C₂³×C₃³×C₉ #14519382

order	1944
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 8253633024
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂³×C₃⁶

Aliases

C₂³×C₃³×C₉

6336 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 1944

A minimal faithful permutation representation — 4 generators on 24 points:

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

1944 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 3776);