Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
| direct product | AGL(1,𝔽5)×ΓL(1,𝔽25) |
| Fitting | C3×C5×C8 ⋊ C2×C4 |
| Hall | C3×C5 ⋊ C4×M16 |
| Sylow | C5 ⋊ C4×ΓL(1,𝔽25) |
| Sylow | C3 ⋊ M16×AGL(1,𝔽5) |
284 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 96 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
90 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 5843);