direct product, abelian, monomial, 2-elementary
Aliases: C2×C14, SmallGroup(28,4)
Series: Derived ►Chief ►Lower central ►Upper central
| C1 — C2×C14 |
| C1 — C2×C14 |
| C1 — C2×C14 |
Generators and relations for C2×C14
G = < a,b | a2=b14=1, ab=ba >
Character table of C2×C14
| class | 1 | 2A | 2B | 2C | 7A | 7B | 7C | 7D | 7E | 7F | 14A | 14B | 14C | 14D | 14E | 14F | 14G | 14H | 14I | 14J | 14K | 14L | 14M | 14N | 14O | 14P | 14Q | 14R | |
| size | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | |
| ρ1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | trivial |
| ρ2 | 1 | -1 | 1 | -1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | 1 | -1 | -1 | -1 | -1 | -1 | 1 | linear of order 2 |
| ρ3 | 1 | 1 | -1 | -1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | linear of order 2 |
| ρ4 | 1 | -1 | -1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | 1 | 1 | 1 | 1 | 1 | -1 | linear of order 2 |
| ρ5 | 1 | 1 | 1 | 1 | ζ74 | ζ75 | ζ76 | ζ7 | ζ72 | ζ73 | ζ76 | ζ74 | ζ75 | ζ76 | ζ7 | ζ7 | ζ72 | ζ73 | ζ74 | ζ75 | ζ76 | ζ72 | ζ7 | ζ72 | ζ73 | ζ74 | ζ75 | ζ73 | linear of order 7 |
| ρ6 | 1 | -1 | 1 | -1 | ζ74 | ζ75 | ζ76 | ζ7 | ζ72 | ζ73 | -ζ76 | ζ74 | ζ75 | ζ76 | ζ7 | -ζ7 | -ζ72 | -ζ73 | -ζ74 | -ζ75 | -ζ76 | ζ72 | -ζ7 | -ζ72 | -ζ73 | -ζ74 | -ζ75 | ζ73 | linear of order 14 |
| ρ7 | 1 | 1 | -1 | -1 | ζ74 | ζ75 | ζ76 | ζ7 | ζ72 | ζ73 | -ζ76 | -ζ74 | -ζ75 | -ζ76 | -ζ7 | ζ7 | ζ72 | ζ73 | ζ74 | ζ75 | ζ76 | -ζ72 | -ζ7 | -ζ72 | -ζ73 | -ζ74 | -ζ75 | -ζ73 | linear of order 14 |
| ρ8 | 1 | -1 | -1 | 1 | ζ74 | ζ75 | ζ76 | ζ7 | ζ72 | ζ73 | ζ76 | -ζ74 | -ζ75 | -ζ76 | -ζ7 | -ζ7 | -ζ72 | -ζ73 | -ζ74 | -ζ75 | -ζ76 | -ζ72 | ζ7 | ζ72 | ζ73 | ζ74 | ζ75 | -ζ73 | linear of order 14 |
| ρ9 | 1 | 1 | 1 | 1 | ζ7 | ζ73 | ζ75 | ζ72 | ζ74 | ζ76 | ζ75 | ζ7 | ζ73 | ζ75 | ζ72 | ζ72 | ζ74 | ζ76 | ζ7 | ζ73 | ζ75 | ζ74 | ζ72 | ζ74 | ζ76 | ζ7 | ζ73 | ζ76 | linear of order 7 |
| ρ10 | 1 | -1 | 1 | -1 | ζ7 | ζ73 | ζ75 | ζ72 | ζ74 | ζ76 | -ζ75 | ζ7 | ζ73 | ζ75 | ζ72 | -ζ72 | -ζ74 | -ζ76 | -ζ7 | -ζ73 | -ζ75 | ζ74 | -ζ72 | -ζ74 | -ζ76 | -ζ7 | -ζ73 | ζ76 | linear of order 14 |
| ρ11 | 1 | 1 | -1 | -1 | ζ7 | ζ73 | ζ75 | ζ72 | ζ74 | ζ76 | -ζ75 | -ζ7 | -ζ73 | -ζ75 | -ζ72 | ζ72 | ζ74 | ζ76 | ζ7 | ζ73 | ζ75 | -ζ74 | -ζ72 | -ζ74 | -ζ76 | -ζ7 | -ζ73 | -ζ76 | linear of order 14 |
| ρ12 | 1 | -1 | -1 | 1 | ζ7 | ζ73 | ζ75 | ζ72 | ζ74 | ζ76 | ζ75 | -ζ7 | -ζ73 | -ζ75 | -ζ72 | -ζ72 | -ζ74 | -ζ76 | -ζ7 | -ζ73 | -ζ75 | -ζ74 | ζ72 | ζ74 | ζ76 | ζ7 | ζ73 | -ζ76 | linear of order 14 |
| ρ13 | 1 | 1 | 1 | 1 | ζ75 | ζ7 | ζ74 | ζ73 | ζ76 | ζ72 | ζ74 | ζ75 | ζ7 | ζ74 | ζ73 | ζ73 | ζ76 | ζ72 | ζ75 | ζ7 | ζ74 | ζ76 | ζ73 | ζ76 | ζ72 | ζ75 | ζ7 | ζ72 | linear of order 7 |
| ρ14 | 1 | -1 | 1 | -1 | ζ75 | ζ7 | ζ74 | ζ73 | ζ76 | ζ72 | -ζ74 | ζ75 | ζ7 | ζ74 | ζ73 | -ζ73 | -ζ76 | -ζ72 | -ζ75 | -ζ7 | -ζ74 | ζ76 | -ζ73 | -ζ76 | -ζ72 | -ζ75 | -ζ7 | ζ72 | linear of order 14 |
| ρ15 | 1 | 1 | -1 | -1 | ζ75 | ζ7 | ζ74 | ζ73 | ζ76 | ζ72 | -ζ74 | -ζ75 | -ζ7 | -ζ74 | -ζ73 | ζ73 | ζ76 | ζ72 | ζ75 | ζ7 | ζ74 | -ζ76 | -ζ73 | -ζ76 | -ζ72 | -ζ75 | -ζ7 | -ζ72 | linear of order 14 |
| ρ16 | 1 | -1 | -1 | 1 | ζ75 | ζ7 | ζ74 | ζ73 | ζ76 | ζ72 | ζ74 | -ζ75 | -ζ7 | -ζ74 | -ζ73 | -ζ73 | -ζ76 | -ζ72 | -ζ75 | -ζ7 | -ζ74 | -ζ76 | ζ73 | ζ76 | ζ72 | ζ75 | ζ7 | -ζ72 | linear of order 14 |
| ρ17 | 1 | 1 | 1 | 1 | ζ72 | ζ76 | ζ73 | ζ74 | ζ7 | ζ75 | ζ73 | ζ72 | ζ76 | ζ73 | ζ74 | ζ74 | ζ7 | ζ75 | ζ72 | ζ76 | ζ73 | ζ7 | ζ74 | ζ7 | ζ75 | ζ72 | ζ76 | ζ75 | linear of order 7 |
| ρ18 | 1 | -1 | 1 | -1 | ζ72 | ζ76 | ζ73 | ζ74 | ζ7 | ζ75 | -ζ73 | ζ72 | ζ76 | ζ73 | ζ74 | -ζ74 | -ζ7 | -ζ75 | -ζ72 | -ζ76 | -ζ73 | ζ7 | -ζ74 | -ζ7 | -ζ75 | -ζ72 | -ζ76 | ζ75 | linear of order 14 |
| ρ19 | 1 | 1 | -1 | -1 | ζ72 | ζ76 | ζ73 | ζ74 | ζ7 | ζ75 | -ζ73 | -ζ72 | -ζ76 | -ζ73 | -ζ74 | ζ74 | ζ7 | ζ75 | ζ72 | ζ76 | ζ73 | -ζ7 | -ζ74 | -ζ7 | -ζ75 | -ζ72 | -ζ76 | -ζ75 | linear of order 14 |
| ρ20 | 1 | -1 | -1 | 1 | ζ72 | ζ76 | ζ73 | ζ74 | ζ7 | ζ75 | ζ73 | -ζ72 | -ζ76 | -ζ73 | -ζ74 | -ζ74 | -ζ7 | -ζ75 | -ζ72 | -ζ76 | -ζ73 | -ζ7 | ζ74 | ζ7 | ζ75 | ζ72 | ζ76 | -ζ75 | linear of order 14 |
| ρ21 | 1 | 1 | 1 | 1 | ζ76 | ζ74 | ζ72 | ζ75 | ζ73 | ζ7 | ζ72 | ζ76 | ζ74 | ζ72 | ζ75 | ζ75 | ζ73 | ζ7 | ζ76 | ζ74 | ζ72 | ζ73 | ζ75 | ζ73 | ζ7 | ζ76 | ζ74 | ζ7 | linear of order 7 |
| ρ22 | 1 | -1 | 1 | -1 | ζ76 | ζ74 | ζ72 | ζ75 | ζ73 | ζ7 | -ζ72 | ζ76 | ζ74 | ζ72 | ζ75 | -ζ75 | -ζ73 | -ζ7 | -ζ76 | -ζ74 | -ζ72 | ζ73 | -ζ75 | -ζ73 | -ζ7 | -ζ76 | -ζ74 | ζ7 | linear of order 14 |
| ρ23 | 1 | 1 | -1 | -1 | ζ76 | ζ74 | ζ72 | ζ75 | ζ73 | ζ7 | -ζ72 | -ζ76 | -ζ74 | -ζ72 | -ζ75 | ζ75 | ζ73 | ζ7 | ζ76 | ζ74 | ζ72 | -ζ73 | -ζ75 | -ζ73 | -ζ7 | -ζ76 | -ζ74 | -ζ7 | linear of order 14 |
| ρ24 | 1 | -1 | -1 | 1 | ζ76 | ζ74 | ζ72 | ζ75 | ζ73 | ζ7 | ζ72 | -ζ76 | -ζ74 | -ζ72 | -ζ75 | -ζ75 | -ζ73 | -ζ7 | -ζ76 | -ζ74 | -ζ72 | -ζ73 | ζ75 | ζ73 | ζ7 | ζ76 | ζ74 | -ζ7 | linear of order 14 |
| ρ25 | 1 | 1 | 1 | 1 | ζ73 | ζ72 | ζ7 | ζ76 | ζ75 | ζ74 | ζ7 | ζ73 | ζ72 | ζ7 | ζ76 | ζ76 | ζ75 | ζ74 | ζ73 | ζ72 | ζ7 | ζ75 | ζ76 | ζ75 | ζ74 | ζ73 | ζ72 | ζ74 | linear of order 7 |
| ρ26 | 1 | -1 | 1 | -1 | ζ73 | ζ72 | ζ7 | ζ76 | ζ75 | ζ74 | -ζ7 | ζ73 | ζ72 | ζ7 | ζ76 | -ζ76 | -ζ75 | -ζ74 | -ζ73 | -ζ72 | -ζ7 | ζ75 | -ζ76 | -ζ75 | -ζ74 | -ζ73 | -ζ72 | ζ74 | linear of order 14 |
| ρ27 | 1 | 1 | -1 | -1 | ζ73 | ζ72 | ζ7 | ζ76 | ζ75 | ζ74 | -ζ7 | -ζ73 | -ζ72 | -ζ7 | -ζ76 | ζ76 | ζ75 | ζ74 | ζ73 | ζ72 | ζ7 | -ζ75 | -ζ76 | -ζ75 | -ζ74 | -ζ73 | -ζ72 | -ζ74 | linear of order 14 |
| ρ28 | 1 | -1 | -1 | 1 | ζ73 | ζ72 | ζ7 | ζ76 | ζ75 | ζ74 | ζ7 | -ζ73 | -ζ72 | -ζ7 | -ζ76 | -ζ76 | -ζ75 | -ζ74 | -ζ73 | -ζ72 | -ζ7 | -ζ75 | ζ76 | ζ75 | ζ74 | ζ73 | ζ72 | -ζ74 | linear of order 14 |
►Regular action on 28 points - transitive group 28T2
Generators in S28
(1 24)(2 25)(3 26)(4 27)(5 28)(6 15)(7 16)(8 17)(9 18)(10 19)(11 20)(12 21)(13 22)(14 23)
(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)
G:=sub<Sym(28)| (1,24)(2,25)(3,26)(4,27)(5,28)(6,15)(7,16)(8,17)(9,18)(10,19)(11,20)(12,21)(13,22)(14,23), (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)>;
G:=Group( (1,24)(2,25)(3,26)(4,27)(5,28)(6,15)(7,16)(8,17)(9,18)(10,19)(11,20)(12,21)(13,22)(14,23), (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) );
G=PermutationGroup([[(1,24),(2,25),(3,26),(4,27),(5,28),(6,15),(7,16),(8,17),(9,18),(10,19),(11,20),(12,21),(13,22),(14,23)], [(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)]])
G:=TransitiveGroup(28,2);
C2×C14 is a maximal subgroup of
C7⋊D4 C7⋊A4
Matrix representation of C2×C14 ►in GL2(𝔽29) generated by
| 28 | 0 |
| 0 | 1 |
| 28 | 0 |
| 0 | 13 |
G:=sub<GL(2,GF(29))| [28,0,0,1],[28,0,0,13] >;
C2×C14 in GAP, Magma, Sage, TeX
C_2\times C_{14} % in TeX
G:=Group("C2xC14"); // GroupNames label
G:=SmallGroup(28,4);
// by ID
G=gap.SmallGroup(28,4);
# by ID
G:=PCGroup([3,-2,-2,-7]);
// Polycyclic
G:=Group<a,b|a^2=b^14=1,a*b=b*a>;
// generators/relations
Export
Subgroup lattice of C2×C14 in TeX
Character table of C2×C14 in TeX