A₄×C₂₇ #66350

order	324
isoclinism	isoclinic class of A₄
automorphism	Aut(G) = D₃×C₉×S₄ (order 1296) · Inn(G) = A₄ · Out(G) = C₂×D₃×C₉
homology	Abelianization (H₁) = C₃×C₂₇ · Schur multiplier (H₂) = C₂×C₃

Aliases

A₄×C₂₇

Fitting	C₂²×C₂₇ ⋊ C₃
derived, Sylow	C₂² ⋊ C₃×C₂₇

32 conjugacy classes of subgroups.

minimal degree	μ(G) = 31
transitive degree	μ_t(G) = 108

A minimal faithful permutation representation — 2 generators on 31 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(324, 42);