C₂×#1313 #11403

order	256
nilpotency class	2
isoclinism	isoclinic class of H(3,ℤ/4)
automorphism	Aut(G) order 8192
homology	Abelianization (H₁) = C₂×C₄×C₈ · Schur multiplier (H₂) = C₂³

Aliases

151 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);(11,12,13,17,14,19,21,25,15,18,20,26,22,16,23,24);(3,4,5,7,6,8,9,10)(12,16,18,19)(13,20)(17,25,26,24)(21,23)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 4391);