Finite Group DatabasebetaFinite Group Databasebeta| order | 8640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | C2×D33×AGL(1,𝔽5) |
| Fitting, socle | C2×C33×C5 ⋊ C23×C4 |
| derived, Hall | C33×C5 ⋊ C24×C4 |
| Sylow | C33 ⋊ C24×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C2×C4×D33 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D33×AGL(1,𝔽5) |
| commutator, hypocenter | C33×C5 | C24×C4 |
| Frattini | C1 | G |
| Fitting, socle | C2×C33×C5 | C23×C4 |
| prime radical | C2×D33×D5 | C2 |
| cosocle | C33×D5 | C25 |
| LCS | G ▷ C33×C5 | |
| UCS | C1 ◁ C2 | |
12420 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
270 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.