C₂×C₅×C₉×C₁₆ #13083895

order	1440
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 768
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

C₂×C₅×C₉×C₁₆

84 conjugacy classes of subgroups.

minimal degree	μ(G) = 32
transitive degree	μ_t(G) = 1440

A minimal faithful permutation representation — 2 generators on 32 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16)(19,20,21,22,23,24,25,26,27)(28,29,30,31,32);(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, 212);