C₂×#1910 #21008

order	256
nilpotency class	3
isoclinism	isoclinic class of #1909
automorphism	Aut(G) order 32768
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁶×C₄

Aliases

939 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)(5,11)(6,14,16,9)(7,13)(8,10)(12,15,18,17);(3,5,11,4,8,13,7,10)(6,12,15,9,16,18,17,14);(3,6)(4,9)(5,12)(7,17)(8,16)(10,14)(11,15)(13,18)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 13996);