C₂×#1861 #20866

order	256
nilpotency class	3
isoclinism	isoclinic class of #453
automorphism	Aut(G) order 8192
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁶

Aliases

679 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 32

A minimal faithful permutation representation — 4 generators on 18 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 13854);