C₂²×#2354 #7625332

order	512
nilpotency class	2
isoclinism	isoclinic class of D₄²
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₄ · Schur multiplier (H₂) = C₂¹³×C₄

Aliases

14210 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);(5,6,8,7)(9,10,11,12)(14,15)(18,19);(6,7)(13,14,17,15)(16,19,20,18);(13,15,17,14)(16,19,20,18);(5,7,8,6)(13,16,17,20)(14,18,15,19)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7532528);