Finite Group DatabasebetaFinite Group Databasebeta| order | 25857 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C17 · Schur multiplier (H2) = C3 |
| Fitting, socle, Hall | C132×C17 ⋊ C32 |
| derived, Sylow | C132 ⋊ C32×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | C13⋊C32 |
| commutator, cosocle, hypocenter | C132 | C32×C17 |
| Frattini | C1 | G |
| Fitting, socle | C132×C17 | C32 |
| LCS | G ▷ C132 | |
| UCS | C1 ◁ C17 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 663 |
833 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25857, 10);