C₂×#1940 #21142

order	256
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	Aut(G) order 131072
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁵

Aliases

591 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)(8,10)(11,12,16,13,15,17,14,18);(4,6)(11,13,16,17,15,18,14,12);(7,8,9,10)(11,14,15,16)(12,13,17,18)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 14130);