D₉×C₃⋊D₃ #66427

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

Aliases

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

122 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:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(324, 119);