C₄×#347 #12540

order	256
nilpotency class	2
isoclinism	isoclinic class of H(3,ℤ/4)
automorphism	Aut(G) order 16384
homology	Abelianization (H₁) = C₄³ · Schur multiplier (H₂) = C₄²

Aliases

209 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 64

A minimal faithful permutation representation — 3 generators on 20 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 5528);