C₂²×#1923 #6371613

order	512
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₈ · Schur multiplier (H₂) = C₂⁹×C₄

Aliases

4810 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 256

A minimal faithful permutation representation — 5 generators on 20 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6278809);