Finite Group DatabasebetaFinite Group Databasebeta| order | 10800 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | D3×#14268487 |
| Fitting, socle, derived, Hall | C33×C52 ⋊ C24 |
| Sylow | C33 ⋊ C22×D52 |
| Sylow | C52 ⋊ C2×D33 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C33×C52 | C24 |
| LCS | G ▷ C33×C52 | |
| UCS | C1 | |
3032 conjugacy classes of subgroups.
234 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#72210392 |
| maximal normal subgroup of | D3×#72210392 |
Past the SmallGroups library coverage — no SmallGroups id.