C₂×#1884 #20946

order	256
nilpotency class	3
isoclinism	isoclinic class of #453
automorphism	Aut(G) order 16384
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁷

Aliases

897 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 32

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 13934);