C₂²×C₄×C₈×C₁₉ #14560726

order	2432
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 3538944
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁵×C₄

Aliases

C₂²×C₄×C₈×C₁₉

760 conjugacy classes of subgroups.

minimal degree	μ(G) = 35
transitive degree	μ_t(G) = 2432

A minimal faithful permutation representation — 4 generators on 35 points:

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

2432 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1601);