C₂×#1738 #20350

order	256
nilpotency class	3
isoclinism	isoclinic class of AGL(1,ℤ/8)
automorphism	Aut(G) order 262144
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂⁷

Aliases

1055 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 64

A minimal faithful permutation representation — 4 generators on 22 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 13338);