C₂⁵×C₄² #10585866

order	512
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 1006568535490560
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂²⁰×C₄

Aliases

C₂⁵×C₄²

129858 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 512

A minimal faithful permutation representation — 7 generators on 18 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10493062);