Finite Group DatabasebetaFinite Group Databasebeta| order | 4320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×D32×ΓL(1,𝔽16) |
| Fitting, socle | C2×C33×C5 ⋊ C22×C4 |
| derived, Hall | C33×C5 ⋊ C23×C4 |
| Sylow | C33 ⋊ C23×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C2×D32×Dic3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D32×ΓL(1,𝔽16) |
| commutator, hypocenter | C33×C5 | C23×C4 |
| Frattini | C1 | G |
| Fitting, socle | C2×C33×C5 | C22×C4 |
| prime radical | C2×C3×D32×D5 | C2 |
| cosocle | C33×D5 | C24 |
| LCS | G ▷ C33×C5 | |
| UCS | C1 ◁ C2 | |
2244 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
162 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D33×AGL(1,𝔽5) |
| maximal normal subgroup of | C2×D33×AGL(1,𝔽5) |
Past the SmallGroups library coverage — no SmallGroups id.