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G = C2×C14order 28 = 22·7

Abelian group of type [2,14]

direct product, abelian, monomial, 2-elementary

Aliases: C2×C14, SmallGroup(28,4)

Series: Derived Chief Lower central Upper central

C1 — C2×C14
C1C7C14 — 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 12A2B2C7A7B7C7D7E7F14A14B14C14D14E14F14G14H14I14J14K14L14M14N14O14P14Q14R
 size 1111111111111111111111111111
ρ11111111111111111111111111111    trivial
ρ21-11-1111111-11111-1-1-1-1-1-11-1-1-1-1-11    linear of order 2
ρ311-1-1111111-1-1-1-1-1111111-1-1-1-1-1-1-1    linear of order 2
ρ41-1-111111111-1-1-1-1-1-1-1-1-1-1-111111-1    linear of order 2
ρ51111ζ74ζ75ζ76ζ7ζ72ζ73ζ76ζ74ζ75ζ76ζ7ζ7ζ72ζ73ζ74ζ75ζ76ζ72ζ7ζ72ζ73ζ74ζ75ζ73    linear of order 7
ρ61-11-1ζ74ζ75ζ76ζ7ζ72ζ7376ζ74ζ75ζ76ζ777273747576ζ72772737475ζ73    linear of order 14
ρ711-1-1ζ74ζ75ζ76ζ7ζ72ζ73767475767ζ7ζ72ζ73ζ74ζ75ζ767277273747573    linear of order 14
ρ81-1-11ζ74ζ75ζ76ζ7ζ72ζ73ζ7674757677727374757672ζ7ζ72ζ73ζ74ζ7573    linear of order 14
ρ91111ζ7ζ73ζ75ζ72ζ74ζ76ζ75ζ7ζ73ζ75ζ72ζ72ζ74ζ76ζ7ζ73ζ75ζ74ζ72ζ74ζ76ζ7ζ73ζ76    linear of order 7
ρ101-11-1ζ7ζ73ζ75ζ72ζ74ζ7675ζ7ζ73ζ75ζ7272747677375ζ74727476773ζ76    linear of order 14
ρ1111-1-1ζ7ζ73ζ75ζ72ζ74ζ76757737572ζ72ζ74ζ76ζ7ζ73ζ757472747677376    linear of order 14
ρ121-1-11ζ7ζ73ζ75ζ72ζ74ζ76ζ7577375727274767737574ζ72ζ74ζ76ζ7ζ7376    linear of order 14
ρ131111ζ75ζ7ζ74ζ73ζ76ζ72ζ74ζ75ζ7ζ74ζ73ζ73ζ76ζ72ζ75ζ7ζ74ζ76ζ73ζ76ζ72ζ75ζ7ζ72    linear of order 7
ρ141-11-1ζ75ζ7ζ74ζ73ζ76ζ7274ζ75ζ7ζ74ζ7373767275774ζ76737672757ζ72    linear of order 14
ρ1511-1-1ζ75ζ7ζ74ζ73ζ76ζ72747577473ζ73ζ76ζ72ζ75ζ7ζ747673767275772    linear of order 14
ρ161-1-11ζ75ζ7ζ74ζ73ζ76ζ72ζ7475774737376727577476ζ73ζ76ζ72ζ75ζ772    linear of order 14
ρ171111ζ72ζ76ζ73ζ74ζ7ζ75ζ73ζ72ζ76ζ73ζ74ζ74ζ7ζ75ζ72ζ76ζ73ζ7ζ74ζ7ζ75ζ72ζ76ζ75    linear of order 7
ρ181-11-1ζ72ζ76ζ73ζ74ζ7ζ7573ζ72ζ76ζ73ζ7474775727673ζ7747757276ζ75    linear of order 14
ρ1911-1-1ζ72ζ76ζ73ζ74ζ7ζ757372767374ζ74ζ7ζ75ζ72ζ76ζ73774775727675    linear of order 14
ρ201-1-11ζ72ζ76ζ73ζ74ζ7ζ75ζ7372767374747757276737ζ74ζ7ζ75ζ72ζ7675    linear of order 14
ρ211111ζ76ζ74ζ72ζ75ζ73ζ7ζ72ζ76ζ74ζ72ζ75ζ75ζ73ζ7ζ76ζ74ζ72ζ73ζ75ζ73ζ7ζ76ζ74ζ7    linear of order 7
ρ221-11-1ζ76ζ74ζ72ζ75ζ73ζ772ζ76ζ74ζ72ζ7575737767472ζ73757377674ζ7    linear of order 14
ρ2311-1-1ζ76ζ74ζ72ζ75ζ73ζ77276747275ζ75ζ73ζ7ζ76ζ74ζ72737573776747    linear of order 14
ρ241-1-11ζ76ζ74ζ72ζ75ζ73ζ7ζ72767472757573776747273ζ75ζ73ζ7ζ76ζ747    linear of order 14
ρ251111ζ73ζ72ζ7ζ76ζ75ζ74ζ7ζ73ζ72ζ7ζ76ζ76ζ75ζ74ζ73ζ72ζ7ζ75ζ76ζ75ζ74ζ73ζ72ζ74    linear of order 7
ρ261-11-1ζ73ζ72ζ7ζ76ζ75ζ747ζ73ζ72ζ7ζ7676757473727ζ757675747372ζ74    linear of order 14
ρ2711-1-1ζ73ζ72ζ7ζ76ζ75ζ7477372776ζ76ζ75ζ74ζ73ζ72ζ775767574737274    linear of order 14
ρ281-1-11ζ73ζ72ζ7ζ76ζ75ζ74ζ773727767675747372775ζ76ζ75ζ74ζ73ζ7274    linear of order 14

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

Matrix representation of C2×C14 in GL2(𝔽29) generated by

280
01
,
280
013
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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