Finite Group DatabasebetaFinite Group Databasebeta| order | 4320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32×C4 · Schur multiplier (H2) = C26×C3 |
| direct product | C22×C32×D3×AGL(1,𝔽5) |
| Fitting, socle | C22×C33×C5 ⋊ C2×C4 |
| derived | C3×C5 ⋊ C23×C32×C4 |
| Hall | C33×C5 ⋊ C23×C4 |
| Sylow | C33 ⋊ C23×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C22×C32×C4×D3 |
3264 conjugacy classes of subgroups.
| transitive degree | μt(G) = 360 |
540 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22×D3×C3⋊D3×AGL(1,𝔽5) |
| maximal normal subgroup of | C22×D3×C3⋊D3×AGL(1,𝔽5) |
Past the SmallGroups library coverage — no SmallGroups id.