C₂×#430 #2915

order	128
nilpotency class	3
isoclinism	isoclinic class of AGL(1,ℤ/8)
automorphism	Aut(G) order 8192
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁵

Aliases

230 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 32

A minimal faithful permutation representation — 4 generators on 18 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(128, 1647);