C₂²×#2363 #7625365

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

Aliases

15778 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)(13,14,17,16)(15,18,20,19);(9,11,12,10)(14,16)(18,19);(5,6)(7,8)(13,15,17,20)(14,18,16,19);(13,16,17,14)(15,19,20,18)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7532561);