Finite Group DatabasebetaFinite Group Databasebeta| order | 22290 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D2229 |
| unambiguous semidirect product | C3⋊(C5×D743) |
| unambiguous semidirect product | C743⋊(C5×D3) |
| Fitting, socle, Hall | C3×C5×C743 ⋊ C2 |
| derived, Hall | C3×C743 ⋊ C2×C5 |
| Hall | C5×C743 ⋊ D3 |
| Sylow | C743 ⋊ C5×D3 |
| Hall | C3×C5 ⋊ D743 |
| Sylow | C3 ⋊ C5×D743 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D2229 |
| commutator, cosocle, hypocenter | C3×C743 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C743 | C2 |
| LCS | G ▷ C3×C743 | |
| UCS | C1 ◁ C5 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11145 |
5580 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22290, 6);