Finite Group DatabasebetaFinite Group Databasebeta| order | 29940 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C499 · Schur multiplier (H2) = C1 |
| direct product | ΓL(1,𝔽16)×C499 |
| unambiguous semidirect product | C3⋊(AGL(1,𝔽5)×C499) |
| Fitting, socle, Hall | C3×C5×C499 ⋊ C4 |
| derived, Hall | C3×C5 ⋊ C4×C499 |
| Hall | C5×C499 ⋊ Dic3 |
| Hall | C3×C499 ⋊ AGL(1,𝔽5) |
| Sylow | C5 ⋊ Dic3×C499 |
| Sylow | C3 ⋊ AGL(1,𝔽5)×C499 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C499 | ΓL(1,𝔽16) |
| commutator, hypocenter | C3×C5 | C4×C499 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C499 | C4 |
| prime radical | C3×D5×C499 | C2 |
| cosocle | C3×D5 | C2×C499 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C499 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7485 |
4491 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29940, 24);