C₃²×C₄×C₅×C₈ #13085122

order	1440
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 24576
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃×C₄

Aliases

C₃²×C₄×C₅×C₈

264 conjugacy classes of subgroups.

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 1440

A minimal faithful permutation representation — 2 generators on 23 points:

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

1440 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 1439);