C₂×C₃²×C₄×C₂₇ #14517786

order	1944
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 559872
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂×C₃³

Aliases

C₂×C₃²×C₄×C₂₇

576 conjugacy classes of subgroups.

minimal degree	μ(G) = 39
transitive degree	μ_t(G) = 1944

A minimal faithful permutation representation — 3 generators on 39 points:

(1,2,3,4)(7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33);(5,6)(34,35,36);(37,38,39)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 2180);