C₂×C₃×C₃⋊D₉ #66450

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

Aliases

direct product	C₂×C₃×C₃⋊D₉
unambiguous semidirect product	(C₂×C₃)⋊(C₃×D₉)

	subgroup	G/H
center, hypercenter	C₂×C₃	C₃⋊D₉
commutator, cosocle, hypocenter	C₃×C₉	C₂²×C₃
Frattini	C₃	C₂×C₃×C₃⋊D₃
Fitting	C₂×C₃²×C₉	C₂
socle	C₂×C₃³	D₃
LCS	G ▷ C₃×C₉
UCS	C₁ ◁ C₂×C₃

130 conjugacy classes of subgroups.

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 108

A minimal faithful permutation representation — 3 generators on 17 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(324, 142);