Finite Group DatabasebetaFinite Group Databasebeta| order | 10800 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26×C3 |
| direct product | D3×D52×C3⋊D3 |
| Fitting, socle, derived, Hall | C33×C52 ⋊ C24 |
| Sylow | C33 ⋊ C22×D52 |
| Sylow | C52 ⋊ C22×D3×C3⋊D3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C33×C52 | C24 |
| LCS | G ▷ C33×C52 | |
| UCS | C1 | |
4192 conjugacy classes of subgroups.
| transitive degree | μt(G) = 180 |
288 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×C3⋊D3×D5⋊AGL(1,𝔽5) |
| maximal normal subgroup of | D3×C3⋊D3×D5⋊AGL(1,𝔽5) |
Past the SmallGroups library coverage — no SmallGroups id.