)(14 56 21 35)(57 106 71 85)(58 107 72 86)(59 108 73 87)(60 109 74 88)(61 110 75 89)(62 111 76 90)(63 112 77 91)(64 99 78 92)(65 100 79 93)(66 101 80 94)(67 102 81 95)(68 103 82 96)(69 104 83 97)(70 105 84 98)(113 163 128 153)(114 164 129 154)(115 165 130 141)(116 166 131 142)(117 167 132 143)(118 168 133 144)(119 155 134 145)(120 156 135 146)(121 157 136 147)(122 158 137 148)(123 159 138 149)(124 160 139 150)(125 161 140 151)(126 162 127 152)(169 217 196 204)(170 218 183 205)(171 219 184 206)(172 220 185 207)(173 221 186 208)(174 222 187 209)(175 223 188 210)(176 224 189 197)(177 211 190 198)(178 212 191 199)(179 213 192 200)(180 214 193 201)(181 215 194 202)(182 216 195 203)
G:=sub<Sym(224)| (1,78)(2,79)(3,80)(4,81)(5,82)(6,83)(7,84)(8,71)(9,72)(10,73)(11,74)(12,75)(13,76)(14,77)(15,57)(16,58)(17,59)(18,60)(19,61)(20,62)(21,63)(22,64)(23,65)(24,66)(25,67)(26,68)(27,69)(28,70)(29,106)(30,107)(31,108)(32,109)(33,110)(34,111)(35,112)(36,99)(37,100)(38,101)(39,102)(40,103)(41,104)(42,105)(43,92)(44,93)(45,94)(46,95)(47,96)(48,97)(49,98)(50,85)(51,86)(52,87)(53,88)(54,89)(55,90)(56,91)(113,195)(114,196)(115,183)(116,184)(117,185)(118,186)(119,187)(120,188)(121,189)(122,190)(123,191)(124,192)(125,193)(126,194)(127,181)(128,182)(129,169)(130,170)(131,171)(132,172)(133,173)(134,174)(135,175)(136,176)(137,177)(138,178)(139,179)(140,180)(141,218)(142,219)(143,220)(144,221)(145,222)(146,223)(147,224)(148,211)(149,212)(150,213)(151,214)(152,215)(153,216)(154,217)(155,209)(156,210)(157,197)(158,198)(159,199)(160,200)(161,201)(162,202)(163,203)(164,204)(165,205)(166,206)(167,207)(168,208), (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), (1,133,8,140)(2,132,9,139)(3,131,10,138)(4,130,11,137)(5,129,12,136)(6,128,13,135)(7,127,14,134)(15,125,22,118)(16,124,23,117)(17,123,24,116)(18,122,25,115)(19,121,26,114)(20,120,27,113)(21,119,28,126)(29,168,36,161)(30,167,37,160)(31,166,38,159)(32,165,39,158)(33,164,40,157)(34,163,41,156)(35,162,42,155)(43,151,50,144)(44,150,51,143)(45,149,52,142)(46,148,53,141)(47,147,54,154)(48,146,55,153)(49,145,56,152)(57,193,64,186)(58,192,65,185)(59,191,66,184)(60,190,67,183)(61,189,68,196)(62,188,69,195)(63,187,70,194)(71,180,78,173)(72,179,79,172)(73,178,80,171)(74,177,81,170)(75,176,82,169)(76,175,83,182)(77,174,84,181)(85,221,92,214)(86,220,93,213)(87,219,94,212)(88,218,95,211)(89,217,96,224)(90,216,97,223)(91,215,98,222)(99,201,106,208)(100,200,107,207)(101,199,108,206)(102,198,109,205)(103,197,110,204)(104,210,111,203)(105,209,112,202), (1,43,22,36)(2,44,23,37)(3,45,24,38)(4,46,25,39)(5,47,26,40)(6,48,27,41)(7,49,28,42)(8,50,15,29)(9,51,16,30)(10,52,17,31)(11,53,18,32)(12,54,19,33)(13,55,20,34)(14,56,21,35)(57,106,71,85)(58,107,72,86)(59,108,73,87)(60,109,74,88)(61,110,75,89)(62,111,76,90)(63,112,77,91)(64,99,78,92)(65,100,79,93)(66,101,80,94)(67,102,81,95)(68,103,82,96)(69,104,83,97)(70,105,84,98)(113,163,128,153)(114,164,129,154)(115,165,130,141)(116,166,131,142)(117,167,132,143)(118,168,133,144)(119,155,134,145)(120,156,135,146)(121,157,136,147)(122,158,137,148)(123,159,138,149)(124,160,139,150)(125,161,140,151)(126,162,127,152)(169,217,196,204)(170,218,183,205)(171,219,184,206)(172,220,185,207)(173,221,186,208)(174,222,187,209)(175,223,188,210)(176,224,189,197)(177,211,190,198)(178,212,191,199)(179,213,192,200)(180,214,193,201)(181,215,194,202)(182,216,195,203)>;
G:=Group( (1,78)(2,79)(3,80)(4,81)(5,82)(6,83)(7,84)(8,71)(9,72)(10,73)(11,74)(12,75)(13,76)(14,77)(15,57)(16,58)(17,59)(18,60)(19,61)(20,62)(21,63)(22,64)(23,65)(24,66)(25,67)(26,68)(27,69)(28,70)(29,106)(30,107)(31,108)(32,109)(33,110)(34,111)(35,112)(36,99)(37,100)(38,101)(39,102)(40,103)(41,104)(42,105)(43,92)(44,93)(45,94)(46,95)(47,96)(48,97)(49,98)(50,85)(51,86)(52,87)(53,88)(54,89)(55,90)(56,91)(113,195)(114,196)(115,183)(116,184)(117,185)(118,186)(119,187)(120,188)(121,189)(122,190)(123,191)(124,192)(125,193)(126,194)(127,181)(128,182)(129,169)(130,170)(131,171)(132,172)(133,173)(134,174)(135,175)(136,176)(137,177)(138,178)(139,179)(140,180)(141,218)(142,219)(143,220)(144,221)(145,222)(146,223)(147,224)(148,211)(149,212)(150,213)(151,214)(152,215)(153,216)(154,217)(155,209)(156,210)(157,197)(158,198)(159,199)(160,200)(161,201)(162,202)(163,203)(164,204)(165,205)(166,206)(167,207)(168,208), (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), (1,133,8,140)(2,132,9,139)(3,131,10,138)(4,130,11,137)(5,129,12,136)(6,128,13,135)(7,127,14,134)(15,125,22,118)(16,124,23,117)(17,123,24,116)(18,122,25,115)(19,121,26,114)(20,120,27,113)(21,119,28,126)(29,168,36,161)(30,167,37,160)(31,166,38,159)(32,165,39,158)(33,164,40,157)(34,163,41,156)(35,162,42,155)(43,151,50,144)(44,150,51,143)(45,149,52,142)(46,148,53,141)(47,147,54,154)(48,146,55,153)(49,145,56,152)(57,193,64,186)(58,192,65,185)(59,191,66,184)(60,190,67,183)(61,189,68,196)(62,188,69,195)(63,187,70,194)(71,180,78,173)(72,179,79,172)(73,178,80,171)(74,177,81,170)(75,176,82,169)(76,175,83,182)(77,174,84,181)(85,221,92,214)(86,220,93,213)(87,219,94,212)(88,218,95,211)(89,217,96,224)(90,216,97,223)(91,215,98,222)(99,201,106,208)(100,200,107,207)(101,199,108,206)(102,198,109,205)(103,197,110,204)(104,210,111,203)(105,209,112,202), (1,43,22,36)(2,44,23,37)(3,45,24,38)(4,46,25,39)(5,47,26,40)(6,48,27,41)(7,49,28,42)(8,50,15,29)(9,51,16,30)(10,52,17,31)(11,53,18,32)(12,54,19,33)(13,55,20,34)(14,56,21,35)(57,106,71,85)(58,107,72,86)(59,108,73,87)(60,109,74,88)(61,110,75,89)(62,111,76,90)(63,112,77,91)(64,99,78,92)(65,100,79,93)(66,101,80,94)(67,102,81,95)(68,103,82,96)(69,104,83,97)(70,105,84,98)(113,163,128,153)(114,164,129,154)(115,165,130,141)(116,166,131,142)(117,167,132,143)(118,168,133,144)(119,155,134,145)(120,156,135,146)(121,157,136,147)(122,158,137,148)(123,159,138,149)(124,160,139,150)(125,161,140,151)(126,162,127,152)(169,217,196,204)(170,218,183,205)(171,219,184,206)(172,220,185,207)(173,221,186,208)(174,222,187,209)(175,223,188,210)(176,224,189,197)(177,211,190,198)(178,212,191,199)(179,213,192,200)(180,214,193,201)(181,215,194,202)(182,216,195,203) );
G=PermutationGroup([[(1,78),(2,79),(3,80),(4,81),(5,82),(6,83),(7,84),(8,71),(9,72),(10,73),(11,74),(12,75),(13,76),(14,77),(15,57),(16,58),(17,59),(18,60),(19,61),(20,62),(21,63),(22,64),(23,65),(24,66),(25,67),(26,68),(27,69),(28,70),(29,106),(30,107),(31,108),(32,109),(33,110),(34,111),(35,112),(36,99),(37,100),(38,101),(39,102),(40,103),(41,104),(42,105),(43,92),(44,93),(45,94),(46,95),(47,96),(48,97),(49,98),(50,85),(51,86),(52,87),(53,88),(54,89),(55,90),(56,91),(113,195),(114,196),(115,183),(116,184),(117,185),(118,186),(119,187),(120,188),(121,189),(122,190),(123,191),(124,192),(125,193),(126,194),(127,181),(128,182),(129,169),(130,170),(131,171),(132,172),(133,173),(134,174),(135,175),(136,176),(137,177),(138,178),(139,179),(140,180),(141,218),(142,219),(143,220),(144,221),(145,222),(146,223),(147,224),(148,211),(149,212),(150,213),(151,214),(152,215),(153,216),(154,217),(155,209),(156,210),(157,197),(158,198),(159,199),(160,200),(161,201),(162,202),(163,203),(164,204),(165,205),(166,206),(167,207),(168,208)], [(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)], [(1,133,8,140),(2,132,9,139),(3,131,10,138),(4,130,11,137),(5,129,12,136),(6,128,13,135),(7,127,14,134),(15,125,22,118),(16,124,23,117),(17,123,24,116),(18,122,25,115),(19,121,26,114),(20,120,27,113),(21,119,28,126),(29,168,36,161),(30,167,37,160),(31,166,38,159),(32,165,39,158),(33,164,40,157),(34,163,41,156),(35,162,42,155),(43,151,50,144),(44,150,51,143),(45,149,52,142),(46,148,53,141),(47,147,54,154),(48,146,55,153),(49,145,56,152),(57,193,64,186),(58,192,65,185),(59,191,66,184),(60,190,67,183),(61,189,68,196),(62,188,69,195),(63,187,70,194),(71,180,78,173),(72,179,79,172),(73,178,80,171),(74,177,81,170),(75,176,82,169),(76,175,83,182),(77,174,84,181),(85,221,92,214),(86,220,93,213),(87,219,94,212),(88,218,95,211),(89,217,96,224),(90,216,97,223),(91,215,98,222),(99,201,106,208),(100,200,107,207),(101,199,108,206),(102,198,109,205),(103,197,110,204),(104,210,111,203),(105,209,112,202)], [(1,43,22,36),(2,44,23,37),(3,45,24,38),(4,46,25,39),(5,47,26,40),(6,48,27,41),(7,49,28,42),(8,50,15,29),(9,51,16,30),(10,52,17,31),(11,53,18,32),(12,54,19,33),(13,55,20,34),(14,56,21,35),(57,106,71,85),(58,107,72,86),(59,108,73,87),(60,109,74,88),(61,110,75,89),(62,111,76,90),(63,112,77,91),(64,99,78,92),(65,100,79,93),(66,101,80,94),(67,102,81,95),(68,103,82,96),(69,104,83,97),(70,105,84,98),(113,163,128,153),(114,164,129,154),(115,165,130,141),(116,166,131,142),(117,167,132,143),(118,168,133,144),(119,155,134,145),(120,156,135,146),(121,157,136,147),(122,158,137,148),(123,159,138,149),(124,160,139,150),(125,161,140,151),(126,162,127,152),(169,217,196,204),(170,218,183,205),(171,219,184,206),(172,220,185,207),(173,221,186,208),(174,222,187,209),(175,223,188,210),(176,224,189,197),(177,211,190,198),(178,212,191,199),(179,213,192,200),(180,214,193,201),(181,215,194,202),(182,216,195,203)]])
C2×Dic7⋊C4 is a maximal subgroup of
(C2×Dic7)⋊C8 (C2×C28)⋊Q8 C14.(C4×Q8) Dic7⋊C42 C7⋊(C42⋊8C4) Dic7⋊C4⋊C4 C4⋊Dic7⋊7C4 C4⋊Dic7⋊8C4 C14.(C4×D4) (C2×Dic7)⋊Q8 C2.(C28⋊Q8) (C2×Dic7).Q8 (C2×C28).28D4 (C2×C4).Dic14 C14.(C4⋊Q8) D14⋊(C4⋊C4) D14⋊C4⋊C4 D14⋊C4⋊5C4 (C2×Dic7)⋊3D4 (C22×D7).9D4 (C22×D7).Q8 C28⋊4(C4⋊C4) (C2×C42).D7 (C2×C42)⋊D7 C24.44D14 C24.3D14 C24.4D14 C24.46D14 C24.6D14 C24.7D14 C24.9D14 C24.13D14 C24.14D14 Dic7⋊(C4⋊C4) C28⋊(C4⋊C4) (C4×Dic7)⋊8C4 C22.23(Q8×D7) (C2×C4)⋊Dic14 (C2×C28).287D4 (C2×C28).288D4 (C2×C4).44D28 (C2×C28).54D4 D14⋊C4⋊6C4 (C2×C28).289D4 (C2×C4).45D28 C24.62D14 C24.20D14 C14.C22≀C2 C2×C4×Dic14 C2×D7×C4⋊C4 C42.96D14 D4⋊5Dic14 C42.104D14 C42.108D14 C42.118D14 C14.682- 1+4 C14.342+ 1+4 C14.352+ 1+4 C14.752- 1+4 C14.522+ 1+4 C14.572+ 1+4 C14.802- 1+4 C14.822- 1+4 C2×C4×C7⋊D4 C14.1042- 1+4
C2×Dic7⋊C4 is a maximal quotient of
C28⋊4(C4⋊C4) C24.44D14 C24.46D14 C4.Dic7⋊C4 C28⋊(C4⋊C4) (C4×Dic7)⋊8C4 (C4×Dic7)⋊9C4 C28.(C2×Q8) C28.45(C4⋊C4) Dic7⋊C8⋊C2 Dic7⋊4M4(2) C28.439(C2×D4) C23.Dic14 C24.62D14
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 | D14 | D14 | Dic14 | C4×D7 | C7⋊D4 |
| kernel | C2×Dic7⋊C4 | Dic7⋊C4 | C22×Dic7 | C22×C28 | C2×Dic7 | C2×C14 | C2×C14 | C22×C4 | C2×C4 | C23 | C22 | C22 | C22 |
| # reps | 1 | 4 | 2 | 1 | 8 | 2 | 2 | 3 | 6 | 3 | 12 | 12 | 12 |
Matrix representation of C2×Dic7⋊C4 ►in GL4(𝔽29) generated by
| 28 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 0 | 11 | 1 |
| 0 | 0 | 28 | 0 |
| 28 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 |
| 0 | 0 | 22 | 7 |
| 0 | 0 | 26 | 7 |
| 12 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 |
| 0 | 0 | 16 | 24 |
| 0 | 0 | 5 | 13 |
G:=sub<GL(4,GF(29))| [28,0,0,0,0,28,0,0,0,0,1,0,0,0,0,1],[1,0,0,0,0,1,0,0,0,0,11,28,0,0,1,0],[28,0,0,0,0,28,0,0,0,0,22,26,0,0,7,7],[12,0,0,0,0,28,0,0,0,0,16,5,0,0,24,13] >;
C2×Dic7⋊C4 in GAP, Magma, Sage, TeX
C_2\times {\rm Dic}_7\rtimes C_4 % in TeX
G:=Group("C2xDic7:C4"); // GroupNames label
G:=SmallGroup(224,118);
// by ID
G=gap.SmallGroup(224,118);
# by ID
G:=PCGroup([6,-2,-2,-2,-2,-2,-7,96,362,50,6917]);
// Polycyclic
G:=Group<a,b,c,d|a^2=b^14=d^4=1,c^2=b^7,a*b=b*a,a*c=c*a,a*d=d*a,c*b*c^-1=b^-1,b*d=d*b,d*c*d^-1=b^7*c>;
// generators/relations