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G = C₁₇  order 17

Cyclic group

p-group, cyclic, elementary abelian, simple, monomial

Aliases: C₁₇, also denoted Z₁₇, SmallGroup(17,1)

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

Generators and relations for C₁₇
 G = < a | a¹⁷=1 >

Character table of C₁₇

(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17)

G:=sub<Sym(17)| (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)>;

G:=Group( (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17) );

G=PermutationGroup([[(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)]])

G:=TransitiveGroup(17,1);

C₁₇ is a maximal subgroup of   D₁₇  C₂₈₉
C₁₇ is a maximal quotient of   C₂₈₉

Matrix representation of C₁₇ ►in GL₁(𝔽₁₀₃) generated by

G:=sub<GL(1,GF(103))| [100] >;

C₁₇ in GAP, Magma, Sage, TeX

C_{17}

% in TeX

G:=Group("C17");

// GroupNames label

G:=SmallGroup(17,1);

// by ID

G=gap.SmallGroup(17,1);

# by ID

G:=PCGroup([1,-17]:ExponentLimit:=1);

// Polycyclic

G:=Group<a|a^17=1>;

// generators/relations

Export

Subgroup lattice of C₁₇ in TeX
Character table of C₁₇ in TeX