C₂×#1996 #21331

order	256
nilpotency class	3
isoclinism	isoclinic class of #1468
automorphism	Aut(G) order 65536
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁵×C₄

Aliases

849 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 64

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 14319);