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G = C27order 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

C1 — C27
C1C3C9 — C27
C1 — C27
C1 — C27
C1C3C3C3C3C3C3C9C9 — C27

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


Character table of C27

 class 13A3B9A9B9C9D9E9F27A27B27C27D27E27F27G27H27I27J27K27L27M27N27O27P27Q27R
 size 111111111111111111111111111
ρ1111111111111111111111111111    trivial
ρ21ζ32ζ3ζ273ζ276ζ2712ζ2721ζ2715ζ2724ζ2726ζ272ζ2710ζ2719ζ2711ζ2720ζ274ζ277ζ275ζ278ζ2713ζ2722ζ2716ζ2725ζ2714ζ2723ζ2717ζ27    linear of order 27 faithful
ρ31ζ3ζ32ζ276ζ2712ζ2724ζ2715ζ273ζ2721ζ2725ζ274ζ2720ζ2711ζ2722ζ2713ζ278ζ2714ζ2710ζ2716ζ2726ζ2717ζ275ζ2723ζ27ζ2719ζ277ζ272    linear of order 27 faithful
ρ4111ζ3ζ32ζ3ζ3ζ32ζ32ζ98ζ92ζ9ζ9ζ92ζ92ζ94ζ97ζ95ζ98ζ94ζ94ζ97ζ97ζ95ζ95ζ98ζ9    linear of order 9
ρ51ζ32ζ3ζ2712ζ2724ζ2721ζ273ζ276ζ2715ζ2723ζ278ζ2713ζ2722ζ2717ζ2726ζ2716ζ27ζ2720ζ275ζ2725ζ277ζ2710ζ2719ζ272ζ2711ζ2714ζ274    linear of order 27 faithful
ρ61ζ3ζ32ζ2715ζ273ζ276ζ2724ζ2721ζ2712ζ2722ζ2710ζ2723ζ2714ζ27ζ2719ζ2720ζ278ζ2725ζ2713ζ2711ζ272ζ2726ζ2717ζ2716ζ277ζ274ζ275    linear of order 27 faithful
ρ7111ζ32ζ3ζ32ζ32ζ3ζ3ζ97ζ94ζ92ζ92ζ94ζ94ζ98ζ95ζ9ζ97ζ98ζ98ζ95ζ95ζ9ζ9ζ97ζ92    linear of order 9
ρ81ζ32ζ3ζ2721ζ2715ζ273ζ2712ζ2724ζ276ζ2720ζ2714ζ2716ζ2725ζ2723ζ275ζ27ζ2722ζ278ζ272ζ2710ζ2719ζ274ζ2713ζ2717ζ2726ζ2711ζ277    linear of order 27 faithful
ρ91ζ3ζ32ζ2724ζ2721ζ2715ζ276ζ2712ζ273ζ2719ζ2716ζ2726ζ2717ζ277ζ2725ζ275ζ272ζ2713ζ2710ζ2723ζ2714ζ2720ζ2711ζ274ζ2722ζ27ζ278    linear of order 27 faithful
ρ10111111111ζ32ζ32ζ3ζ3ζ32ζ32ζ3ζ3ζ32ζ32ζ3ζ3ζ3ζ3ζ32ζ32ζ32ζ3    linear of order 3
ρ111ζ32ζ3ζ273ζ276ζ2712ζ2721ζ2715ζ2724ζ2717ζ2720ζ2719ζ27ζ272ζ2711ζ2713ζ2716ζ2723ζ2726ζ2722ζ274ζ2725ζ277ζ275ζ2714ζ278ζ2710    linear of order 27 faithful
ρ121ζ3ζ32ζ276ζ2712ζ2724ζ2715ζ273ζ2721ζ2716ζ2722ζ272ζ2720ζ2713ζ274ζ2717ζ2723ζ27ζ277ζ278ζ2726ζ2714ζ275ζ2719ζ2710ζ2725ζ2711    linear of order 27 faithful
ρ13111ζ3ζ32ζ3ζ3ζ32ζ32ζ95ζ98ζ94ζ94ζ98ζ98ζ97ζ9ζ92ζ95ζ97ζ97ζ9ζ9ζ92ζ92ζ95ζ94    linear of order 9
ρ141ζ32ζ3ζ2712ζ2724ζ2721ζ273ζ276ζ2715ζ2714ζ2726ζ2722ζ274ζ278ζ2717ζ2725ζ2710ζ2711ζ2723ζ277ζ2716ζ2719ζ27ζ2720ζ272ζ275ζ2713    linear of order 27 faithful
ρ151ζ3ζ32ζ2715ζ273ζ276ζ2724ζ2721ζ2712ζ2713ζ27ζ275ζ2723ζ2719ζ2710ζ272ζ2717ζ2716ζ274ζ2720ζ2711ζ278ζ2726ζ277ζ2725ζ2722ζ2714    linear of order 27 faithful
ρ16111ζ32ζ3ζ32ζ32ζ3ζ3ζ94ζ9ζ95ζ95ζ9ζ9ζ92ζ98ζ97ζ94ζ92ζ92ζ98ζ98ζ97ζ97ζ94ζ95    linear of order 9
ρ171ζ32ζ3ζ2721ζ2715ζ273ζ2712ζ2724ζ276ζ2711ζ275ζ2725ζ277ζ2714ζ2723ζ2710ζ274ζ2726ζ2720ζ2719ζ27ζ2713ζ2722ζ278ζ2717ζ272ζ2716    linear of order 27 faithful
ρ181ζ3ζ32ζ2724ζ2721ζ2715ζ276ζ2712ζ273ζ2710ζ277ζ278ζ2726ζ2725ζ2716ζ2714ζ2711ζ274ζ27ζ275ζ2723ζ272ζ2720ζ2722ζ2713ζ2719ζ2717    linear of order 27 faithful
ρ19111111111ζ3ζ3ζ32ζ32ζ3ζ3ζ32ζ32ζ3ζ3ζ32ζ32ζ32ζ32ζ3ζ3ζ3ζ32    linear of order 3
ρ201ζ32ζ3ζ273ζ276ζ2712ζ2721ζ2715ζ2724ζ278ζ2711ζ27ζ2710ζ2720ζ272ζ2722ζ2725ζ2714ζ2717ζ274ζ2713ζ277ζ2716ζ2723ζ275ζ2726ζ2719    linear of order 27 faithful
ρ211ζ3ζ32ζ276ζ2712ζ2724ζ2715ζ273ζ2721ζ277ζ2713ζ2711ζ272ζ274ζ2722ζ2726ζ275ζ2719ζ2725ζ2717ζ278ζ2723ζ2714ζ2710ζ27ζ2716ζ2720    linear of order 27 faithful
ρ22111ζ3ζ32ζ3ζ3ζ32ζ32ζ92ζ95ζ97ζ97ζ95ζ95ζ9ζ94ζ98ζ92ζ9ζ9ζ94ζ94ζ98ζ98ζ92ζ97    linear of order 9
ρ231ζ32ζ3ζ2712ζ2724ζ2721ζ273ζ276ζ2715ζ275ζ2717ζ274ζ2713ζ2726ζ278ζ277ζ2719ζ272ζ2714ζ2716ζ2725ζ27ζ2710ζ2711ζ2720ζ2723ζ2722    linear of order 27 faithful
ρ241ζ3ζ32ζ2715ζ273ζ276ζ2724ζ2721ζ2712ζ274ζ2719ζ2714ζ275ζ2710ζ27ζ2711ζ2726ζ277ζ2722ζ272ζ2720ζ2717ζ278ζ2725ζ2716ζ2713ζ2723    linear of order 27 faithful
ρ25111ζ32ζ3ζ32ζ32ζ3ζ3ζ9ζ97ζ98ζ98ζ97ζ97ζ95ζ92ζ94ζ9ζ95ζ95ζ92ζ92ζ94ζ94ζ9ζ98    linear of order 9
ρ261ζ32ζ3ζ2721ζ2715ζ273ζ2712ζ2724ζ276ζ272ζ2723ζ277ζ2716ζ275ζ2714ζ2719ζ2713ζ2717ζ2711ζ27ζ2710ζ2722ζ274ζ2726ζ278ζ2720ζ2725    linear of order 27 faithful
ρ271ζ3ζ32ζ2724ζ2721ζ2715ζ276ζ2712ζ273ζ27ζ2725ζ2717ζ278ζ2716ζ277ζ2723ζ2720ζ2722ζ2719ζ2714ζ275ζ2711ζ272ζ2713ζ274ζ2710ζ2726    linear of order 27 faithful

Permutation representations of C27
Regular action on 27 points - transitive group 27T1
Generators in S27
(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);

Matrix representation of C27 in GL1(𝔽109) generated by

7
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

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