Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of AGL(1,𝔽16) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2 |
| direct product | C22×AGL(1,𝔽16) |
| unambiguous semidirect product | (C22×C22⋊A4)⋊C5 |
| Fitting, socle, Sylow | C26 ⋊ C3×C5 |
| derived | C24 ⋊ C22×C3×C5 |
| Hall | C22×C24⋊C5 ⋊ C3 |
| Hall | C22×C22⋊A4 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | AGL(1,𝔽16) |
| commutator, cosocle, hypocenter | C24 | C22×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C26 | C3×C5 |
| LCS | G ▷ C24 | |
| UCS | C1 ◁ C22 | |
236 conjugacy classes of subgroups.
| transitive degree | μt(G) = 60 |
64 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 11365);