C₂×#1865 #20871

order	256
nilpotency class	3
isoclinism	isoclinic class of #447
automorphism	Aut(G) order 131072
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁶

Aliases

771 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 256

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 13859);