C₂³×#6891 #14518559

order	1944
nilpotency class	2
isoclinism	isoclinic class of C₃²⋊H(3,𝔽₃)
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃³ · Schur multiplier (H₂) = C₂³×C₃³

Aliases

	subgroup	G/H
center, socle	C₂³×C₃²	C₃³
commutator, Frattini, cosocle	C₃²	C₂³×C₃³
prime radical	C₂³×C₃⁴	C₃
LCS	G ▷ C₃² ▷ C₁
UCS	C₁ ◁ C₂³×C₃² ◁ G

2016 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 216

A minimal faithful permutation representation — 3 generators on 24 points:

(1,2)(7,8,10,9,12,14,13,11,15)(16,17,19)(18,21,23)(20,24,22);(3,4)(8,11,12)(10,14,15);(5,6)(17,20,21)(19,23,24)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 2953);