Finite Group DatabasebetaFinite Group Databasebeta| order | 4320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | D33×AGL(1,𝔽5) |
| Fitting, socle, derived, Hall | C33×C5 ⋊ C23×C4 |
| Sylow | C33 ⋊ C23×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C4×D33 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C33×C5 | C23×C4 |
| prime radical | D33×D5 | C2 |
| cosocle | C33×D5 | C24 |
| LCS | G ▷ C33×C5 | |
| UCS | C1 | |
2244 conjugacy classes of subgroups; only the 264 normal subgroups are shown.
This group has 2244 conjugacy classes of subgroups — too many to draw. Only its 264 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
135 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.