direct product, metabelian, nilpotent (class 2), monomial, 2-elementary
Aliases: C14×C22.D4, (C23×C28)⋊7C2, (C23×C4)⋊6C14, C23.49(C7×D4), C24.35(C2×C14), C22.61(D4×C14), (C2×C28).657C23, (C2×C14).344C24, (C22×C28)⋊59C22, (C22×D4).10C14, C14.183(C22×D4), (C22×C14).171D4, C23.5(C22×C14), (D4×C14).316C22, (C23×C14).92C22, C22.18(C23×C14), (C22×C14).259C23, C2.7(D4×C2×C14), (C14×C4⋊C4)⋊43C2, (C2×C4⋊C4)⋊16C14, C4⋊C4⋊11(C2×C14), (D4×C2×C14).23C2, C2.7(C14×C4○D4), (C7×C4⋊C4)⋊67C22, (C2×C22⋊C4)⋊10C14, C22⋊C4⋊12(C2×C14), (C14×C22⋊C4)⋊30C2, (C22×C4)⋊17(C2×C14), (C2×D4).61(C2×C14), C14.226(C2×C4○D4), (C2×C14).415(C2×D4), C22.31(C7×C4○D4), (C7×C22⋊C4)⋊66C22, (C2×C4).13(C22×C14), (C2×C14).231(C4○D4), SmallGroup(448,1307)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C14×C22.D4
G = < a,b,c,d,e | a14=b2=c2=d4=e2=1, ab=ba, ac=ca, ad=da, ae=ea, dbd-1=ebe=bc=cb, cd=dc, ce=ec, ede=cd-1 >
Subgroups: 530 in 342 conjugacy classes, 178 normal (22 characteristic)
C1, C2, C2, C2, C4, C22, C22, C22, C7, C2×C4, C2×C4, D4, C23, C23, C23, C14, C14, C14, C22⋊C4, C4⋊C4, C22×C4, C22×C4, C22×C4, C2×D4, C2×D4, C24, C28, C2×C14, C2×C14, C2×C14, C2×C22⋊C4, C2×C22⋊C4, C2×C4⋊C4, C22.D4, C23×C4, C22×D4, C2×C28, C2×C28, C7×D4, C22×C14, C22×C14, C22×C14, C2×C22.D4, C7×C22⋊C4, C7×C4⋊C4, C22×C28, C22×C28, C22×C28, D4×C14, D4×C14, C23×C14, C14×C22⋊C4, C14×C22⋊C4, C14×C4⋊C4, C7×C22.D4, C23×C28, D4×C2×C14, C14×C22.D4
Quotients: C1, C2, C22, C7, D4, C23, C14, C2×D4, C4○D4, C24, C2×C14, C22.D4, C22×D4, C2×C4○D4, C7×D4, C22×C14, C2×C22.D4, D4×C14, C7×C4○D4, C23×C14, C7×C22.D4, D4×C2×C14, C14×C4○D4, C14×C22.D4
►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)
(15 178)(16 179)(17 180)(18 181)(19 182)(20 169)(21 170)(22 171)(23 172)(24 173)(25 174)(26 175)(27 176)(28 177)(29 152)(30 153)(31 154)(32 141)(33 142)(34 143)(35 144)(36 145)(37 146)(38 147)(39 148)(40 149)(41 150)(42 151)(85 104)(86 105)(87 106)(88 107)(89 108)(90 109)(91 110)(92 111)(93 112)(94 99)(95 100)(96 101)(97 102)(98 103)(127 158)(128 159)(129 160)(130 161)(131 162)(132 163)(133 164)(134 165)(135 166)(136 167)(137 168)(138 155)(139 156)(140 157)
(1 189)(2 190)(3 191)(4 192)(5 193)(6 194)(7 195)(8 196)(9 183)(10 184)(11 185)(12 186)(13 187)(14 188)(15 178)(16 179)(17 180)(18 181)(19 182)(20 169)(21 170)(22 171)(23 172)(24 173)(25 174)(26 175)(27 176)(28 177)(29 152)(30 153)(31 154)(32 141)(33 142)(34 143)(35 144)(36 145)(37 146)(38 147)(39 148)(40 149)(41 150)(42 151)(43 219)(44 220)(45 221)(46 222)(47 223)(48 224)(49 211)(50 212)(51 213)(52 214)(53 215)(54 216)(55 217)(56 218)(57 125)(58 126)(59 113)(60 114)(61 115)(62 116)(63 117)(64 118)(65 119)(66 120)(67 121)(68 122)(69 123)(70 124)(71 198)(72 199)(73 200)(74 201)(75 202)(76 203)(77 204)(78 205)(79 206)(80 207)(81 208)(82 209)(83 210)(84 197)(85 104)(86 105)(87 106)(88 107)(89 108)(90 109)(91 110)(92 111)(93 112)(94 99)(95 100)(96 101)(97 102)(98 103)(127 158)(128 159)(129 160)(130 161)(131 162)(132 163)(133 164)(134 165)(135 166)(136 167)(137 168)(138 155)(139 156)(140 157)
(1 155 223 147)(2 156 224 148)(3 157 211 149)(4 158 212 150)(5 159 213 151)(6 160 214 152)(7 161 215 153)(8 162 216 154)(9 163 217 141)(10 164 218 142)(11 165 219 143)(12 166 220 144)(13 167 221 145)(14 168 222 146)(15 207 103 117)(16 208 104 118)(17 209 105 119)(18 210 106 120)(19 197 107 121)(20 198 108 122)(21 199 109 123)(22 200 110 124)(23 201 111 125)(24 202 112 126)(25 203 99 113)(26 204 100 114)(27 205 101 115)(28 206 102 116)(29 194 129 52)(30 195 130 53)(31 196 131 54)(32 183 132 55)(33 184 133 56)(34 185 134 43)(35 186 135 44)(36 187 136 45)(37 188 137 46)(38 189 138 47)(39 190 139 48)(40 191 140 49)(41 192 127 50)(42 193 128 51)(57 172 74 92)(58 173 75 93)(59 174 76 94)(60 175 77 95)(61 176 78 96)(62 177 79 97)(63 178 80 98)(64 179 81 85)(65 180 82 86)(66 181 83 87)(67 182 84 88)(68 169 71 89)(69 170 72 90)(70 171 73 91)
(1 17)(2 18)(3 19)(4 20)(5 21)(6 22)(7 23)(8 24)(9 25)(10 26)(11 27)(12 28)(13 15)(14 16)(29 200)(30 201)(31 202)(32 203)(33 204)(34 205)(35 206)(36 207)(37 208)(38 209)(39 210)(40 197)(41 198)(42 199)(43 96)(44 97)(45 98)(46 85)(47 86)(48 87)(49 88)(50 89)(51 90)(52 91)(53 92)(54 93)(55 94)(56 95)(57 161)(58 162)(59 163)(60 164)(61 165)(62 166)(63 167)(64 168)(65 155)(66 156)(67 157)(68 158)(69 159)(70 160)(71 150)(72 151)(73 152)(74 153)(75 154)(76 141)(77 142)(78 143)(79 144)(80 145)(81 146)(82 147)(83 148)(84 149)(99 217)(100 218)(101 219)(102 220)(103 221)(104 222)(105 223)(106 224)(107 211)(108 212)(109 213)(110 214)(111 215)(112 216)(113 132)(114 133)(115 134)(116 135)(117 136)(118 137)(119 138)(120 139)(121 140)(122 127)(123 128)(124 129)(125 130)(126 131)(169 192)(170 193)(171 194)(172 195)(173 196)(174 183)(175 184)(176 185)(177 186)(178 187)(179 188)(180 189)(181 190)(182 191)
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), (15,178)(16,179)(17,180)(18,181)(19,182)(20,169)(21,170)(22,171)(23,172)(24,173)(25,174)(26,175)(27,176)(28,177)(29,152)(30,153)(31,154)(32,141)(33,142)(34,143)(35,144)(36,145)(37,146)(38,147)(39,148)(40,149)(41,150)(42,151)(85,104)(86,105)(87,106)(88,107)(89,108)(90,109)(91,110)(92,111)(93,112)(94,99)(95,100)(96,101)(97,102)(98,103)(127,158)(128,159)(129,160)(130,161)(131,162)(132,163)(133,164)(134,165)(135,166)(136,167)(137,168)(138,155)(139,156)(140,157), (1,189)(2,190)(3,191)(4,192)(5,193)(6,194)(7,195)(8,196)(9,183)(10,184)(11,185)(12,186)(13,187)(14,188)(15,178)(16,179)(17,180)(18,181)(19,182)(20,169)(21,170)(22,171)(23,172)(24,173)(25,174)(26,175)(27,176)(28,177)(29,152)(30,153)(31,154)(32,141)(33,142)(34,143)(35,144)(36,145)(37,146)(38,147)(39,148)(40,149)(41,150)(42,151)(43,219)(44,220)(45,221)(46,222)(47,223)(48,224)(49,211)(50,212)(51,213)(52,214)(53,215)(54,216)(55,217)(56,218)(57,125)(58,126)(59,113)(60,114)(61,115)(62,116)(63,117)(64,118)(65,119)(66,120)(67,121)(68,122)(69,123)(70,124)(71,198)(72,199)(73,200)(74,201)(75,202)(76,203)(77,204)(78,205)(79,206)(80,207)(81,208)(82,209)(83,210)(84,197)(85,104)(86,105)(87,106)(88,107)(89,108)(90,109)(91,110)(92,111)(93,112)(94,99)(95,100)(96,101)(97,102)(98,103)(127,158)(128,159)(129,160)(130,161)(131,162)(132,163)(133,164)(134,165)(135,166)(136,167)(137,168)(138,155)(139,156)(140,157), (1,155,223,147)(2,156,224,148)(3,157,211,149)(4,158,212,150)(5,159,213,151)(6,160,214,152)(7,161,215,153)(8,162,216,154)(9,163,217,141)(10,164,218,142)(11,165,219,143)(12,166,220,144)(13,167,221,145)(14,168,222,146)(15,207,103,117)(16,208,104,118)(17,209,105,119)(18,210,106,120)(19,197,107,121)(20,198,108,122)(21,199,109,123)(22,200,110,124)(23,201,111,125)(24,202,112,126)(25,203,99,113)(26,204,100,114)(27,205,101,115)(28,206,102,116)(29,194,129,52)(30,195,130,53)(31,196,131,54)(32,183,132,55)(33,184,133,56)(34,185,134,43)(35,186,135,44)(36,187,136,45)(37,188,137,46)(38,189,138,47)(39,190,139,48)(40,191,140,49)(41,192,127,50)(42,193,128,51)(57,172,74,92)(58,173,75,93)(59,174,76,94)(60,175,77,95)(61,176,78,96)(62,177,79,97)(63,178,80,98)(64,179,81,85)(65,180,82,86)(66,181,83,87)(67,182,84,88)(68,169,71,89)(69,170,72,90)(70,171,73,91), (1,17)(2,18)(3,19)(4,20)(5,21)(6,22)(7,23)(8,24)(9,25)(10,26)(11,27)(12,28)(13,15)(14,16)(29,200)(30,201)(31,202)(32,203)(33,204)(34,205)(35,206)(36,207)(37,208)(38,209)(39,210)(40,197)(41,198)(42,199)(43,96)(44,97)(45,98)(46,85)(47,86)(48,87)(49,88)(50,89)(51,90)(52,91)(53,92)(54,93)(55,94)(56,95)(57,161)(58,162)(59,163)(60,164)(61,165)(62,166)(63,167)(64,168)(65,155)(66,156)(67,157)(68,158)(69,159)(70,160)(71,150)(72,151)(73,152)(74,153)(75,154)(76,141)(77,142)(78,143)(79,144)(80,145)(81,146)(82,147)(83,148)(84,149)(99,217)(100,218)(101,219)(102,220)(103,221)(104,222)(105,223)(106,224)(107,211)(108,212)(109,213)(110,214)(111,215)(112,216)(113,132)(114,133)(115,134)(116,135)(117,136)(118,137)(119,138)(120,139)(121,140)(122,127)(123,128)(124,129)(125,130)(126,131)(169,192)(170,193)(171,194)(172,195)(173,196)(174,183)(175,184)(176,185)(177,186)(178,187)(179,188)(180,189)(181,190)(182,191)>;
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), (15,178)(16,179)(17,180)(18,181)(19,182)(20,169)(21,170)(22,171)(23,172)(24,173)(25,174)(26,175)(27,176)(28,177)(29,152)(30,153)(31,154)(32,141)(33,142)(34,143)(35,144)(36,145)(37,146)(38,147)(39,148)(40,149)(41,150)(42,151)(85,104)(86,105)(87,106)(88,107)(89,108)(90,109)(91,110)(92,111)(93,112)(94,99)(95,100)(96,101)(97,102)(98,103)(127,158)(128,159)(129,160)(130,161)(131,162)(132,163)(133,164)(134,165)(135,166)(136,167)(137,168)(138,155)(139,156)(140,157), (1,189)(2,190)(3,191)(4,192)(5,193)(6,194)(7,195)(8,196)(9,183)(10,184)(11,185)(12,186)(13,187)(14,188)(15,178)(16,179)(17,180)(18,181)(19,182)(20,169)(21,170)(22,171)(23,172)(24,173)(25,174)(26,175)(27,176)(28,177)(29,152)(30,153)(31,154)(32,141)(33,142)(34,143)(35,144)(36,145)(37,146)(38,147)(39,148)(40,149)(41,150)(42,151)(43,219)(44,220)(45,221)(46,222)(47,223)(48,224)(49,211)(50,212)(51,213)(52,214)(53,215)(54,216)(55,217)(56,218)(57,125)(58,126)(59,113)(60,114)(61,115)(62,116)(63,117)(64,118)(65,119)(66,120)(67,121)(68,122)(69,123)(70,124)(71,198)(72,199)(73,200)(74,201)(75,202)(76,203)(77,204)(78,205)(79,206)(80,207)(81,208)(82,209)(83,210)(84,197)(85,104)(86,105)(87,106)(88,107)(89,108)(90,109)(91,110)(92,111)(93,112)(94,99)(95,100)(96,101)(97,102)(98,103)(127,158)(128,159)(129,160)(130,161)(131,162)(132,163)(133,164)(134,165)(135,166)(136,167)(137,168)(138,155)(139,156)(140,157), (1,155,223,147)(2,156,224,148)(3,157,211,149)(4,158,212,150)(5,159,213,151)(6,160,214,152)(7,161,215,153)(8,162,216,154)(9,163,217,141)(10,164,218,142)(11,165,219,143)(12,166,220,144)(13,167,221,145)(14,168,222,146)(15,207,103,117)(16,208,104,118)(17,209,105,119)(18,210,106,120)(19,197,107,121)(20,198,108,122)(21,199,109,123)(22,200,110,124)(23,201,111,125)(24,202,112,126)(25,203,99,113)(26,204,100,114)(27,205,101,115)(28,206,102,116)(29,194,129,52)(30,195,130,53)(31,196,131,54)(32,183,132,55)(33,184,133,56)(34,185,134,43)(35,186,135,44)(36,187,136,45)(37,188,137,46)(38,189,138,47)(39,190,139,48)(40,191,140,49)(41,192,127,50)(42,193,128,51)(57,172,74,92)(58,173,75,93)(59,174,76,94)(60,175,77,95)(61,176,78,96)(62,177,79,97)(63,178,80,98)(64,179,81,85)(65,180,82,86)(66,181,83,87)(67,182,84,88)(68,169,71,89)(69,170,72,90)(70,171,73,91), (1,17)(2,18)(3,19)(4,20)(5,21)(6,22)(7,23)(8,24)(9,25)(10,26)(11,27)(12,28)(13,15)(14,16)(29,200)(30,201)(31,202)(32,203)(33,204)(34,205)(35,206)(36,207)(37,208)(38,209)(39,210)(40,197)(41,198)(42,199)(43,96)(44,97)(45,98)(46,85)(47,86)(48,87)(49,88)(50,89)(51,90)(52,91)(53,92)(54,93)(55,94)(56,95)(57,161)(58,162)(59,163)(60,164)(61,165)(62,166)(63,167)(64,168)(65,155)(66,156)(67,157)(68,158)(69,159)(70,160)(71,150)(72,151)(73,152)(74,153)(75,154)(76,141)(77,142)(78,143)(79,144)(80,145)(81,146)(82,147)(83,148)(84,149)(99,217)(100,218)(101,219)(102,220)(103,221)(104,222)(105,223)(106,224)(107,211)(108,212)(109,213)(110,214)(111,215)(112,216)(113,132)(114,133)(115,134)(116,135)(117,136)(118,137)(119,138)(120,139)(121,140)(122,127)(123,128)(124,129)(125,130)(126,131)(169,192)(170,193)(171,194)(172,195)(173,196)(174,183)(175,184)(176,185)(177,186)(178,187)(179,188)(180,189)(181,190)(182,191) );
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)], [(15,178),(16,179),(17,180),(18,181),(19,182),(20,169),(21,170),(22,171),(23,172),(24,173),(25,174),(26,175),(27,176),(28,177),(29,152),(30,153),(31,154),(32,141),(33,142),(34,143),(35,144),(36,145),(37,146),(38,147),(39,148),(40,149),(41,150),(42,151),(85,104),(86,105),(87,106),(88,107),(89,108),(90,109),(91,110),(92,111),(93,112),(94,99),(95,100),(96,101),(97,102),(98,103),(127,158),(128,159),(129,160),(130,161),(131,162),(132,163),(133,164),(134,165),(135,166),(136,167),(137,168),(138,155),(139,156),(140,157)], [(1,189),(2,190),(3,191),(4,192),(5,193),(6,194),(7,195),(8,196),(9,183),(10,184),(11,185),(12,186),(13,187),(14,188),(15,178),(16,179),(17,180),(18,181),(19,182),(20,169),(21,170),(22,171),(23,172),(24,173),(25,174),(26,175),(27,176),(28,177),(29,152),(30,153),(31,154),(32,141),(33,142),(34,143),(35,144),(36,145),(37,146),(38,147),(39,148),(40,149),(41,150),(42,151),(43,219),(44,220),(45,221),(46,222),(47,223),(48,224),(49,211),(50,212),(51,213),(52,214),(53,215),(54,216),(55,217),(56,218),(57,125),(58,126),(59,113),(60,114),(61,115),(62,116),(63,117),(64,118),(65,119),(66,120),(67,121),(68,122),(69,123),(70,124),(71,198),(72,199),(73,200),(74,201),(75,202),(76,203),(77,204),(78,205),(79,206),(80,207),(81,208),(82,209),(83,210),(84,197),(85,104),(86,105),(87,106),(88,107),(89,108),(90,109),(91,110),(92,111),(93,112),(94,99),(95,100),(96,101),(97,102),(98,103),(127,158),(128,159),(129,160),(130,161),(131,162),(132,163),(133,164),(134,165),(135,166),(136,167),(137,168),(138,155),(139,156),(140,157)], [(1,155,223,147),(2,156,224,148),(3,157,211,149),(4,158,212,150),(5,159,213,151),(6,160,214,152),(7,161,215,153),(8,162,216,154),(9,163,217,141),(10,164,218,142),(11,165,219,143),(12,166,220,144),(13,167,221,145),(14,168,222,146),(15,207,103,117),(16,208,104,118),(17,209,105,119),(18,210,106,120),(19,197,107,121),(20,198,108,122),(21,199,109,123),(22,200,110,124),(23,201,111,125),(24,202,112,126),(25,203,99,113),(26,204,100,114),(27,205,101,115),(28,206,102,116),(29,194,129,52),(30,195,130,53),(31,196,131,54),(32,183,132,55),(33,184,133,56),(34,185,134,43),(35,186,135,44),(36,187,136,45),(37,188,137,46),(38,189,138,47),(39,190,139,48),(40,191,140,49),(41,192,127,50),(42,193,128,51),(57,172,74,92),(58,173,75,93),(59,174,76,94),(60,175,77,95),(61,176,78,96),(62,177,79,97),(63,178,80,98),(64,179,81,85),(65,180,82,86),(66,181,83,87),(67,182,84,88),(68,169,71,89),(69,170,72,90),(70,171,73,91)], [(1,17),(2,18),(3,19),(4,20),(5,21),(6,22),(7,23),(8,24),(9,25),(10,26),(11,27),(12,28),(13,15),(14,16),(29,200),(30,201),(31,202),(32,203),(33,204),(34,205),(35,206),(36,207),(37,208),(38,209),(39,210),(40,197),(41,198),(42,199),(43,96),(44,97),(45,98),(46,85),(47,86),(48,87),(49,88),(50,89),(51,90),(52,91),(53,92),(54,93),(55,94),(56,95),(57,161),(58,162),(59,163),(60,164),(61,165),(62,166),(63,167),(64,168),(65,155),(66,156),(67,157),(68,158),(69,159),(70,160),(71,150),(72,151),(73,152),(74,153),(75,154),(76,141),(77,142),(78,143),(79,144),(80,145),(81,146),(82,147),(83,148),(84,149),(99,217),(100,218),(101,219),(102,220),(103,221),(104,222),(105,223),(106,224),(107,211),(108,212),(109,213),(110,214),(111,215),(112,216),(113,132),(114,133),(115,134),(116,135),(117,136),(118,137),(119,138),(120,139),(121,140),(122,127),(123,128),(124,129),(125,130),(126,131),(169,192),(170,193),(171,194),(172,195),(173,196),(174,183),(175,184),(176,185),(177,186),(178,187),(179,188),(180,189),(181,190),(182,191)]])
196 conjugacy classes
| class | 1 | 2A | ··· | 2G | 2H | 2I | 2J | 2K | 2L | 2M | 4A | ··· | 4H | 4I | ··· | 4N | 7A | ··· | 7F | 14A | ··· | 14AP | 14AQ | ··· | 14BN | 14BO | ··· | 14BZ | 28A | ··· | 28AV | 28AW | ··· | 28CF |
| order | 1 | 2 | ··· | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 4 | ··· | 4 | 7 | ··· | 7 | 14 | ··· | 14 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | ··· | 1 | 2 | 2 | 2 | 2 | 4 | 4 | 2 | ··· | 2 | 4 | ··· | 4 | 1 | ··· | 1 | 1 | ··· | 1 | 2 | ··· | 2 | 4 | ··· | 4 | 2 | ··· | 2 | 4 | ··· | 4 |
196 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 |
| type | + | + | + | + | + | + | + | |||||||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C7 | C14 | C14 | C14 | C14 | C14 | D4 | C4○D4 | C7×D4 | C7×C4○D4 |
| kernel | C14×C22.D4 | C14×C22⋊C4 | C14×C4⋊C4 | C7×C22.D4 | C23×C28 | D4×C2×C14 | C2×C22.D4 | C2×C22⋊C4 | C2×C4⋊C4 | C22.D4 | C23×C4 | C22×D4 | C22×C14 | C2×C14 | C23 | C22 |
| # reps | 1 | 3 | 2 | 8 | 1 | 1 | 6 | 18 | 12 | 48 | 6 | 6 | 4 | 8 | 24 | 48 |
Matrix representation of C14×C22.D4 ►in GL6(𝔽29)
| 9 | 0 | 0 | 0 | 0 | 0 |
| 0 | 9 | 0 | 0 | 0 | 0 |
| 0 | 0 | 7 | 0 | 0 | 0 |
| 0 | 0 | 0 | 7 | 0 | 0 |
| 0 | 0 | 0 | 0 | 13 | 0 |
| 0 | 0 | 0 | 0 | 0 | 13 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 10 | 28 |
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 |
| 0 | 17 | 0 | 0 | 0 | 0 |
| 17 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 17 | 0 | 0 |
| 0 | 0 | 17 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 27 | 12 |
| 0 | 0 | 0 | 0 | 7 | 2 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 5 | 28 |
| 0 | 0 | 0 | 0 | 24 | 24 |
G:=sub<GL(6,GF(29))| [9,0,0,0,0,0,0,9,0,0,0,0,0,0,7,0,0,0,0,0,0,7,0,0,0,0,0,0,13,0,0,0,0,0,0,13],[1,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,28,0,0,0,0,0,0,1,10,0,0,0,0,0,28],[28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[0,17,0,0,0,0,17,0,0,0,0,0,0,0,0,17,0,0,0,0,17,0,0,0,0,0,0,0,27,7,0,0,0,0,12,2],[0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,28,0,0,0,0,28,0,0,0,0,0,0,0,5,24,0,0,0,0,28,24] >;
C14×C22.D4 in GAP, Magma, Sage, TeX
C_{14}\times C_2^2.D_4 % in TeX
G:=Group("C14xC2^2.D4"); // GroupNames label
G:=SmallGroup(448,1307);
// by ID
G=gap.SmallGroup(448,1307);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-7,-2,-2,1597,4790,604]);
// Polycyclic
G:=Group<a,b,c,d,e|a^14=b^2=c^2=d^4=e^2=1,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,d*b*d^-1=e*b*e=b*c=c*b,c*d=d*c,c*e=e*c,e*d*e=c*d^-1>;
// generators/relations