C₂×#1744 #20361

order	256
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	Aut(G) order 1048576
homology	Abelianization (H₁) = C₂²×C₄×C₈ · Schur multiplier (H₂) = C₂⁴×C₄²

Aliases

719 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);(7,8)(9,12)(10,11)(13,14)(15,16,17,19,18,20,21,22);(3,4,5,6)(8,11)(12,14);(7,9,10,13)(8,12,11,14)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 13349);