C₃³×C₅×C₈ #11761913

order	1080
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 179712
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃³

Aliases

C₃³×C₅×C₈

224 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 1080

A minimal faithful permutation representation — 3 generators on 22 points:

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

1080 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1080, 259);