Finite Group DatabasebetaFinite Group Databasebeta| order | 25899 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C89 · Schur multiplier (H2) = C1 |
| direct product | C89×C97⋊C3 |
| unambiguous semidirect product | C97⋊(C3×C89) |
| unambiguous semidirect product | (C89×C97)⋊C3 |
| Fitting, socle, Hall | C89×C97 ⋊ C3 |
| derived, Sylow | C97 ⋊ C3×C89 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C89 | C97⋊C3 |
| commutator, cosocle, hypocenter | C97 | C3×C89 |
| Frattini | C1 | G |
| Fitting, socle | C89×C97 | C3 |
| LCS | G ▷ C97 | |
| UCS | C1 ◁ C89 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8633 |
3115 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25899, 1);