C₄×#2678 #521183

order	512
nilpotency class	2
isoclinism	isoclinic class of #2668
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁸×C₄

Aliases

5028 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 128

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 428379);