Finite Group DatabasebetaFinite Group Databasebeta| order | 36162 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×D2009 |
| unambiguous semidirect product | C41⋊(C9×D49) |
| Fitting, Hall | C9×C41×C49 ⋊ C2 |
| derived, Hall | C41×C49 ⋊ C2×C9 |
| Hall | C9×C49 ⋊ D41 |
| Hall | C9×C41 ⋊ D49 |
| Sylow | C49 ⋊ C9×D41 |
| Sylow | C41 ⋊ C9×D49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | D2009 |
| commutator, hypocenter | C41×C49 | C2×C9 |
| Frattini | C3×C7 | C3×D287 |
| Fitting | C9×C41×C49 | C2 |
| socle | C3×C7×C41 | C3×D7 |
| prime radical | C3×D2009 | C3 |
| cosocle | C3×C41×C49 | C2×C3 |
| LCS | G ▷ C41×C49 | |
| UCS | C1 ◁ C9 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18081 |
9054 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36162, 8);