C₂×#354 #2125

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) = C₂⁴

Aliases

142 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)(5,11,13,18)(6,14,16,9)(7,10)(8,12)(15,17);(3,5,7,13)(4,8,10,17)(6,15,16,12)(9,18,14,11)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(128, 857);