C₂⁴×C₁₃×C₁₆ #15748959

order	3328
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 495452160
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂¹⁰

Aliases

C₂⁴×C₁₃×C₁₆

2590 conjugacy classes of subgroups.

minimal degree	μ(G) = 37
transitive degree	μ_t(G) = 3328

A minimal faithful permutation representation — 5 generators on 37 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16)(25,26,27,28,29,30,31,32,33,34,35,36,37);(17,18);(19,20);(21,22);(23,24)

3328 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 55608);