direct product, cyclic, abelian, monomial
Aliases: C14, also denoted Z14, SmallGroup(14,2)
Series: Derived ►Chief ►Lower central ►Upper central
| C1 — C14 |
| C1 — C14 |
| C1 — C14 |
Generators and relations for C14
G = < a | a14=1 >
Character table of C14
| class | 1 | 2 | 7A | 7B | 7C | 7D | 7E | 7F | 14A | 14B | 14C | 14D | 14E | 14F | |
| size | 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 | trivial |
| ρ2 | 1 | -1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | linear of order 2 |
| ρ3 | 1 | 1 | ζ72 | ζ73 | ζ74 | ζ75 | ζ76 | ζ7 | ζ76 | ζ72 | ζ73 | ζ74 | ζ75 | ζ7 | linear of order 7 |
| ρ4 | 1 | -1 | ζ72 | ζ73 | ζ74 | ζ75 | ζ76 | ζ7 | -ζ76 | -ζ72 | -ζ73 | -ζ74 | -ζ75 | -ζ7 | linear of order 14 faithful |
| ρ5 | 1 | 1 | ζ74 | ζ76 | ζ7 | ζ73 | ζ75 | ζ72 | ζ75 | ζ74 | ζ76 | ζ7 | ζ73 | ζ72 | linear of order 7 |
| ρ6 | 1 | -1 | ζ74 | ζ76 | ζ7 | ζ73 | ζ75 | ζ72 | -ζ75 | -ζ74 | -ζ76 | -ζ7 | -ζ73 | -ζ72 | linear of order 14 faithful |
| ρ7 | 1 | 1 | ζ76 | ζ72 | ζ75 | ζ7 | ζ74 | ζ73 | ζ74 | ζ76 | ζ72 | ζ75 | ζ7 | ζ73 | linear of order 7 |
| ρ8 | 1 | -1 | ζ76 | ζ72 | ζ75 | ζ7 | ζ74 | ζ73 | -ζ74 | -ζ76 | -ζ72 | -ζ75 | -ζ7 | -ζ73 | linear of order 14 faithful |
| ρ9 | 1 | 1 | ζ7 | ζ75 | ζ72 | ζ76 | ζ73 | ζ74 | ζ73 | ζ7 | ζ75 | ζ72 | ζ76 | ζ74 | linear of order 7 |
| ρ10 | 1 | -1 | ζ7 | ζ75 | ζ72 | ζ76 | ζ73 | ζ74 | -ζ73 | -ζ7 | -ζ75 | -ζ72 | -ζ76 | -ζ74 | linear of order 14 faithful |
| ρ11 | 1 | 1 | ζ73 | ζ7 | ζ76 | ζ74 | ζ72 | ζ75 | ζ72 | ζ73 | ζ7 | ζ76 | ζ74 | ζ75 | linear of order 7 |
| ρ12 | 1 | -1 | ζ73 | ζ7 | ζ76 | ζ74 | ζ72 | ζ75 | -ζ72 | -ζ73 | -ζ7 | -ζ76 | -ζ74 | -ζ75 | linear of order 14 faithful |
| ρ13 | 1 | 1 | ζ75 | ζ74 | ζ73 | ζ72 | ζ7 | ζ76 | ζ7 | ζ75 | ζ74 | ζ73 | ζ72 | ζ76 | linear of order 7 |
| ρ14 | 1 | -1 | ζ75 | ζ74 | ζ73 | ζ72 | ζ7 | ζ76 | -ζ7 | -ζ75 | -ζ74 | -ζ73 | -ζ72 | -ζ76 | linear of order 14 faithful |
►Regular action on 14 points - transitive group 14T1
Generators in S14
(1 2 3 4 5 6 7 8 9 10 11 12 13 14)
G:=sub<Sym(14)| (1,2,3,4,5,6,7,8,9,10,11,12,13,14)>;
G:=Group( (1,2,3,4,5,6,7,8,9,10,11,12,13,14) );
G=PermutationGroup([[(1,2,3,4,5,6,7,8,9,10,11,12,13,14)]])
G:=TransitiveGroup(14,1);
C14 is a maximal subgroup of
Dic7 C29⋊C14
C14 is a maximal quotient of C29⋊C14
| action | f(x) | Disc(f) |
|---|---|---|
| 14T1 | x14+25x12+214x10+767x8+1194x6+686x4+53x2+1 | -214·1712·2912·414 |
Matrix representation of C14 ►in GL1(𝔽29) generated by
| 4 |
G:=sub<GL(1,GF(29))| [4] >;
C14 in GAP, Magma, Sage, TeX
C_{14} % in TeX
G:=Group("C14"); // GroupNames label
G:=SmallGroup(14,2);
// by ID
G=gap.SmallGroup(14,2);
# by ID
G:=PCGroup([2,-2,-7]);
// Polycyclic
G:=Group<a|a^14=1>;
// generators/relations
Export
Subgroup lattice of C14 in TeX
Character table of C14 in TeX