Finite Group DatabasebetaFinite Group Databasebeta| order | 4320 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210×C3 |
| direct product | C22×D3×D5×C3⋊D3 |
| Fitting, socle | C22×C33×C5 ⋊ C23 |
| derived, Hall | C33×C5 ⋊ C25 |
| Sylow | C33 ⋊ C24×D5 |
| Sylow | C5 ⋊ C23×D3×C3⋊D3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D3×D5×C3⋊D3 |
| commutator, cosocle, hypocenter | C33×C5 | C25 |
| Frattini | C1 | G |
| Fitting, socle | C22×C33×C5 | C23 |
| LCS | G ▷ C33×C5 | |
| UCS | C1 ◁ C22 | |
10048 conjugacy classes of subgroups.
| transitive degree | μt(G) = 360 |
288 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.