C₂×C₃²×C₈×C₉ #13048041

order	1296
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 373248
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂×C₃³

Aliases

C₂×C₃²×C₈×C₉

550 conjugacy classes of subgroups.

minimal degree	μ(G) = 25
transitive degree	μ_t(G) = 1296

A minimal faithful permutation representation — 3 generators on 25 points:

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

1296 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1296, 1759);