C₄×#2849 #607624

order	512
nilpotency class	2
isoclinism	isoclinic class of #2846
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂¹⁰

Aliases

8588 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)(9,10)(11,12)(13,14)(15,18)(16,17)(19,20);(14,17)(18,20);(6,8)(13,15,16,19)(14,18,17,20);(10,12)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 514820);