C₂×#432 #2918

order	128
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	Aut(G) order 16384
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁵

Aliases

244 conjugacy classes of subgroups.

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

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(128, 1650);