Finite Group DatabasebetaFinite Group Databasebeta| order | 10365 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C691⋊C3)⋊C5 |
| unambiguous semidirect product | (C691⋊C5)⋊C3 |
| Fitting, socle, derived, Sylow | C691 ⋊ C3×C5 |
| Hall | C691⋊C5 ⋊ C3 |
| Hall | C691⋊C3 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C691 | C3×C5 |
| LCS | G ▷ C691 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
3,5,691|c^a=c^437,c^b=c^13261 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10365, 1);