C₂×C₇×C₉² #11765698

order	1134
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 23328
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₉

Aliases

C₂×C₇×C₉²

92 conjugacy classes of subgroups.

minimal degree	μ(G) = 27
transitive degree	μ_t(G) = 1134

A minimal faithful permutation representation — 2 generators on 27 points:

(1,2)(3,4,5,6,7,8,9,10,11)(21,22,23,24,25,26,27);(12,13,14,15,16,17,18,19,20)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1134, 128);