C₃×C₇×C₈×C₉ #13094182

order	1512
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 2592
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃

Aliases

C₃×C₇×C₈×C₉

80 conjugacy classes of subgroups.

minimal degree	μ(G) = 27
transitive degree	μ_t(G) = 1512

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

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

1512 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1512, 79);