Finite Group DatabasebetaFinite Group Databasebeta| order | 22542 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C289 · Schur multiplier (H2) = C1 |
| direct product | D39×C289 |
| unambiguous semidirect product | C3⋊(D13×C289) |
| unambiguous semidirect product | C13⋊(D3×C289) |
| Fitting, Hall | C3×C13×C289 ⋊ C2 |
| derived, Hall | C3×C13 ⋊ C2×C289 |
| Hall | C13×C289 ⋊ D3 |
| Hall | C3×C289 ⋊ D13 |
| Sylow | C13 ⋊ D3×C289 |
| Sylow | C3 ⋊ D13×C289 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C289 | D39 |
| commutator, hypocenter | C3×C13 | C2×C289 |
| Frattini | C17 | C17×D39 |
| Fitting | C3×C13×C289 | C2 |
| socle, cosocle | C3×C13×C17 | C2×C17 |
| prime radical | C17×D39 | C17 |
| LCS | G ▷ C3×C13 | |
| UCS | C1 ◁ C289 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11271 |
6069 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22542, 11);