Finite Group DatabasebetaFinite Group Databasebeta| order | 36162 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D6027 |
| unambiguous semidirect product | C3⋊(C3×D2009) |
| unambiguous semidirect product | C41⋊(C3×D147) |
| Fitting, Hall | C32×C41×C49 ⋊ C2 |
| derived | C3×C41×C49 ⋊ C2×C3 |
| Hall | C41×C49 ⋊ C3×D3 |
| Hall | C32×C49 ⋊ D41 |
| Hall | C32×C41 ⋊ D49 |
| Sylow | C49 ⋊ C3×D123 |
| Sylow | C41 ⋊ C3×D147 |
| Sylow | C32 ⋊ D2009 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D6027 |
| commutator, cosocle, hypocenter | C3×C41×C49 | C2×C3 |
| Frattini | C7 | C3×D861 |
| Fitting | C32×C41×C49 | C2 |
| socle | C32×C7×C41 | D7 |
| LCS | G ▷ C3×C41×C49 | |
| UCS | C1 ◁ C3 | |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12054 |
9045 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36162, 28);