C₄×#3496 #7625640

order	512
nilpotency class	2
isoclinism	isoclinic class of #3484
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₄ · Schur multiplier (H₂) = C₂¹⁴

Aliases

12018 conjugacy classes of subgroups.

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 128

A minimal faithful permutation representation — 6 generators on 16 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7532836);