C₂×#355 #2130

order	128
nilpotency class	4
isoclinism	isoclinic class of #353
automorphism	Aut(G) = #72238724 (order 2048) · Inn(G) = #99 · Out(G) = C₂×#120
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂³

Aliases

130 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 3 generators on 18 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(128, 862);