Finite Group DatabasebetaFinite Group Databasebeta| order | 22990 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C19⋊#11925895 |
| Fitting, socle, derived, Hall | C112×C19 ⋊ C2×C5 |
| Hall | C19×#10597243 ⋊ C2 |
| Hall | C11×D209 ⋊ C5 |
| Hall | #10597243 ⋊ D19 |
| Sylow | C112 ⋊ C5×D19 |
| Sylow | C19 ⋊ #11925895 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C112×C19 | C2×C5 |
| LCS | G ▷ C112×C19 | |
| UCS | C1 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 418 |
Polycyclic presentation:
2,5,11^2,19|c^a=c^10,e^a=e^18,c^b=c^4,d^b=d^4286 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22990, 27);