C₂×#2168 #33430

order	256
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	Aut(G) order 8192
homology	Abelianization (H₁) = C₂³×C₈ · Schur multiplier (H₂) = C₂⁵

Aliases

377 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 128

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 26418);