Finite Group DatabasebetaFinite Group Databasebeta| order | 22990 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×D605 |
| unambiguous semidirect product | C5⋊(C19×D121) |
| unambiguous semidirect product | C121⋊(D5×C19) |
| Fitting, Hall | C5×C19×C121 ⋊ C2 |
| derived, Hall | C5×C121 ⋊ C2×C19 |
| Hall | C19×C121 ⋊ D5 |
| Sylow | C121 ⋊ D5×C19 |
| Hall | C5×C19 ⋊ D121 |
| Sylow | C5 ⋊ C19×D121 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | D605 |
| commutator, cosocle, hypocenter | C5×C121 | C2×C19 |
| Frattini | C11 | C19×D55 |
| Fitting | C5×C19×C121 | C2 |
| socle | C5×C11×C19 | D11 |
| LCS | G ▷ C5×C121 | |
| UCS | C1 ◁ C19 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11495 |
5776 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22990, 8);