C₂×#1368 #11998

order	256
nilpotency class	4
isoclinism	isoclinic class of #365
automorphism	Aut(G) order 8192
homology	Abelianization (H₁) = C₂²×C₈ · Schur multiplier (H₂) = C₂³

Aliases

127 conjugacy classes of subgroups.

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 256

A minimal faithful permutation representation — 3 generators on 26 points:

(1,2);(3,4,5,7,6,8,9,10)(12,16,17,22)(13,19)(14,21)(18,25,24,23)(20,26);(11,12,13,16,14,18,19,23,15,17,20,22,21,24,26,25)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 4986);