C₃³×C₅×C₁₃ #13182181

order	1755
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 539136
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃³

Aliases

C₃³×C₅×C₁₃

112 conjugacy classes of subgroups.

minimal degree	μ(G) = 27
transitive degree	μ_t(G) = 1755

A minimal faithful permutation representation — 3 generators on 27 points:

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

1755 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1755, 14);