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G = C₂₇  order 27 = 3³

Cyclic group

p-group, cyclic, abelian, monomial

Aliases: C₂₇, also denoted Z₂₇, SmallGroup(27,1)

Series: Derived ►Chief ►Lower central ►Upper central ►Jennings

Generators and relations for C₂₇
 G = < a | a²⁷=1 >

Character table of C₂₇

(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)

G:=sub<Sym(27)| (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)>;

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) );

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)]])

G:=TransitiveGroup(27,1);

C₂₇ is a maximal subgroup of   D₂₇  C₈₁  C₂₇⋊C₃  C₉.A₄  C₇⋊C₂₇  C₁₃⋊C₂₇
C₂₇ is a maximal quotient of   C₈₁  C₉.A₄  C₇⋊C₂₇  C₁₃⋊C₂₇

Matrix representation of C₂₇ ►in GL₁(𝔽₁₀₉) generated by

G:=sub<GL(1,GF(109))| [7] >;

C₂₇ in GAP, Magma, Sage, TeX

C_{27}

% in TeX

G:=Group("C27");

// GroupNames label

G:=SmallGroup(27,1);

// by ID

G=gap.SmallGroup(27,1);

# by ID

G:=PCGroup([3,-3,-3,-3,9,22]);

// Polycyclic

G:=Group<a|a^27=1>;

// generators/relations

Export

Subgroup lattice of C₂₇ in TeX
Character table of C₂₇ in TeX