Finite Group DatabasebetaFinite Group Databasebeta| order | 20230 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D2023 |
| unambiguous semidirect product | C7⋊(C5×D289) |
| unambiguous semidirect product | C289⋊(C5×D7) |
| Fitting, Hall | C5×C7×C289 ⋊ C2 |
| derived, Hall | C7×C289 ⋊ C2×C5 |
| Hall | C5×C289 ⋊ D7 |
| Sylow | C289 ⋊ C5×D7 |
| Hall | C5×C7 ⋊ D289 |
| Sylow | C7 ⋊ C5×D289 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D2023 |
| commutator, cosocle, hypocenter | C7×C289 | C2×C5 |
| Frattini | C17 | C5×D119 |
| Fitting | C5×C7×C289 | C2 |
| socle | C5×C7×C17 | D17 |
| LCS | G ▷ C7×C289 | |
| UCS | C1 ◁ C5 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10115 |
5065 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20230, 4);