C₃²×C₄ #156

order	36
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) = C₂×GL(2,𝔽₃) (order 96) · Inn(G) = C₁ · Out(G) = C₂×GL(2,𝔽₃)
holomorph	G ⋊ Aut(G) = D₄×AGL(2,𝔽₃)
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃

Aliases

C₃²×C₄

18 conjugacy classes of subgroups.

minimal degree	μ(G) = 10
transitive degree	μ_t(G) = 36

A minimal faithful permutation representation — 2 generators on 10 points:

(1,2,3,4)(5,6,7);(8,9,10)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36, 8);