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G = C28order 28 = 22·7

Cyclic group

direct product, cyclic, abelian, monomial

Aliases: C28, also denoted Z28, SmallGroup(28,2)

Series: Derived Chief Lower central Upper central

C1 — C28
C1C2C14 — C28
C1 — C28
C1 — C28

Generators and relations for C28
 G = < a | a28=1 >


Character table of C28

 class 124A4B7A7B7C7D7E7F14A14B14C14D14E14F28A28B28C28D28E28F28G28H28I28J28K28L
 size 1111111111111111111111111111
ρ11111111111111111111111111111    trivial
ρ211-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1    linear of order 2
ρ31-1-ii111111-1-1-1-1-1-1ii-ii-ii-ii-ii-i-i    linear of order 4
ρ41-1i-i111111-1-1-1-1-1-1-i-ii-ii-ii-ii-iii    linear of order 4
ρ51111ζ72ζ73ζ74ζ75ζ76ζ7ζ73ζ75ζ72ζ76ζ74ζ7ζ76ζ7ζ72ζ72ζ73ζ73ζ74ζ74ζ75ζ75ζ76ζ7    linear of order 7
ρ61-1ζ2ζ2ζ72ζ73ζ74ζ75ζ76ζ773757276747ζ4ζ76ζ4ζ7ζ43ζ72ζ4ζ72ζ43ζ73ζ4ζ73ζ43ζ74ζ4ζ74ζ43ζ75ζ4ζ75ζ43ζ76ζ43ζ7    linear of order 28 faithful
ρ711-1-1ζ72ζ73ζ74ζ75ζ76ζ7ζ73ζ75ζ72ζ76ζ74ζ77677272737374747575767    linear of order 14
ρ81-1ζ2ζ2ζ72ζ73ζ74ζ75ζ76ζ773757276747ζ43ζ76ζ43ζ7ζ4ζ72ζ43ζ72ζ4ζ73ζ43ζ73ζ4ζ74ζ43ζ74ζ4ζ75ζ43ζ75ζ4ζ76ζ4ζ7    linear of order 28 faithful
ρ91111ζ74ζ76ζ7ζ73ζ75ζ72ζ76ζ73ζ74ζ75ζ7ζ72ζ75ζ72ζ74ζ74ζ76ζ76ζ7ζ7ζ73ζ73ζ75ζ72    linear of order 7
ρ101-1ζ2ζ2ζ74ζ76ζ7ζ73ζ75ζ7276737475772ζ4ζ75ζ4ζ72ζ43ζ74ζ4ζ74ζ43ζ76ζ4ζ76ζ43ζ7ζ4ζ7ζ43ζ73ζ4ζ73ζ43ζ75ζ43ζ72    linear of order 28 faithful
ρ1111-1-1ζ74ζ76ζ7ζ73ζ75ζ72ζ76ζ73ζ74ζ75ζ7ζ727572747476767773737572    linear of order 14
ρ121-1ζ2ζ2ζ74ζ76ζ7ζ73ζ75ζ7276737475772ζ43ζ75ζ43ζ72ζ4ζ74ζ43ζ74ζ4ζ76ζ43ζ76ζ4ζ7ζ43ζ7ζ4ζ73ζ43ζ73ζ4ζ75ζ4ζ72    linear of order 28 faithful
ρ131111ζ76ζ72ζ75ζ7ζ74ζ73ζ72ζ7ζ76ζ74ζ75ζ73ζ74ζ73ζ76ζ76ζ72ζ72ζ75ζ75ζ7ζ7ζ74ζ73    linear of order 7
ρ141-1ζ2ζ2ζ76ζ72ζ75ζ7ζ74ζ7372776747573ζ4ζ74ζ4ζ73ζ43ζ76ζ4ζ76ζ43ζ72ζ4ζ72ζ43ζ75ζ4ζ75ζ43ζ7ζ4ζ7ζ43ζ74ζ43ζ73    linear of order 28 faithful
ρ1511-1-1ζ76ζ72ζ75ζ7ζ74ζ73ζ72ζ7ζ76ζ74ζ75ζ737473767672727575777473    linear of order 14
ρ161-1ζ2ζ2ζ76ζ72ζ75ζ7ζ74ζ7372776747573ζ43ζ74ζ43ζ73ζ4ζ76ζ43ζ76ζ4ζ72ζ43ζ72ζ4ζ75ζ43ζ75ζ4ζ7ζ43ζ7ζ4ζ74ζ4ζ73    linear of order 28 faithful
ρ171111ζ7ζ75ζ72ζ76ζ73ζ74ζ75ζ76ζ7ζ73ζ72ζ74ζ73ζ74ζ7ζ7ζ75ζ75ζ72ζ72ζ76ζ76ζ73ζ74    linear of order 7
ρ181-1ζ2ζ2ζ7ζ75ζ72ζ76ζ73ζ7475767737274ζ4ζ73ζ4ζ74ζ43ζ7ζ4ζ7ζ43ζ75ζ4ζ75ζ43ζ72ζ4ζ72ζ43ζ76ζ4ζ76ζ43ζ73ζ43ζ74    linear of order 28 faithful
ρ1911-1-1ζ7ζ75ζ72ζ76ζ73ζ74ζ75ζ76ζ7ζ73ζ72ζ747374777575727276767374    linear of order 14
ρ201-1ζ2ζ2ζ7ζ75ζ72ζ76ζ73ζ7475767737274ζ43ζ73ζ43ζ74ζ4ζ7ζ43ζ7ζ4ζ75ζ43ζ75ζ4ζ72ζ43ζ72ζ4ζ76ζ43ζ76ζ4ζ73ζ4ζ74    linear of order 28 faithful
ρ211111ζ73ζ7ζ76ζ74ζ72ζ75ζ7ζ74ζ73ζ72ζ76ζ75ζ72ζ75ζ73ζ73ζ7ζ7ζ76ζ76ζ74ζ74ζ72ζ75    linear of order 7
ρ221-1ζ2ζ2ζ73ζ7ζ76ζ74ζ72ζ7577473727675ζ4ζ72ζ4ζ75ζ43ζ73ζ4ζ73ζ43ζ7ζ4ζ7ζ43ζ76ζ4ζ76ζ43ζ74ζ4ζ74ζ43ζ72ζ43ζ75    linear of order 28 faithful
ρ2311-1-1ζ73ζ7ζ76ζ74ζ72ζ75ζ7ζ74ζ73ζ72ζ76ζ757275737377767674747275    linear of order 14
ρ241-1ζ2ζ2ζ73ζ7ζ76ζ74ζ72ζ7577473727675ζ43ζ72ζ43ζ75ζ4ζ73ζ43ζ73ζ4ζ7ζ43ζ7ζ4ζ76ζ43ζ76ζ4ζ74ζ43ζ74ζ4ζ72ζ4ζ75    linear of order 28 faithful
ρ251111ζ75ζ74ζ73ζ72ζ7ζ76ζ74ζ72ζ75ζ7ζ73ζ76ζ7ζ76ζ75ζ75ζ74ζ74ζ73ζ73ζ72ζ72ζ7ζ76    linear of order 7
ρ261-1ζ2ζ2ζ75ζ74ζ73ζ72ζ7ζ7674727577376ζ4ζ7ζ4ζ76ζ43ζ75ζ4ζ75ζ43ζ74ζ4ζ74ζ43ζ73ζ4ζ73ζ43ζ72ζ4ζ72ζ43ζ7ζ43ζ76    linear of order 28 faithful
ρ2711-1-1ζ75ζ74ζ73ζ72ζ7ζ76ζ74ζ72ζ75ζ7ζ73ζ767767575747473737272776    linear of order 14
ρ281-1ζ2ζ2ζ75ζ74ζ73ζ72ζ7ζ7674727577376ζ43ζ7ζ43ζ76ζ4ζ75ζ43ζ75ζ4ζ74ζ43ζ74ζ4ζ73ζ43ζ73ζ4ζ72ζ43ζ72ζ4ζ7ζ4ζ76    linear of order 28 faithful

Permutation representations of C28
Regular action on 28 points - transitive group 28T1
Generators in S28
(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)| (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28)>;

G:=Group( (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28) );

G=PermutationGroup([(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28)])

G:=TransitiveGroup(28,1);

Polynomial with Galois group C28 over ℚ
actionf(x)Disc(f)
28T1x28+x27+x26+x25+x24+x23+x22+x21+x20+x19+x18+x17+x16+x15+x14+x13+x12+x11+x10+x9+x8+x7+x6+x5+x4+x3+x2+x+12927

Matrix representation of C28 in GL1(𝔽29) generated by

26
G:=sub<GL(1,GF(29))| [26] >;

C28 in GAP, Magma, Sage, TeX

C_{28}
% in TeX

G:=Group("C28");
// GroupNames label

G:=SmallGroup(28,2);
// by ID

G=gap.SmallGroup(28,2);
# by ID

G:=PCGroup([3,-2,-7,-2,42]);
// Polycyclic

G:=Group<a|a^28=1>;
// generators/relations

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