C₂×#365 #2154

order	128
nilpotency class	4
isoclinism	isoclinic class of #365
automorphism	Aut(G) = #72231669 (order 1024) · Inn(G) = #106 · Out(G) = C₂⁵
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂²

Aliases

76 conjugacy classes of subgroups.

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

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(128, 886);