C₂⁴×C₄²×C₅ #11985358

order	1280
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 507343011840
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂¹⁴×C₄

Aliases

C₂⁴×C₄²×C₅

24030 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 1280

A minimal faithful permutation representation — 6 generators on 21 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 55626);