C₂×#1733 #20342

order	256
nilpotency class	3
isoclinism	isoclinic class of AGL(1,ℤ/8)
automorphism	Aut(G) order 131072
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂⁷

Aliases

1135 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 64

A minimal faithful permutation representation — 4 generators on 22 points:

(1,2);(3,4,5,6)(7,8)(9,15)(10,18)(11,14)(12,17)(13,19)(16,21)(20,22);(7,9)(8,12,14,20)(10,17)(11,16)(13,15,18,21)(19,22);(9,16)(12,20)(15,21)(17,22)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 13330);