C₂×#1286 #7955

order	256
nilpotency class	3
isoclinism	isoclinic class of #1284
automorphism	Aut(G) order 16384
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂³×C₄

Aliases

351 conjugacy classes of subgroups.

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 64

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 943);