order	117
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂×C₃²×C₄ (order 72) · Inn(G) = C₁ · Out(G) = C₂×C₃²×C₄
holomorph	G ⋊ Aut(G) = AGL(1,ℤ/9)×AGL(1,𝔽₁₃)
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₁₇
abelian	C₉×C₁₃

Subgroups

6 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 117

A minimal faithful permutation representation — 1 generator on 22 points:

(1,2,3,4,5,6,7,8,9)(10,11,12,13,14,15,16,17,18,19,20,21,22)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(117, 2);