C₂×#1990 #21316

order	256
nilpotency class	3
isoclinism	isoclinic class of #465
automorphism	Aut(G) order 524288
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁵×C₄

Aliases

775 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);(3,4,5,6)(7,8)(9,13)(10,11)(12,14)(16,19)(17,21)(20,22);(4,6)(8,11)(12,13)(15,16,17,19,18,20,21,22);(7,9,10,14)(8,12,11,13)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 14304);