order	216
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂³×C₉ (order 72) · Inn(G) = C₁ · Out(G) = C₂³×C₉
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₂₁₆
abelian	C₈×C₂₇

Subgroups

16 conjugacy classes of subgroups.

minimal degree	μ(G) = 35
transitive degree	μ_t(G) = 216

A minimal faithful permutation representation — 1 generator on 35 points:

(1,2,3,4,5,6,7,8)(9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(216, 2);