Finite Group DatabasebetaFinite Group Databasebeta| order | 25857 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C17 · Schur multiplier (H2) = C13 |
| direct product | C17×#13095201 |
| derived, Sylow | C132 ⋊ C9×C17 |
| Hall | C132×C17 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C17 | #92789 |
| commutator, hypocenter | C132 | C9×C17 |
| Frattini | C3 | C17×#92789 |
| Fitting, socle, prime radical | C3×C132×C17 | C3 |
| cosocle | C3×C132 | C3×C17 |
| LCS | G ▷ C132 | |
| UCS | C1 ◁ C3×C17 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1989 |
3009 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25857, 6);