C₃²×C₄⋊C₄ #3760

order	144
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	Aut(G) = #120×GL(2,𝔽₃) (order 1536) · Inn(G) = C₂² · Out(G) = D₄×GL(2,𝔽₃)
homology	Abelianization (H₁) = C₂×C₃²×C₄ · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product	C₃²×C₄⋊C₄
unambiguous semidirect product	C₄⋊(C₃²×C₄)

78 conjugacy classes of subgroups.

minimal degree	μ(G) = 14
transitive degree	μ_t(G) = 144

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(144, 103);