C₈²×C₂₇ #13134064

order	1728
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 27648
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₈

Aliases

C₈²×C₂₇

148 conjugacy classes of subgroups.

minimal degree	μ(G) = 43
transitive degree	μ_t(G) = 1728

A minimal faithful permutation representation — 2 generators on 43 points:

(1,2,3,4,5,6,7,8)(17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43);(9,10,11,12,13,14,15,16)

1728 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 127);