C₂²×#1113 #89122

order	432
isoclinism	isoclinic class of #1113
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁶

Aliases

Fitting, socle	C₂²×C₃³ ⋊ C₂²
derived, Sylow	C₃³ ⋊ C₂⁴

	subgroup	G/H
center, hypercenter	C₂²	#1113
commutator, cosocle, hypocenter	C₃³	C₂⁴
Frattini	C₁	G
Fitting, socle	C₂²×C₃³	C₂²
LCS	G ▷ C₃³
UCS	C₁ ◁ C₂²

642 conjugacy classes of subgroups.

minimal degree	μ(G) = 13
transitive degree	μ_t(G) = 48

A minimal faithful permutation representation — 4 generators on 13 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 769);