C₂⁵×A₄ #87591

order	384
isoclinism	isoclinic class of A₄
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₃ · Schur multiplier (H₂) = C₂¹¹

Aliases

direct product	C₂⁵×A₄
unambiguous semidirect product	C₂²⋊(C₂⁵×C₃)

Fitting, socle, Sylow	C₂⁷ ⋊ C₃
derived	C₂² ⋊ C₂⁵×C₃

	subgroup	G/H
center, hypercenter	C₂⁵	A₄
commutator, cosocle, hypocenter	C₂²	C₂⁵×C₃
Frattini	C₁	G
Fitting, socle	C₂⁷	C₃
LCS	G ▷ C₂²
UCS	C₁ ◁ C₂⁵

10984 conjugacy classes of subgroups.

minimal degree	μ(G) = 14
transitive degree	μ_t(G) = 96

A minimal faithful permutation representation — 5 generators on 14 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 20167);