C₂×#329 #1522

order	128
nilpotency class	3
isoclinism	isoclinic class of #327
automorphism	Aut(G) = #72234442 (order 4096) · Inn(G) = C₂²⋊C₄ · Out(G) = C₂×#2196
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂³

Aliases

142 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 64

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(128, 254);