C₂×C₃²×D₉ #66444

order	324
isoclinism	isoclinic class of D₉
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃² · Schur multiplier (H₂) = C₂×C₃

Aliases

C₂×C₃²×D₉

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

122 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 2 generators on 17 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(324, 136);