C₂×#1914 #21015

order	256
nilpotency class	3
isoclinism	isoclinic class of #1913
automorphism	Aut(G) order 32768
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁷

Aliases

931 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);(3,4,7,11,8,10,17,5)(6,13,15,18,14,9,16,12);(3,5,7,10,8,11,17,4)(6,12,16,13,14,18,15,9);(3,6)(4,9)(5,12)(7,16)(8,14)(10,13)(11,18)(15,17)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 14003);