A₄×C₂²⋊C₉ #88877

order	432
isoclinism	isoclinic class of A₄²
automorphism	?
homology	Abelianization (H₁) = C₃×C₉ · Schur multiplier (H₂) = C₂²×C₃

Aliases

direct product	A₄×C₂²⋊C₉
unambiguous semidirect product	(C₂²×A₄)⋊C₉

C₂⁴ ⋊ C₃×C₉

	subgroup	G/H
center, Frattini, hypercenter	C₃	A₄²
commutator, hypocenter	C₂⁴	C₃×C₉
Fitting, socle, cosocle	C₂⁴×C₃	C₃²
prime radical	C₂²×C₃×A₄	C₃
LCS	G ▷ C₂⁴
UCS	C₁ ◁ C₃

74 conjugacy classes of subgroups.

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 54

A minimal faithful permutation representation — 2 generators on 17 points:

(1,4)(2,3)(6,7,8)(9,10,12,11,13,15,14,16,17);(2,3,4)(5,8)(6,7)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 524);