C₃×A₄² #89103

order	432
isoclinism	isoclinic class of A₄²
automorphism	?
homology	Abelianization (H₁) = C₃³ · Schur multiplier (H₂) = C₂²×C₃³

Aliases

direct product	C₃×A₄²
unambiguous semidirect product	(C₂²×A₄)⋊C₃²
unambiguous semidirect product	(C₂²⋊A₄)⋊C₃²

Fitting, socle	C₂⁴×C₃ ⋊ C₃²
derived, Sylow	C₂⁴ ⋊ C₃³

	subgroup	G/H
center, hypercenter	C₃	A₄²
commutator, cosocle, hypocenter	C₂⁴	C₃³
Frattini	C₁	G
Fitting, socle	C₂⁴×C₃	C₃²
LCS	G ▷ C₂⁴
UCS	C₁ ◁ C₃

158 conjugacy classes of subgroups.

minimal degree	μ(G) = 11
transitive degree	μ_t(G) = 36

A minimal faithful permutation representation — 3 generators on 11 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 750);