C₂×C₃×C₇×C₂₇ #11765701

order	1134
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 1944
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃

Aliases

C₂×C₃×C₇×C₂₇

56 conjugacy classes of subgroups.

minimal degree	μ(G) = 39
transitive degree	μ_t(G) = 1134

A minimal faithful permutation representation — 2 generators on 39 points:

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

1134 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1134, 131);