C₂×#349 #2114

order	128
nilpotency class	3
isoclinism	isoclinic class of #99
automorphism	Aut(G) = #72218347 (order 1024) · Inn(G) = C₂²⋊C₄ · Out(G) = C₂³×D₄
homology	Abelianization (H₁) = C₂²×C₈ · Schur multiplier (H₂) = C₂³

Aliases

118 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);(3,4,5,9,6,10,12,16,7,8,11,14,13,15,17,18);(4,8)(5,11)(10,15)(12,17)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(128, 846);