C₂×#1903 #20994

order	256
nilpotency class	3
isoclinism	isoclinic class of #1902
automorphism	Aut(G) order 16384
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁷

Aliases

891 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);(3,4,9,12)(5,8,11,7)(6,13)(10,14)(15,17)(16,18);(3,5,7,4,9,11,8,12)(6,13,15,10,16,18,14,17);(3,6)(4,10)(5,13)(7,15)(8,14)(9,16)(11,18)(12,17)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 13982);