Finite Group DatabasebetaFinite Group Databasebeta| order | 4320 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C26 |
| direct product | C3×D5×#3811 |
| Fitting | C22×C33×C5 ⋊ C23 |
| Hall | C33×C5 ⋊ C22×D4 |
| Sylow | C33 ⋊ C2×D4×D5 |
| Sylow | C5 ⋊ C2×C3×#3811 |
2436 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
288 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×AGL(1,𝔽5)×#3811 |
| maximal normal subgroup of | C3×AGL(1,𝔽5)×#3811 |
Past the SmallGroups library coverage — no SmallGroups id.