D₉² #66344

order	324
isoclinism	isoclinic class of D₉²
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

direct product	D₉²
unambiguous semidirect product	(C₉×D₉)⋊C₂
unambiguous semidirect product	(C₉⋊D₉)⋊C₂

C₉² ⋊ C₂²

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₉²	C₂²
Frattini, socle	C₃²	D₃²
LCS	G ▷ C₉²
UCS	C₁

59 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 18

A minimal faithful permutation representation — 2 generators on 18 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(324, 36);