Finite Group DatabasebetaFinite Group Databasebeta| order | 10800 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23×C3 |
| direct product | C3×C3⋊D3×D5⋊AGL(1,𝔽5) |
| Fitting, socle, Hall | C33×C52 ⋊ C22×C4 |
| derived | C32×C52 ⋊ C22×C3×C4 |
| Sylow | C33 ⋊ C2×D5⋊AGL(1,𝔽5) |
| Sylow | C52 ⋊ C2×C3×C4×C3⋊D3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C3⋊D3×D5⋊AGL(1,𝔽5) |
| commutator, hypocenter | C32×C52 | C22×C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C33×C52 | C22×C4 |
| prime radical | C3×D52×C3⋊D3 | C2 |
| cosocle | C32×C5⋊D5 | C23×C3 |
| LCS | G ▷ C32×C52 | |
| UCS | C1 ◁ C3 | |
1792 conjugacy classes of subgroups.
| transitive degree | μt(G) = 180 |
252 conjugacy classes — view the full character table.
| 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.