Copied to
clipboard

G = C14order 14 = 2·7

Cyclic group

direct product, cyclic, abelian, monomial

Aliases: C14, also denoted Z14, SmallGroup(14,2)

Series: Derived Chief Lower central Upper central

C1 — C14
C1C7 — C14
C1 — C14
C1 — C14

Generators and relations for C14
 G = < a | a14=1 >


Character table of C14

 class 127A7B7C7D7E7F14A14B14C14D14E14F
 size 11111111111111
ρ111111111111111    trivial
ρ21-1111111-1-1-1-1-1-1    linear of order 2
ρ311ζ72ζ73ζ74ζ75ζ76ζ7ζ76ζ72ζ73ζ74ζ75ζ7    linear of order 7
ρ41-1ζ72ζ73ζ74ζ75ζ76ζ776727374757    linear of order 14 faithful
ρ511ζ74ζ76ζ7ζ73ζ75ζ72ζ75ζ74ζ76ζ7ζ73ζ72    linear of order 7
ρ61-1ζ74ζ76ζ7ζ73ζ75ζ7275747677372    linear of order 14 faithful
ρ711ζ76ζ72ζ75ζ7ζ74ζ73ζ74ζ76ζ72ζ75ζ7ζ73    linear of order 7
ρ81-1ζ76ζ72ζ75ζ7ζ74ζ7374767275773    linear of order 14 faithful
ρ911ζ7ζ75ζ72ζ76ζ73ζ74ζ73ζ7ζ75ζ72ζ76ζ74    linear of order 7
ρ101-1ζ7ζ75ζ72ζ76ζ73ζ7473775727674    linear of order 14 faithful
ρ1111ζ73ζ7ζ76ζ74ζ72ζ75ζ72ζ73ζ7ζ76ζ74ζ75    linear of order 7
ρ121-1ζ73ζ7ζ76ζ74ζ72ζ7572737767475    linear of order 14 faithful
ρ1311ζ75ζ74ζ73ζ72ζ7ζ76ζ7ζ75ζ74ζ73ζ72ζ76    linear of order 7
ρ141-1ζ75ζ74ζ73ζ72ζ7ζ7677574737276    linear of order 14 faithful

Permutation representations of C14
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);

Polynomial with Galois group C14 over ℚ
actionf(x)Disc(f)
14T1x14+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

׿
×
𝔽