C₃²×#226 #88966

order	432
isoclinism	isoclinic class of #226
automorphism	?
homology	Abelianization (H₁) = C₂×C₃² · Schur multiplier (H₂) = C₃

Aliases

	subgroup	G/H
center, socle, hypercenter	C₂×C₃²	S₄
commutator, cosocle, hypocenter	SL(2,𝔽₃)	C₂×C₃²
Frattini	C₂	C₃²×S₄
Fitting	C₃²×Q₈	D₃
prime radical	C₃²×SL(2,𝔽₃)	C₂
LCS	G ▷ SL(2,𝔽₃)
UCS	C₁ ◁ C₂×C₃²

102 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 144

A minimal faithful permutation representation — 2 generators on 22 points:

(1,15,10,7,5,6,12,13)(2,3,14,9,8,11,16,4)(20,21,22);(3,9,12)(4,10,11)(6,13,16)(7,14,15)(17,18,19)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 613);