Finite Group DatabasebetaFinite Group Databasebeta| order | 10365 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C3×C691⋊C5 |
| unambiguous semidirect product | (C3×C691)⋊C5 |
| Fitting, socle, Hall | C3×C691 ⋊ C5 |
| derived, Sylow | C691 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C691⋊C5 |
| commutator, cosocle, hypocenter | C691 | C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C691 | C5 |
| LCS | G ▷ C691 | |
| UCS | C1 ◁ C3 | |
8 conjugacy classes of subgroups.
429 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C3×C691⋊C5, C3×D691⋊C5, D3×C691⋊C5, … |
| maximal normal subgroup of | C2×C3×C691⋊C5, C3×D691⋊C5, D3×C691⋊C5, … |
| maximal quotient of | C2×C3×C691⋊C5, C9×C691⋊C5, C32×C691⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10365, 2);