C₂²×#2326 #7625296

order	512
nilpotency class	2
isoclinism	isoclinic class of #534
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₄ · Schur multiplier (H₂) = C₂¹³×C₄

Aliases

13818 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 6 generators on 20 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7532492);