C₂×#1891 #20963

order	256
nilpotency class	3
isoclinism	isoclinic class of B(4,𝔽₂)
automorphism	Aut(G) order 16384
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁷

Aliases

935 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);(3,4,7,11,8,5,9,13)(6,12,15,18,14,10,16,17);(3,5,7,13,8,4,9,11)(6,12,16,17,14,10,15,18);(3,6)(4,10)(5,12)(7,16)(8,14)(9,15)(11,18)(13,17)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 13951);