Finite Group DatabasebetaFinite Group Databasebeta| order | 9720 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | AGL(1,𝔽5)×#92302 |
| Fitting, Hall | C5×#6891 ⋊ C2×C4 |
| derived | C5×C32⋊C9 ⋊ C2×C3×C4 |
| Sylow | #6891 ⋊ C2×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C4×#92302 |
1106 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 1106 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) = 90 |
195 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#13091120, AGL(1,𝔽5)×(((C3⋊D3)⋊C9)⋊C2)⋊C3 |
| maximal normal subgroup of | AGL(1,𝔽5)×(((C3⋊D3)⋊C9)⋊C2)⋊C3 |
Past the SmallGroups library coverage — no SmallGroups id.