Finite Group DatabasebetaFinite Group Databasebeta| order | 22990 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C11 · Schur multiplier (H2) = C1 |
| direct product | C5×C11×D209 |
| unambiguous semidirect product | C19⋊(C5×C11×D11) |
| Fitting, socle, Hall | C5×C112×C19 ⋊ C2 |
| derived | C11×C19 ⋊ C2×C5×C11 |
| Hall | C112×C19 ⋊ C2×C5 |
| Hall | C5×C112 ⋊ D19 |
| Sylow | C112 ⋊ C5×D19 |
| Hall | C5×C19 ⋊ C11×D11 |
| Sylow | C19 ⋊ C5×C11×D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C11 | D209 |
| commutator, cosocle, hypocenter | C11×C19 | C2×C5×C11 |
| Frattini | C1 | G |
| Fitting, socle | C5×C112×C19 | C2 |
| LCS | G ▷ C11×C19 | |
| UCS | C1 ◁ C5×C11 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2090 |
5830 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22990, 46);