C₂×#347 #2109

order	128
nilpotency class	2
isoclinism	isoclinic class of H(3,ℤ/4)
automorphism	Aut(G) = #72216294 (order 1024) · Inn(G) = C₄² · Out(G) = C₂×#120
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂²

Aliases

84 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);(3,4,5,9,6,11,13,17,7,10,12,18,14,8,15,16);(4,8,10,11)(5,12)(9,17,18,16)(13,15)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(128, 841);