Finite Group DatabasebetaFinite Group Databasebeta| order | 20730 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C3×D691⋊C5 |
| unambiguous semidirect product | (C3×D691)⋊C5 |
| Fitting, socle, Hall | C3×C691 ⋊ C2×C5 |
| derived, Sylow | C691 ⋊ C2×C3×C5 |
| Hall | C3×C691⋊C5 ⋊ C2 |
| Hall | C3×D691 ⋊ C5 |
| Hall | C691⋊C5 ⋊ C2×C3 |
| Hall | D691 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D691⋊C5 |
| commutator, cosocle, hypocenter | C691 | C2×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C691 | C2×C5 |
| LCS | G ▷ C691 | |
| UCS | C1 ◁ C3 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2073 |
237 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20730, 12);