metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: D14⋊C8⋊18C2, C22⋊C8⋊12D7, (C4×D7).47D4, (C2×D28).8C4, C4.196(D4×D7), C14.8(C8○D4), C28.355(C2×D4), (C2×C8).163D14, C23.12(C4×D7), C28.55D4⋊2C2, (C2×Dic14).8C4, (C22×C4).78D14, (C2×C56).171C22, (C2×C28).822C23, C2.10(D28.C4), D14.1(C22⋊C4), Dic7.2(C22⋊C4), (C22×C28).93C22, C2.10(D28.2C4), (D7×C2×C8)⋊14C2, (C2×C4).31(C4×D7), (C2×C7⋊D4).4C4, (C2×C8⋊D7)⋊12C2, (C7×C22⋊C8)⋊16C2, (C2×C28).39(C2×C4), (C2×C4○D28).1C2, C14.9(C2×C22⋊C4), C2.10(D7×C22⋊C4), C22.104(C2×C4×D7), C7⋊1((C22×C8)⋊C2), (C2×C7⋊C8).301C22, (C2×C4×D7).274C22, (C2×C14).77(C22×C4), (C22×C14).40(C2×C4), (C2×Dic7).50(C2×C4), (C22×D7).12(C2×C4), (C2×C4).764(C22×D7), SmallGroup(448,261)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for D14⋊C8⋊C2
G = < a,b,c,d | a14=b2=c8=d2=1, bab=a-1, ac=ca, ad=da, cbc-1=a7b, dbd=bc4, dcd=a7c5 >
Subgroups: 764 in 158 conjugacy classes, 55 normal (47 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C8, C2×C4, C2×C4, D4, Q8, C23, C23, D7, C14, C14, C2×C8, C2×C8, M4(2), C22×C4, C22×C4, C2×D4, C2×Q8, C4○D4, Dic7, Dic7, C28, C28, D14, D14, C2×C14, C2×C14, C22⋊C8, C22⋊C8, C22×C8, C2×M4(2), C2×C4○D4, C7⋊C8, C56, Dic14, C4×D7, C4×D7, D28, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C22×D7, C22×C14, (C22×C8)⋊C2, C8×D7, C8⋊D7, C2×C7⋊C8, C2×C56, C2×Dic14, C2×C4×D7, C2×D28, C4○D28, C2×C7⋊D4, C22×C28, D14⋊C8, C28.55D4, C7×C22⋊C8, D7×C2×C8, C2×C8⋊D7, C2×C4○D28, D14⋊C8⋊C2
Quotients: C1, C2, C4, C22, C2×C4, D4, C23, D7, C22⋊C4, C22×C4, C2×D4, D14, C2×C22⋊C4, C8○D4, C4×D7, C22×D7, (C22×C8)⋊C2, C2×C4×D7, D4×D7, D7×C22⋊C4, D28.2C4, D28.C4, D14⋊C8⋊C2
►On 224 points
Generators in S224
(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 74)(2 73)(3 72)(4 71)(5 84)(6 83)(7 82)(8 81)(9 80)(10 79)(11 78)(12 77)(13 76)(14 75)(15 130)(16 129)(17 128)(18 127)(19 140)(20 139)(21 138)(22 137)(23 136)(24 135)(25 134)(26 133)(27 132)(28 131)(29 110)(30 109)(31 108)(32 107)(33 106)(34 105)(35 104)(36 103)(37 102)(38 101)(39 100)(40 99)(41 112)(42 111)(43 199)(44 198)(45 197)(46 210)(47 209)(48 208)(49 207)(50 206)(51 205)(52 204)(53 203)(54 202)(55 201)(56 200)(57 150)(58 149)(59 148)(60 147)(61 146)(62 145)(63 144)(64 143)(65 142)(66 141)(67 154)(68 153)(69 152)(70 151)(85 184)(86 183)(87 196)(88 195)(89 194)(90 193)(91 192)(92 191)(93 190)(94 189)(95 188)(96 187)(97 186)(98 185)(113 212)(114 211)(115 224)(116 223)(117 222)(118 221)(119 220)(120 219)(121 218)(122 217)(123 216)(124 215)(125 214)(126 213)(155 179)(156 178)(157 177)(158 176)(159 175)(160 174)(161 173)(162 172)(163 171)(164 170)(165 169)(166 182)(167 181)(168 180)
(1 86 162 120 49 57 30 27)(2 87 163 121 50 58 31 28)(3 88 164 122 51 59 32 15)(4 89 165 123 52 60 33 16)(5 90 166 124 53 61 34 17)(6 91 167 125 54 62 35 18)(7 92 168 126 55 63 36 19)(8 93 155 113 56 64 37 20)(9 94 156 114 43 65 38 21)(10 95 157 115 44 66 39 22)(11 96 158 116 45 67 40 23)(12 97 159 117 46 68 41 24)(13 98 160 118 47 69 42 25)(14 85 161 119 48 70 29 26)(71 187 169 223 204 154 106 136)(72 188 170 224 205 141 107 137)(73 189 171 211 206 142 108 138)(74 190 172 212 207 143 109 139)(75 191 173 213 208 144 110 140)(76 192 174 214 209 145 111 127)(77 193 175 215 210 146 112 128)(78 194 176 216 197 147 99 129)(79 195 177 217 198 148 100 130)(80 196 178 218 199 149 101 131)(81 183 179 219 200 150 102 132)(82 184 180 220 201 151 103 133)(83 185 181 221 202 152 104 134)(84 186 182 222 203 153 105 135)
(1 180)(2 181)(3 182)(4 169)(5 170)(6 171)(7 172)(8 173)(9 174)(10 175)(11 176)(12 177)(13 178)(14 179)(15 146)(16 147)(17 148)(18 149)(19 150)(20 151)(21 152)(22 153)(23 154)(24 141)(25 142)(26 143)(27 144)(28 145)(29 81)(30 82)(31 83)(32 84)(33 71)(34 72)(35 73)(36 74)(37 75)(38 76)(39 77)(40 78)(41 79)(42 80)(43 111)(44 112)(45 99)(46 100)(47 101)(48 102)(49 103)(50 104)(51 105)(52 106)(53 107)(54 108)(55 109)(56 110)(57 213)(58 214)(59 215)(60 216)(61 217)(62 218)(63 219)(64 220)(65 221)(66 222)(67 223)(68 224)(69 211)(70 212)(85 139)(86 140)(87 127)(88 128)(89 129)(90 130)(91 131)(92 132)(93 133)(94 134)(95 135)(96 136)(97 137)(98 138)(113 184)(114 185)(115 186)(116 187)(117 188)(118 189)(119 190)(120 191)(121 192)(122 193)(123 194)(124 195)(125 196)(126 183)(155 208)(156 209)(157 210)(158 197)(159 198)(160 199)(161 200)(162 201)(163 202)(164 203)(165 204)(166 205)(167 206)(168 207)
G:=sub<Sym(224)| (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), (1,74)(2,73)(3,72)(4,71)(5,84)(6,83)(7,82)(8,81)(9,80)(10,79)(11,78)(12,77)(13,76)(14,75)(15,130)(16,129)(17,128)(18,127)(19,140)(20,139)(21,138)(22,137)(23,136)(24,135)(25,134)(26,133)(27,132)(28,131)(29,110)(30,109)(31,108)(32,107)(33,106)(34,105)(35,104)(36,103)(37,102)(38,101)(39,100)(40,99)(41,112)(42,111)(43,199)(44,198)(45,197)(46,210)(47,209)(48,208)(49,207)(50,206)(51,205)(52,204)(53,203)(54,202)(55,201)(56,200)(57,150)(58,149)(59,148)(60,147)(61,146)(62,145)(63,144)(64,143)(65,142)(66,141)(67,154)(68,153)(69,152)(70,151)(85,184)(86,183)(87,196)(88,195)(89,194)(90,193)(91,192)(92,191)(93,190)(94,189)(95,188)(96,187)(97,186)(98,185)(113,212)(114,211)(115,224)(116,223)(117,222)(118,221)(119,220)(120,219)(121,218)(122,217)(123,216)(124,215)(125,214)(126,213)(155,179)(156,178)(157,177)(158,176)(159,175)(160,174)(161,173)(162,172)(163,171)(164,170)(165,169)(166,182)(167,181)(168,180), (1,86,162,120,49,57,30,27)(2,87,163,121,50,58,31,28)(3,88,164,122,51,59,32,15)(4,89,165,123,52,60,33,16)(5,90,166,124,53,61,34,17)(6,91,167,125,54,62,35,18)(7,92,168,126,55,63,36,19)(8,93,155,113,56,64,37,20)(9,94,156,114,43,65,38,21)(10,95,157,115,44,66,39,22)(11,96,158,116,45,67,40,23)(12,97,159,117,46,68,41,24)(13,98,160,118,47,69,42,25)(14,85,161,119,48,70,29,26)(71,187,169,223,204,154,106,136)(72,188,170,224,205,141,107,137)(73,189,171,211,206,142,108,138)(74,190,172,212,207,143,109,139)(75,191,173,213,208,144,110,140)(76,192,174,214,209,145,111,127)(77,193,175,215,210,146,112,128)(78,194,176,216,197,147,99,129)(79,195,177,217,198,148,100,130)(80,196,178,218,199,149,101,131)(81,183,179,219,200,150,102,132)(82,184,180,220,201,151,103,133)(83,185,181,221,202,152,104,134)(84,186,182,222,203,153,105,135), (1,180)(2,181)(3,182)(4,169)(5,170)(6,171)(7,172)(8,173)(9,174)(10,175)(11,176)(12,177)(13,178)(14,179)(15,146)(16,147)(17,148)(18,149)(19,150)(20,151)(21,152)(22,153)(23,154)(24,141)(25,142)(26,143)(27,144)(28,145)(29,81)(30,82)(31,83)(32,84)(33,71)(34,72)(35,73)(36,74)(37,75)(38,76)(39,77)(40,78)(41,79)(42,80)(43,111)(44,112)(45,99)(46,100)(47,101)(48,102)(49,103)(50,104)(51,105)(52,106)(53,107)(54,108)(55,109)(56,110)(57,213)(58,214)(59,215)(60,216)(61,217)(62,218)(63,219)(64,220)(65,221)(66,222)(67,223)(68,224)(69,211)(70,212)(85,139)(86,140)(87,127)(88,128)(89,129)(90,130)(91,131)(92,132)(93,133)(94,134)(95,135)(96,136)(97,137)(98,138)(113,184)(114,185)(115,186)(116,187)(117,188)(118,189)(119,190)(120,191)(121,192)(122,193)(123,194)(124,195)(125,196)(126,183)(155,208)(156,209)(157,210)(158,197)(159,198)(160,199)(161,200)(162,201)(163,202)(164,203)(165,204)(166,205)(167,206)(168,207)>;
G:=Group( (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), (1,74)(2,73)(3,72)(4,71)(5,84)(6,83)(7,82)(8,81)(9,80)(10,79)(11,78)(12,77)(13,76)(14,75)(15,130)(16,129)(17,128)(18,127)(19,140)(20,139)(21,138)(22,137)(23,136)(24,135)(25,134)(26,133)(27,132)(28,131)(29,110)(30,109)(31,108)(32,107)(33,106)(34,105)(35,104)(36,103)(37,102)(38,101)(39,100)(40,99)(41,112)(42,111)(43,199)(44,198)(45,197)(46,210)(47,209)(48,208)(49,207)(50,206)(51,205)(52,204)(53,203)(54,202)(55,201)(56,200)(57,150)(58,149)(59,148)(60,147)(61,146)(62,145)(63,144)(64,143)(65,142)(66,141)(67,154)(68,153)(69,152)(70,151)(85,184)(86,183)(87,196)(88,195)(89,194)(90,193)(91,192)(92,191)(93,190)(94,189)(95,188)(96,187)(97,186)(98,185)(113,212)(114,211)(115,224)(116,223)(117,222)(118,221)(119,220)(120,219)(121,218)(122,217)(123,216)(124,215)(125,214)(126,213)(155,179)(156,178)(157,177)(158,176)(159,175)(160,174)(161,173)(162,172)(163,171)(164,170)(165,169)(166,182)(167,181)(168,180), (1,86,162,120,49,57,30,27)(2,87,163,121,50,58,31,28)(3,88,164,122,51,59,32,15)(4,89,165,123,52,60,33,16)(5,90,166,124,53,61,34,17)(6,91,167,125,54,62,35,18)(7,92,168,126,55,63,36,19)(8,93,155,113,56,64,37,20)(9,94,156,114,43,65,38,21)(10,95,157,115,44,66,39,22)(11,96,158,116,45,67,40,23)(12,97,159,117,46,68,41,24)(13,98,160,118,47,69,42,25)(14,85,161,119,48,70,29,26)(71,187,169,223,204,154,106,136)(72,188,170,224,205,141,107,137)(73,189,171,211,206,142,108,138)(74,190,172,212,207,143,109,139)(75,191,173,213,208,144,110,140)(76,192,174,214,209,145,111,127)(77,193,175,215,210,146,112,128)(78,194,176,216,197,147,99,129)(79,195,177,217,198,148,100,130)(80,196,178,218,199,149,101,131)(81,183,179,219,200,150,102,132)(82,184,180,220,201,151,103,133)(83,185,181,221,202,152,104,134)(84,186,182,222,203,153,105,135), (1,180)(2,181)(3,182)(4,169)(5,170)(6,171)(7,172)(8,173)(9,174)(10,175)(11,176)(12,177)(13,178)(14,179)(15,146)(16,147)(17,148)(18,149)(19,150)(20,151)(21,152)(22,153)(23,154)(24,141)(25,142)(26,143)(27,144)(28,145)(29,81)(30,82)(31,83)(32,84)(33,71)(34,72)(35,73)(36,74)(37,75)(38,76)(39,77)(40,78)(41,79)(42,80)(43,111)(44,112)(45,99)(46,100)(47,101)(48,102)(49,103)(50,104)(51,105)(52,106)(53,107)(54,108)(55,109)(56,110)(57,213)(58,214)(59,215)(60,216)(61,217)(62,218)(63,219)(64,220)(65,221)(66,222)(67,223)(68,224)(69,211)(70,212)(85,139)(86,140)(87,127)(88,128)(89,129)(90,130)(91,131)(92,132)(93,133)(94,134)(95,135)(96,136)(97,137)(98,138)(113,184)(114,185)(115,186)(116,187)(117,188)(118,189)(119,190)(120,191)(121,192)(122,193)(123,194)(124,195)(125,196)(126,183)(155,208)(156,209)(157,210)(158,197)(159,198)(160,199)(161,200)(162,201)(163,202)(164,203)(165,204)(166,205)(167,206)(168,207) );
G=PermutationGroup([[(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)], [(1,74),(2,73),(3,72),(4,71),(5,84),(6,83),(7,82),(8,81),(9,80),(10,79),(11,78),(12,77),(13,76),(14,75),(15,130),(16,129),(17,128),(18,127),(19,140),(20,139),(21,138),(22,137),(23,136),(24,135),(25,134),(26,133),(27,132),(28,131),(29,110),(30,109),(31,108),(32,107),(33,106),(34,105),(35,104),(36,103),(37,102),(38,101),(39,100),(40,99),(41,112),(42,111),(43,199),(44,198),(45,197),(46,210),(47,209),(48,208),(49,207),(50,206),(51,205),(52,204),(53,203),(54,202),(55,201),(56,200),(57,150),(58,149),(59,148),(60,147),(61,146),(62,145),(63,144),(64,143),(65,142),(66,141),(67,154),(68,153),(69,152),(70,151),(85,184),(86,183),(87,196),(88,195),(89,194),(90,193),(91,192),(92,191),(93,190),(94,189),(95,188),(96,187),(97,186),(98,185),(113,212),(114,211),(115,224),(116,223),(117,222),(118,221),(119,220),(120,219),(121,218),(122,217),(123,216),(124,215),(125,214),(126,213),(155,179),(156,178),(157,177),(158,176),(159,175),(160,174),(161,173),(162,172),(163,171),(164,170),(165,169),(166,182),(167,181),(168,180)], [(1,86,162,120,49,57,30,27),(2,87,163,121,50,58,31,28),(3,88,164,122,51,59,32,15),(4,89,165,123,52,60,33,16),(5,90,166,124,53,61,34,17),(6,91,167,125,54,62,35,18),(7,92,168,126,55,63,36,19),(8,93,155,113,56,64,37,20),(9,94,156,114,43,65,38,21),(10,95,157,115,44,66,39,22),(11,96,158,116,45,67,40,23),(12,97,159,117,46,68,41,24),(13,98,160,118,47,69,42,25),(14,85,161,119,48,70,29,26),(71,187,169,223,204,154,106,136),(72,188,170,224,205,141,107,137),(73,189,171,211,206,142,108,138),(74,190,172,212,207,143,109,139),(75,191,173,213,208,144,110,140),(76,192,174,214,209,145,111,127),(77,193,175,215,210,146,112,128),(78,194,176,216,197,147,99,129),(79,195,177,217,198,148,100,130),(80,196,178,218,199,149,101,131),(81,183,179,219,200,150,102,132),(82,184,180,220,201,151,103,133),(83,185,181,221,202,152,104,134),(84,186,182,222,203,153,105,135)], [(1,180),(2,181),(3,182),(4,169),(5,170),(6,171),(7,172),(8,173),(9,174),(10,175),(11,176),(12,177),(13,178),(14,179),(15,146),(16,147),(17,148),(18,149),(19,150),(20,151),(21,152),(22,153),(23,154),(24,141),(25,142),(26,143),(27,144),(28,145),(29,81),(30,82),(31,83),(32,84),(33,71),(34,72),(35,73),(36,74),(37,75),(38,76),(39,77),(40,78),(41,79),(42,80),(43,111),(44,112),(45,99),(46,100),(47,101),(48,102),(49,103),(50,104),(51,105),(52,106),(53,107),(54,108),(55,109),(56,110),(57,213),(58,214),(59,215),(60,216),(61,217),(62,218),(63,219),(64,220),(65,221),(66,222),(67,223),(68,224),(69,211),(70,212),(85,139),(86,140),(87,127),(88,128),(89,129),(90,130),(91,131),(92,132),(93,133),(94,134),(95,135),(96,136),(97,137),(98,138),(113,184),(114,185),(115,186),(116,187),(117,188),(118,189),(119,190),(120,191),(121,192),(122,193),(123,194),(124,195),(125,196),(126,183),(155,208),(156,209),(157,210),(158,197),(159,198),(160,199),(161,200),(162,201),(163,202),(164,203),(165,204),(166,205),(167,206),(168,207)]])
88 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 7A | 7B | 7C | 8A | 8B | 8C | 8D | 8E | 8F | 8G | 8H | 8I | 8J | 8K | 8L | 14A | ··· | 14I | 14J | ··· | 14O | 28A | ··· | 28L | 28M | ··· | 28R | 56A | ··· | 56X |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 | 56 | ··· | 56 |
| size | 1 | 1 | 1 | 1 | 4 | 14 | 14 | 28 | 1 | 1 | 1 | 1 | 4 | 14 | 14 | 28 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 14 | 14 | 14 | 14 | 28 | 28 | 2 | ··· | 2 | 4 | ··· | 4 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 |
88 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | ||||||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C4 | C4 | C4 | D4 | D7 | D14 | D14 | C8○D4 | C4×D7 | C4×D7 | D28.2C4 | D4×D7 | D28.C4 |
| kernel | D14⋊C8⋊C2 | D14⋊C8 | C28.55D4 | C7×C22⋊C8 | D7×C2×C8 | C2×C8⋊D7 | C2×C4○D28 | C2×Dic14 | C2×D28 | C2×C7⋊D4 | C4×D7 | C22⋊C8 | C2×C8 | C22×C4 | C14 | C2×C4 | C23 | C2 | C4 | C2 |
| # reps | 1 | 2 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 4 | 4 | 3 | 6 | 3 | 8 | 6 | 6 | 24 | 6 | 6 |
Matrix representation of D14⋊C8⋊C2 ►in GL6(𝔽113)
| 112 | 10 | 0 | 0 | 0 | 0 |
| 71 | 80 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 112 | 0 |
| 0 | 0 | 0 | 0 | 0 | 112 |
| 9 | 112 | 0 | 0 | 0 | 0 |
| 80 | 104 | 0 | 0 | 0 | 0 |
| 0 | 0 | 15 | 9 | 0 | 0 |
| 0 | 0 | 63 | 98 | 0 | 0 |
| 0 | 0 | 0 | 0 | 82 | 60 |
| 0 | 0 | 0 | 0 | 97 | 31 |
| 15 | 0 | 0 | 0 | 0 | 0 |
| 0 | 15 | 0 | 0 | 0 | 0 |
| 0 | 0 | 18 | 56 | 0 | 0 |
| 0 | 0 | 53 | 95 | 0 | 0 |
| 0 | 0 | 0 | 0 | 30 | 43 |
| 0 | 0 | 0 | 0 | 50 | 83 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 91 | 0 | 0 |
| 0 | 0 | 0 | 112 | 0 | 0 |
| 0 | 0 | 0 | 0 | 31 | 53 |
| 0 | 0 | 0 | 0 | 16 | 82 |
G:=sub<GL(6,GF(113))| [112,71,0,0,0,0,10,80,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,112,0,0,0,0,0,0,112],[9,80,0,0,0,0,112,104,0,0,0,0,0,0,15,63,0,0,0,0,9,98,0,0,0,0,0,0,82,97,0,0,0,0,60,31],[15,0,0,0,0,0,0,15,0,0,0,0,0,0,18,53,0,0,0,0,56,95,0,0,0,0,0,0,30,50,0,0,0,0,43,83],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,91,112,0,0,0,0,0,0,31,16,0,0,0,0,53,82] >;
D14⋊C8⋊C2 in GAP, Magma, Sage, TeX
D_{14}\rtimes C_8\rtimes C_2 % in TeX
G:=Group("D14:C8:C2"); // GroupNames label
G:=SmallGroup(448,261);
// by ID
G=gap.SmallGroup(448,261);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,477,219,58,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^14=b^2=c^8=d^2=1,b*a*b=a^-1,a*c=c*a,a*d=d*a,c*b*c^-1=a^7*b,d*b*d=b*c^4,d*c*d=a^7*c^5>;
// generators/relations