Finite Group DatabasebetaFinite Group Databasebeta| order | 25770 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D2577 |
| unambiguous semidirect product | C3⋊(C5×D859) |
| unambiguous semidirect product | C859⋊(C5×D3) |
| Fitting, socle, Hall | C3×C5×C859 ⋊ C2 |
| derived, Hall | C3×C859 ⋊ C2×C5 |
| Hall | C5×C859 ⋊ D3 |
| Sylow | C859 ⋊ C5×D3 |
| Hall | C3×C5 ⋊ D859 |
| Sylow | C3 ⋊ C5×D859 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D2577 |
| commutator, cosocle, hypocenter | C3×C859 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C859 | C2 |
| LCS | G ▷ C3×C859 | |
| UCS | C1 ◁ C5 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12885 |
6450 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25770, 7);