C₂×#1984 #21298

order	256
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	Aut(G) order 262144
homology	Abelianization (H₁) = C₂³×C₈ · Schur multiplier (H₂) = C₂⁵×C₄

Aliases

751 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 256

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 14286);