Finite Group DatabasebetaFinite Group Databasebeta| order | 10368 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C25 |
| direct product | D3×#10595527⋊C3 |
| Fitting, derived | C24×C33 ⋊ C23×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C24×C33 | C23×C3 |
| Frattini | C22 | D33×A4 |
| socle | C22×C33 | C23×A4 |
| LCS | G ▷ C24×C33 | |
| UCS | C1 | |
10137 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 10137 conjugacy classes of subgroups — too many to draw. Only its 130 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 | D3×#72210357 |
| maximal normal subgroup of | D3×#72210357 |
Past the SmallGroups library coverage — no SmallGroups id.