C₂×#391 #2294

order	128
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	Aut(G) order 131072
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁵×C₄

Aliases

464 conjugacy classes of subgroups.

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

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(128, 1026);