direct product, metabelian, nilpotent (class 2), monomial, 2-elementary
Aliases: C14×C4⋊D4, C4⋊3(D4×C14), C28⋊17(C2×D4), (C2×C28)⋊40D4, C23⋊5(C7×D4), (C23×C4)⋊7C14, C22⋊1(D4×C14), (C23×C28)⋊14C2, (C22×D4)⋊4C14, (C22×C14)⋊14D4, (D4×C14)⋊61C22, C24.15(C2×C14), (C2×C28).655C23, (C2×C14).342C24, (C22×C28)⋊65C22, C14.181(C22×D4), C22.16(C23×C14), C23.69(C22×C14), (C23×C14).12C22, (C22×C14).257C23, C2.5(D4×C2×C14), C4⋊C4⋊9(C2×C14), (D4×C2×C14)⋊19C2, (C2×C4)⋊10(C7×D4), (C2×C4⋊C4)⋊14C14, (C14×C4⋊C4)⋊41C2, (C2×D4)⋊9(C2×C14), (C2×C14)⋊10(C2×D4), C2.5(C14×C4○D4), (C2×C22⋊C4)⋊9C14, (C7×C4⋊C4)⋊65C22, (C14×C22⋊C4)⋊29C2, C22⋊C4⋊11(C2×C14), (C22×C4)⋊18(C2×C14), C14.224(C2×C4○D4), C22.29(C7×C4○D4), (C7×C22⋊C4)⋊65C22, (C2×C4).11(C22×C14), (C2×C14).229(C4○D4), SmallGroup(448,1305)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C14×C4⋊D4
G = < a,b,c,d | a14=b4=c4=d2=1, ab=ba, ac=ca, ad=da, cbc-1=dbd=b-1, dcd=c-1 >
Subgroups: 706 in 426 conjugacy classes, 194 normal (26 characteristic)
C1, C2, C2, C2, C4, 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, C24, C28, C28, C2×C14, C2×C14, C2×C14, C2×C22⋊C4, C2×C4⋊C4, C4⋊D4, C23×C4, C22×D4, C22×D4, C2×C28, C2×C28, C7×D4, C22×C14, C22×C14, C22×C14, C2×C4⋊D4, C7×C22⋊C4, C7×C4⋊C4, C22×C28, C22×C28, C22×C28, D4×C14, D4×C14, C23×C14, C23×C14, C14×C22⋊C4, C14×C4⋊C4, C7×C4⋊D4, C23×C28, D4×C2×C14, D4×C2×C14, C14×C4⋊D4
Quotients: C1, C2, C22, C7, D4, C23, C14, C2×D4, C4○D4, C24, C2×C14, C4⋊D4, C22×D4, C2×C4○D4, C7×D4, C22×C14, C2×C4⋊D4, D4×C14, C7×C4○D4, C23×C14, C7×C4⋊D4, D4×C2×C14, C14×C4○D4, C14×C4⋊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)
(1 109 192 64)(2 110 193 65)(3 111 194 66)(4 112 195 67)(5 99 196 68)(6 100 183 69)(7 101 184 70)(8 102 185 57)(9 103 186 58)(10 104 187 59)(11 105 188 60)(12 106 189 61)(13 107 190 62)(14 108 191 63)(15 52 77 85)(16 53 78 86)(17 54 79 87)(18 55 80 88)(19 56 81 89)(20 43 82 90)(21 44 83 91)(22 45 84 92)(23 46 71 93)(24 47 72 94)(25 48 73 95)(26 49 74 96)(27 50 75 97)(28 51 76 98)(29 175 209 128)(30 176 210 129)(31 177 197 130)(32 178 198 131)(33 179 199 132)(34 180 200 133)(35 181 201 134)(36 182 202 135)(37 169 203 136)(38 170 204 137)(39 171 205 138)(40 172 206 139)(41 173 207 140)(42 174 208 127)(113 162 154 222)(114 163 141 223)(115 164 142 224)(116 165 143 211)(117 166 144 212)(118 167 145 213)(119 168 146 214)(120 155 147 215)(121 156 148 216)(122 157 149 217)(123 158 150 218)(124 159 151 219)(125 160 152 220)(126 161 153 221)
(1 142 40 73)(2 143 41 74)(3 144 42 75)(4 145 29 76)(5 146 30 77)(6 147 31 78)(7 148 32 79)(8 149 33 80)(9 150 34 81)(10 151 35 82)(11 152 36 83)(12 153 37 84)(13 154 38 71)(14 141 39 72)(15 196 119 210)(16 183 120 197)(17 184 121 198)(18 185 122 199)(19 186 123 200)(20 187 124 201)(21 188 125 202)(22 189 126 203)(23 190 113 204)(24 191 114 205)(25 192 115 206)(26 193 116 207)(27 194 117 208)(28 195 118 209)(43 104 159 181)(44 105 160 182)(45 106 161 169)(46 107 162 170)(47 108 163 171)(48 109 164 172)(49 110 165 173)(50 111 166 174)(51 112 167 175)(52 99 168 176)(53 100 155 177)(54 101 156 178)(55 102 157 179)(56 103 158 180)(57 217 132 88)(58 218 133 89)(59 219 134 90)(60 220 135 91)(61 221 136 92)(62 222 137 93)(63 223 138 94)(64 224 139 95)(65 211 140 96)(66 212 127 97)(67 213 128 98)(68 214 129 85)(69 215 130 86)(70 216 131 87)
(1 122)(2 123)(3 124)(4 125)(5 126)(6 113)(7 114)(8 115)(9 116)(10 117)(11 118)(12 119)(13 120)(14 121)(15 37)(16 38)(17 39)(18 40)(19 41)(20 42)(21 29)(22 30)(23 31)(24 32)(25 33)(26 34)(27 35)(28 36)(43 127)(44 128)(45 129)(46 130)(47 131)(48 132)(49 133)(50 134)(51 135)(52 136)(53 137)(54 138)(55 139)(56 140)(57 164)(58 165)(59 166)(60 167)(61 168)(62 155)(63 156)(64 157)(65 158)(66 159)(67 160)(68 161)(69 162)(70 163)(71 197)(72 198)(73 199)(74 200)(75 201)(76 202)(77 203)(78 204)(79 205)(80 206)(81 207)(82 208)(83 209)(84 210)(85 169)(86 170)(87 171)(88 172)(89 173)(90 174)(91 175)(92 176)(93 177)(94 178)(95 179)(96 180)(97 181)(98 182)(99 221)(100 222)(101 223)(102 224)(103 211)(104 212)(105 213)(106 214)(107 215)(108 216)(109 217)(110 218)(111 219)(112 220)(141 184)(142 185)(143 186)(144 187)(145 188)(146 189)(147 190)(148 191)(149 192)(150 193)(151 194)(152 195)(153 196)(154 183)
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), (1,109,192,64)(2,110,193,65)(3,111,194,66)(4,112,195,67)(5,99,196,68)(6,100,183,69)(7,101,184,70)(8,102,185,57)(9,103,186,58)(10,104,187,59)(11,105,188,60)(12,106,189,61)(13,107,190,62)(14,108,191,63)(15,52,77,85)(16,53,78,86)(17,54,79,87)(18,55,80,88)(19,56,81,89)(20,43,82,90)(21,44,83,91)(22,45,84,92)(23,46,71,93)(24,47,72,94)(25,48,73,95)(26,49,74,96)(27,50,75,97)(28,51,76,98)(29,175,209,128)(30,176,210,129)(31,177,197,130)(32,178,198,131)(33,179,199,132)(34,180,200,133)(35,181,201,134)(36,182,202,135)(37,169,203,136)(38,170,204,137)(39,171,205,138)(40,172,206,139)(41,173,207,140)(42,174,208,127)(113,162,154,222)(114,163,141,223)(115,164,142,224)(116,165,143,211)(117,166,144,212)(118,167,145,213)(119,168,146,214)(120,155,147,215)(121,156,148,216)(122,157,149,217)(123,158,150,218)(124,159,151,219)(125,160,152,220)(126,161,153,221), (1,142,40,73)(2,143,41,74)(3,144,42,75)(4,145,29,76)(5,146,30,77)(6,147,31,78)(7,148,32,79)(8,149,33,80)(9,150,34,81)(10,151,35,82)(11,152,36,83)(12,153,37,84)(13,154,38,71)(14,141,39,72)(15,196,119,210)(16,183,120,197)(17,184,121,198)(18,185,122,199)(19,186,123,200)(20,187,124,201)(21,188,125,202)(22,189,126,203)(23,190,113,204)(24,191,114,205)(25,192,115,206)(26,193,116,207)(27,194,117,208)(28,195,118,209)(43,104,159,181)(44,105,160,182)(45,106,161,169)(46,107,162,170)(47,108,163,171)(48,109,164,172)(49,110,165,173)(50,111,166,174)(51,112,167,175)(52,99,168,176)(53,100,155,177)(54,101,156,178)(55,102,157,179)(56,103,158,180)(57,217,132,88)(58,218,133,89)(59,219,134,90)(60,220,135,91)(61,221,136,92)(62,222,137,93)(63,223,138,94)(64,224,139,95)(65,211,140,96)(66,212,127,97)(67,213,128,98)(68,214,129,85)(69,215,130,86)(70,216,131,87), (1,122)(2,123)(3,124)(4,125)(5,126)(6,113)(7,114)(8,115)(9,116)(10,117)(11,118)(12,119)(13,120)(14,121)(15,37)(16,38)(17,39)(18,40)(19,41)(20,42)(21,29)(22,30)(23,31)(24,32)(25,33)(26,34)(27,35)(28,36)(43,127)(44,128)(45,129)(46,130)(47,131)(48,132)(49,133)(50,134)(51,135)(52,136)(53,137)(54,138)(55,139)(56,140)(57,164)(58,165)(59,166)(60,167)(61,168)(62,155)(63,156)(64,157)(65,158)(66,159)(67,160)(68,161)(69,162)(70,163)(71,197)(72,198)(73,199)(74,200)(75,201)(76,202)(77,203)(78,204)(79,205)(80,206)(81,207)(82,208)(83,209)(84,210)(85,169)(86,170)(87,171)(88,172)(89,173)(90,174)(91,175)(92,176)(93,177)(94,178)(95,179)(96,180)(97,181)(98,182)(99,221)(100,222)(101,223)(102,224)(103,211)(104,212)(105,213)(106,214)(107,215)(108,216)(109,217)(110,218)(111,219)(112,220)(141,184)(142,185)(143,186)(144,187)(145,188)(146,189)(147,190)(148,191)(149,192)(150,193)(151,194)(152,195)(153,196)(154,183)>;
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), (1,109,192,64)(2,110,193,65)(3,111,194,66)(4,112,195,67)(5,99,196,68)(6,100,183,69)(7,101,184,70)(8,102,185,57)(9,103,186,58)(10,104,187,59)(11,105,188,60)(12,106,189,61)(13,107,190,62)(14,108,191,63)(15,52,77,85)(16,53,78,86)(17,54,79,87)(18,55,80,88)(19,56,81,89)(20,43,82,90)(21,44,83,91)(22,45,84,92)(23,46,71,93)(24,47,72,94)(25,48,73,95)(26,49,74,96)(27,50,75,97)(28,51,76,98)(29,175,209,128)(30,176,210,129)(31,177,197,130)(32,178,198,131)(33,179,199,132)(34,180,200,133)(35,181,201,134)(36,182,202,135)(37,169,203,136)(38,170,204,137)(39,171,205,138)(40,172,206,139)(41,173,207,140)(42,174,208,127)(113,162,154,222)(114,163,141,223)(115,164,142,224)(116,165,143,211)(117,166,144,212)(118,167,145,213)(119,168,146,214)(120,155,147,215)(121,156,148,216)(122,157,149,217)(123,158,150,218)(124,159,151,219)(125,160,152,220)(126,161,153,221), (1,142,40,73)(2,143,41,74)(3,144,42,75)(4,145,29,76)(5,146,30,77)(6,147,31,78)(7,148,32,79)(8,149,33,80)(9,150,34,81)(10,151,35,82)(11,152,36,83)(12,153,37,84)(13,154,38,71)(14,141,39,72)(15,196,119,210)(16,183,120,197)(17,184,121,198)(18,185,122,199)(19,186,123,200)(20,187,124,201)(21,188,125,202)(22,189,126,203)(23,190,113,204)(24,191,114,205)(25,192,115,206)(26,193,116,207)(27,194,117,208)(28,195,118,209)(43,104,159,181)(44,105,160,182)(45,106,161,169)(46,107,162,170)(47,108,163,171)(48,109,164,172)(49,110,165,173)(50,111,166,174)(51,112,167,175)(52,99,168,176)(53,100,155,177)(54,101,156,178)(55,102,157,179)(56,103,158,180)(57,217,132,88)(58,218,133,89)(59,219,134,90)(60,220,135,91)(61,221,136,92)(62,222,137,93)(63,223,138,94)(64,224,139,95)(65,211,140,96)(66,212,127,97)(67,213,128,98)(68,214,129,85)(69,215,130,86)(70,216,131,87), (1,122)(2,123)(3,124)(4,125)(5,126)(6,113)(7,114)(8,115)(9,116)(10,117)(11,118)(12,119)(13,120)(14,121)(15,37)(16,38)(17,39)(18,40)(19,41)(20,42)(21,29)(22,30)(23,31)(24,32)(25,33)(26,34)(27,35)(28,36)(43,127)(44,128)(45,129)(46,130)(47,131)(48,132)(49,133)(50,134)(51,135)(52,136)(53,137)(54,138)(55,139)(56,140)(57,164)(58,165)(59,166)(60,167)(61,168)(62,155)(63,156)(64,157)(65,158)(66,159)(67,160)(68,161)(69,162)(70,163)(71,197)(72,198)(73,199)(74,200)(75,201)(76,202)(77,203)(78,204)(79,205)(80,206)(81,207)(82,208)(83,209)(84,210)(85,169)(86,170)(87,171)(88,172)(89,173)(90,174)(91,175)(92,176)(93,177)(94,178)(95,179)(96,180)(97,181)(98,182)(99,221)(100,222)(101,223)(102,224)(103,211)(104,212)(105,213)(106,214)(107,215)(108,216)(109,217)(110,218)(111,219)(112,220)(141,184)(142,185)(143,186)(144,187)(145,188)(146,189)(147,190)(148,191)(149,192)(150,193)(151,194)(152,195)(153,196)(154,183) );
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)], [(1,109,192,64),(2,110,193,65),(3,111,194,66),(4,112,195,67),(5,99,196,68),(6,100,183,69),(7,101,184,70),(8,102,185,57),(9,103,186,58),(10,104,187,59),(11,105,188,60),(12,106,189,61),(13,107,190,62),(14,108,191,63),(15,52,77,85),(16,53,78,86),(17,54,79,87),(18,55,80,88),(19,56,81,89),(20,43,82,90),(21,44,83,91),(22,45,84,92),(23,46,71,93),(24,47,72,94),(25,48,73,95),(26,49,74,96),(27,50,75,97),(28,51,76,98),(29,175,209,128),(30,176,210,129),(31,177,197,130),(32,178,198,131),(33,179,199,132),(34,180,200,133),(35,181,201,134),(36,182,202,135),(37,169,203,136),(38,170,204,137),(39,171,205,138),(40,172,206,139),(41,173,207,140),(42,174,208,127),(113,162,154,222),(114,163,141,223),(115,164,142,224),(116,165,143,211),(117,166,144,212),(118,167,145,213),(119,168,146,214),(120,155,147,215),(121,156,148,216),(122,157,149,217),(123,158,150,218),(124,159,151,219),(125,160,152,220),(126,161,153,221)], [(1,142,40,73),(2,143,41,74),(3,144,42,75),(4,145,29,76),(5,146,30,77),(6,147,31,78),(7,148,32,79),(8,149,33,80),(9,150,34,81),(10,151,35,82),(11,152,36,83),(12,153,37,84),(13,154,38,71),(14,141,39,72),(15,196,119,210),(16,183,120,197),(17,184,121,198),(18,185,122,199),(19,186,123,200),(20,187,124,201),(21,188,125,202),(22,189,126,203),(23,190,113,204),(24,191,114,205),(25,192,115,206),(26,193,116,207),(27,194,117,208),(28,195,118,209),(43,104,159,181),(44,105,160,182),(45,106,161,169),(46,107,162,170),(47,108,163,171),(48,109,164,172),(49,110,165,173),(50,111,166,174),(51,112,167,175),(52,99,168,176),(53,100,155,177),(54,101,156,178),(55,102,157,179),(56,103,158,180),(57,217,132,88),(58,218,133,89),(59,219,134,90),(60,220,135,91),(61,221,136,92),(62,222,137,93),(63,223,138,94),(64,224,139,95),(65,211,140,96),(66,212,127,97),(67,213,128,98),(68,214,129,85),(69,215,130,86),(70,216,131,87)], [(1,122),(2,123),(3,124),(4,125),(5,126),(6,113),(7,114),(8,115),(9,116),(10,117),(11,118),(12,119),(13,120),(14,121),(15,37),(16,38),(17,39),(18,40),(19,41),(20,42),(21,29),(22,30),(23,31),(24,32),(25,33),(26,34),(27,35),(28,36),(43,127),(44,128),(45,129),(46,130),(47,131),(48,132),(49,133),(50,134),(51,135),(52,136),(53,137),(54,138),(55,139),(56,140),(57,164),(58,165),(59,166),(60,167),(61,168),(62,155),(63,156),(64,157),(65,158),(66,159),(67,160),(68,161),(69,162),(70,163),(71,197),(72,198),(73,199),(74,200),(75,201),(76,202),(77,203),(78,204),(79,205),(80,206),(81,207),(82,208),(83,209),(84,210),(85,169),(86,170),(87,171),(88,172),(89,173),(90,174),(91,175),(92,176),(93,177),(94,178),(95,179),(96,180),(97,181),(98,182),(99,221),(100,222),(101,223),(102,224),(103,211),(104,212),(105,213),(106,214),(107,215),(108,216),(109,217),(110,218),(111,219),(112,220),(141,184),(142,185),(143,186),(144,187),(145,188),(146,189),(147,190),(148,191),(149,192),(150,193),(151,194),(152,195),(153,196),(154,183)]])
196 conjugacy classes
| class | 1 | 2A | ··· | 2G | 2H | 2I | 2J | 2K | 2L | 2M | 2N | 2O | 4A | ··· | 4H | 4I | 4J | 4K | 4L | 7A | ··· | 7F | 14A | ··· | 14AP | 14AQ | ··· | 14BN | 14BO | ··· | 14CL | 28A | ··· | 28AV | 28AW | ··· | 28BT |
| order | 1 | 2 | ··· | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 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 | 4 | 4 | 2 | ··· | 2 | 4 | 4 | 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 | 2 | 2 |
| type | + | + | + | + | + | + | + | + | ||||||||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C7 | C14 | C14 | C14 | C14 | C14 | D4 | D4 | C4○D4 | C7×D4 | C7×D4 | C7×C4○D4 |
| kernel | C14×C4⋊D4 | C14×C22⋊C4 | C14×C4⋊C4 | C7×C4⋊D4 | C23×C28 | D4×C2×C14 | C2×C4⋊D4 | C2×C22⋊C4 | C2×C4⋊C4 | C4⋊D4 | C23×C4 | C22×D4 | C2×C28 | C22×C14 | C2×C14 | C2×C4 | C23 | C22 |
| # reps | 1 | 2 | 1 | 8 | 1 | 3 | 6 | 12 | 6 | 48 | 6 | 18 | 4 | 4 | 4 | 24 | 24 | 24 |
Matrix representation of C14×C4⋊D4 ►in GL6(𝔽29)
| 5 | 0 | 0 | 0 | 0 | 0 |
| 0 | 5 | 0 | 0 | 0 | 0 |
| 0 | 0 | 16 | 0 | 0 | 0 |
| 0 | 0 | 0 | 16 | 0 | 0 |
| 0 | 0 | 0 | 0 | 25 | 0 |
| 0 | 0 | 0 | 0 | 0 | 25 |
| 12 | 25 | 0 | 0 | 0 | 0 |
| 0 | 17 | 0 | 0 | 0 | 0 |
| 0 | 0 | 17 | 0 | 0 | 0 |
| 0 | 0 | 23 | 12 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 |
| 10 | 22 | 0 | 0 | 0 | 0 |
| 2 | 19 | 0 | 0 | 0 | 0 |
| 0 | 0 | 15 | 27 | 0 | 0 |
| 0 | 0 | 26 | 14 | 0 | 0 |
| 0 | 0 | 0 | 0 | 27 | 27 |
| 0 | 0 | 0 | 0 | 17 | 2 |
| 10 | 23 | 0 | 0 | 0 | 0 |
| 2 | 19 | 0 | 0 | 0 | 0 |
| 0 | 0 | 15 | 27 | 0 | 0 |
| 0 | 0 | 25 | 14 | 0 | 0 |
| 0 | 0 | 0 | 0 | 2 | 2 |
| 0 | 0 | 0 | 0 | 13 | 27 |
G:=sub<GL(6,GF(29))| [5,0,0,0,0,0,0,5,0,0,0,0,0,0,16,0,0,0,0,0,0,16,0,0,0,0,0,0,25,0,0,0,0,0,0,25],[12,0,0,0,0,0,25,17,0,0,0,0,0,0,17,23,0,0,0,0,0,12,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[10,2,0,0,0,0,22,19,0,0,0,0,0,0,15,26,0,0,0,0,27,14,0,0,0,0,0,0,27,17,0,0,0,0,27,2],[10,2,0,0,0,0,23,19,0,0,0,0,0,0,15,25,0,0,0,0,27,14,0,0,0,0,0,0,2,13,0,0,0,0,2,27] >;
C14×C4⋊D4 in GAP, Magma, Sage, TeX
C_{14}\times C_4\rtimes D_4 % in TeX
G:=Group("C14xC4:D4"); // GroupNames label
G:=SmallGroup(448,1305);
// by ID
G=gap.SmallGroup(448,1305);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-7,-2,-2,1597,792,4790]);
// Polycyclic
G:=Group<a,b,c,d|a^14=b^4=c^4=d^2=1,a*b=b*a,a*c=c*a,a*d=d*a,c*b*c^-1=d*b*d=b^-1,d*c*d=c^-1>;
// generators/relations