C₂×#360 #2144

order	128
nilpotency class	4
isoclinism	isoclinic class of #360
automorphism	Aut(G) = #72231669 (order 1024) · Inn(G) = #102 · Out(G) = C₂⁵
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂³

Aliases

116 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);(4,8,9,17)(5,11)(6,14)(10,12,15,18)(13,16);(3,4)(5,12)(6,15)(7,9)(8,16)(10,14)(11,17)(13,18)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(128, 876);