C₂×#1928 #21057

order	256
nilpotency class	3
isoclinism	isoclinic class of #447
automorphism	Aut(G) order 131072
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

619 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);(4,5)(7,8,10,9)(11,12)(13,15)(14,16)(17,18);(3,4,6,5)(7,9,10,8)(12,15)(16,17);(3,5,6,4)(12,16)(14,18)(15,17)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 14045);