Finite Group DatabasebetaFinite Group Databasebeta| order | 10368 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C25 |
| direct product | C3×#72210357 |
| Fitting | C24×C33 ⋊ C22×D3 |
| derived | C32×C22⋊A4 ⋊ C23×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #72210357 |
| commutator, cosocle, hypocenter | C32×C22⋊A4 | C23×C3 |
| Frattini | C22 | C3×D32×S4 |
| Fitting | C24×C33 | C22×D3 |
| socle | C22×C33 | C22×S4 |
| LCS | G ▷ C32×C22⋊A4 | |
| UCS | C1 ◁ C3 | |
5123 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 5123 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
198 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#72210357 |
| maximal normal subgroup of | D3×#72210357 |
Past the SmallGroups library coverage — no SmallGroups id.