Finite Group DatabasebetaFinite Group Databasebeta| order | 22990 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | D19×C121⋊C5 |
| unambiguous semidirect product | C19⋊(C2×C121⋊C5) |
| unambiguous semidirect product | (D19×C121)⋊C5 |
| Fitting, derived, Hall | C19×C121 ⋊ C2×C5 |
| Hall | C19×C121⋊C5 ⋊ C2 |
| Hall | D19×C121 ⋊ C5 |
| Sylow | C121 ⋊ C5×D19 |
| Sylow | C19 ⋊ C2×C121⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C19×C121 | C2×C5 |
| Frattini | C11 | D19×C11⋊C5 |
| socle | C11×C19 | C2×C11⋊C5 |
| LCS | G ▷ C19×C121 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2299 |
319 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22990, 10);