C₄×#2342 #513501

order	512
nilpotency class	2
isoclinism	isoclinic class of D₄²
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄² · Schur multiplier (H₂) = C₂⁷×C₄²

Aliases

5710 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);(6,8)(9,10,11,12)(13,14)(15,17)(16,18)(19,20);(5,6)(7,8)(13,15,16,19)(14,17,18,20);(14,18)(17,20);(6,8)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 420697);