C₃²×M₁₆ #3762

order	144
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	Aut(G) = C₂×D₄×GL(2,𝔽₃) (order 768) · Inn(G) = C₂² · Out(G) = C₂²×GL(2,𝔽₃)
homology	Abelianization (H₁) = C₂×C₃²×C₄ · Schur multiplier (H₂) = C₃

Aliases

C₃²×M₁₆

60 conjugacy classes of subgroups.

minimal degree	μ(G) = 14
transitive degree	μ_t(G) = 72

A minimal faithful permutation representation — 2 generators on 14 points:

(1,2,3)(7,8,9,10,11,12,13,14);(4,5,6)(8,12)(10,14)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(144, 105);