D₃×C₃⋊D₉ #66428

order	324
isoclinism	isoclinic class of D₃×C₃⋊D₉
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product	D₃×C₃⋊D₉
unambiguous semidirect product	(C₃×D₃)⋊D₉
unambiguous semidirect product	(D₃×C₉)⋊D₃

C₃²×C₉ ⋊ C₂²

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₃²×C₉	C₂²
Frattini	C₃	D₃×C₃⋊D₃
socle	C₃³	C₂×D₃
LCS	G ▷ C₃²×C₉
UCS	C₁

130 conjugacy classes of subgroups.

minimal degree	μ(G) = 15
transitive degree	μ_t(G) = 54

A minimal faithful permutation representation — 3 generators on 15 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(324, 120);