C₂×#418 #2893

order	128
nilpotency class	3
isoclinism	isoclinic class of AGL(1,ℤ/8)
automorphism	Aut(G) order 32768
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁵×C₄

Aliases

504 conjugacy classes of subgroups.

minimal degree	μ(G) = 14
transitive degree	μ_t(G) = 32

A minimal faithful permutation representation — 4 generators on 14 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(128, 1625);