C₂×#1301 #8075

order	256
nilpotency class	3
isoclinism	isoclinic class of #327
automorphism	Aut(G) order 16384
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂⁴

Aliases

333 conjugacy classes of subgroups.

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 128

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 1063);