Finite Group DatabasebetaFinite Group Databasebeta| order | 10584 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C3×D3×D21⋊D7 |
| Fitting, socle, Hall | C33×C72 ⋊ C23 |
| derived | C32×C72 ⋊ C23×C3 |
| Sylow | C72 ⋊ C2×C3×D32 |
| Sylow | C33 ⋊ C2×D72 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D3×D21⋊D7 |
| commutator, cosocle, hypocenter | C32×C72 | C23×C3 |
| Frattini | C1 | G |
| Fitting, socle | C33×C72 | C23 |
| LCS | G ▷ C32×C72 | |
| UCS | C1 ◁ C3 | |
876 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 876 conjugacy classes of subgroups — too many to draw. Only its 108 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 84 |
459 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D3×#13183634, D3×#72213616 |
| maximal normal subgroup of | C3×D3×#13183634, D3×#72213616 |
Past the SmallGroups library coverage — no SmallGroups id.