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G = C2×C14order 28 = 22·7

Abelian group of type [2,14]

Aliases: C2×C14, SmallGroup(28,4)

Series: Derived Chief Lower central Upper central

 Derived series C1 — C2×C14
 Chief series C1 — C7 — C14 — C2×C14
 Lower central C1 — C2×C14
 Upper central 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

Permutation representations of C2×C14
Regular action on 28 points - transitive group 28T2
Generators in S28
(1 23)(2 24)(3 25)(4 26)(5 27)(6 28)(7 15)(8 16)(9 17)(10 18)(11 19)(12 20)(13 21)(14 22)
(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)| (1,23)(2,24)(3,25)(4,26)(5,27)(6,28)(7,15)(8,16)(9,17)(10,18)(11,19)(12,20)(13,21)(14,22), (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( (1,23)(2,24)(3,25)(4,26)(5,27)(6,28)(7,15)(8,16)(9,17)(10,18)(11,19)(12,20)(13,21)(14,22), (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([(1,23),(2,24),(3,25),(4,26),(5,27),(6,28),(7,15),(8,16),(9,17),(10,18),(11,19),(12,20),(13,21),(14,22)], [(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

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