Finite Group DatabasebetaFinite Group Databasebeta| order | 2160 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4×C5 · Schur multiplier (H2) = C23 |
| direct product | C3×C4×C5×D32 |
| Fitting | C33×C4×C5 ⋊ C22 |
| derived | C32 ⋊ C22×C3×C4×C5 |
| Hall | C33×C5 ⋊ C22×C4 |
| Sylow | C33 ⋊ C22×C4×C5 |
540 conjugacy classes of subgroups.
540 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C4×C5×GO+(4,𝔽2), C3×C4×C5×((C3⋊D3)⋊C3)⋊C2 |
| maximal normal subgroup of | C3×C4×C5×GO+(4,𝔽2) |
| maximal quotient of | C3×C4×C5×((C3⋊D3)⋊C3)⋊C2 |
Past the SmallGroups library coverage — no SmallGroups id.