C₂×C₉⋊D₉ #66382

order	324
isoclinism	isoclinic class of C₉⋊D₉
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂×C₉

Aliases

direct product	C₂×C₉⋊D₉
unambiguous semidirect product	(C₂×C₉)⋊D₉

Fitting	C₂×C₉² ⋊ C₂
derived, Sylow	C₉² ⋊ C₂²

	subgroup	G/H
center, hypercenter	C₂	C₉⋊D₉
commutator, cosocle, hypocenter	C₉²	C₂²
Frattini	C₃²	C₂×C₃⋊D₃
Fitting	C₂×C₉²	C₂
socle	C₂×C₃²	C₃⋊D₃
LCS	G ▷ C₉²
UCS	C₁ ◁ C₂

115 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 162

A minimal faithful permutation representation — 3 generators on 20 points:

(1,2)(4,6)(5,9)(7,8)(10,11)(13,15)(14,18)(16,17)(19,20);(1,2)(3,11,6,9,8,7,5,4,10);(12,20,15,18,17,16,14,13,19)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(324, 74);