C₂×#1436 #13758

order	256
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	Aut(G) order 1048576
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂⁷×C₄

Aliases

1775 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);(4,6)(7,8,10,9)(12,14)(15,16,18,17);(11,12)(13,14)(15,16,18,17);(3,4)(5,6)(7,9,10,8)(11,12)(13,14)(15,17,18,16)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 6746);