C₂×#330 #1523

order	128
nilpotency class	3
isoclinism	isoclinic class of #327
automorphism	Aut(G) = #72233158 (order 4096) · Inn(G) = C₂²⋊C₄ · Out(G) = #12759
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂²

Aliases

116 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 128

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(128, 255);