C₄×C₅×C₈² #11930558

order	1280
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 3145728
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₄²×C₈

Aliases

C₄×C₅×C₈²

750 conjugacy classes of subgroups.

minimal degree	μ(G) = 25
transitive degree	μ_t(G) = 1280

A minimal faithful permutation representation — 3 generators on 25 points:

(1,2,3,4,5,6,7,8)(21,22,23,24,25);(9,10,11,12,13,14,15,16);(17,18,19,20)

1280 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 826);