C₂×#364 #2152

order	128
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	Aut(G) = C₂×#6437575 (order 1024) · Inn(G) = D₄ · Out(G) = C₂²×#120
homology	Abelianization (H₁) = C₂²×C₈ · Schur multiplier (H₂) = C₂²

Aliases

84 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);(3,4,7,12,8,11,16,18,9,13,15,10,6,17,5,14);(3,5,6,15,9,16,8,7)(4,10,11,14,13,12,17,18)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(128, 884);