C₂³×C₃×C₃⋊D₃ #89126

order	432
isoclinism	isoclinic class of C₃⋊D₃
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃ · Schur multiplier (H₂) = C₂⁶×C₃

Aliases

C₂³×C₃×C₃⋊D₃

	subgroup	G/H
center, hypercenter	C₂³×C₃	C₃⋊D₃
commutator, cosocle, hypocenter	C₃²	C₂⁴×C₃
Frattini	C₁	G
Fitting, socle	C₂³×C₃³	C₂
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂³×C₃

932 conjugacy classes of subgroups.

minimal degree	μ(G) = 15
transitive degree	μ_t(G) = 144

A minimal faithful permutation representation — 4 generators on 15 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 773);