Finite Group DatabasebetaFinite Group Databasebeta| order | 9720 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | D5×#92265⋊C2 |
| Fitting, Hall | C5×#6900 ⋊ C23 |
| derived | C5×C92 ⋊ C23×C3 |
| Sylow | #6900 ⋊ C22×D5 |
| Sylow | C5 ⋊ C2×#92265⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C5×C92 | C23×C3 |
| Frattini | C32 | C3×D32×D5 |
| Fitting | C5×#6900 | C23 |
| socle | C32×C5 | C2×C3×D32 |
| LCS | G ▷ C5×C92 | |
| UCS | C1 | |
788 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 788 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
144 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#92265⋊C2 |
| maximal normal subgroup of | AGL(1,𝔽5)×#92265⋊C2 |
Past the SmallGroups library coverage — no SmallGroups id.