C₄×#2364 #513530

order	512
nilpotency class	2
isoclinism	isoclinic class of D₄²
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄² · Schur multiplier (H₂) = C₂⁸×C₄

Aliases

5002 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);(6,8)(9,10,12,11)(14,17)(18,20);(9,11,12,10)(13,14)(15,18)(16,17)(19,20);(5,6,7,8)(13,15,16,19)(14,18,17,20);(14,17)(18,20)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 420726);