C₃×#10624535 #14551985

order	2187
nilpotency class	5
isoclinism	isoclinic class of #10624535
automorphism	?
homology	Abelianization (H₁) = C₃³ · Schur multiplier (H₂) = C₃³×C₉

Aliases

	subgroup	G/H
center, socle	C₃²	#6879
commutator, Frattini, cosocle	C₉²	C₃³
LCS	G ▷ C₉² ▷ C₃×C₉ ▷ C₃² ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃² ◁ C₃³ ◁ C₃²×C₉ ◁ C₃×C₉² ◁ G
LECS	G ▷ C₉² ▷ C₃×C₉ ▷ C₃² ▷ C₃ ▷ C₁

176 conjugacy classes of subgroups.

minimal degree	μ(G) = 84
transitive degree	μ_t(G) = 243

267 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2187, 5844);