C₂×#1974 #21238

order	256
nilpotency class	3
isoclinism	isoclinic class of #465
automorphism	Aut(G) order 65536
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁵×C₄

Aliases

779 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);(4,6)(7,8,11,15,12,16,10,13)(9,17,19,22,20,21,18,14);(3,4,5,6)(8,13,16,15)(14,21,22,17);(7,9,10,18,12,20,11,19)(8,14,15,17,16,22,13,21)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 14226);