Finite Group DatabasebetaFinite Group Databasebeta| order | 36162 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C49 · Schur multiplier (H2) = C3 |
| direct product | C49×C3⋊D123 |
| unambiguous semidirect product | C3⋊(C49×D123) |
| unambiguous semidirect product | C41⋊(C3⋊D3×C49) |
| Fitting, Hall | C32×C41×C49 ⋊ C2 |
| derived, Hall | C32×C41 ⋊ C2×C49 |
| Hall | C41×C49 ⋊ C3⋊D3 |
| Hall | C32×C49 ⋊ D41 |
| Sylow | C41 ⋊ C3⋊D3×C49 |
| Sylow | C32 ⋊ C49×D41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C49 | C3⋊D123 |
| commutator, hypocenter | C32×C41 | C2×C49 |
| Frattini | C7 | C7×C3⋊D123 |
| Fitting | C32×C41×C49 | C2 |
| socle, cosocle | C32×C7×C41 | C2×C7 |
| prime radical | C7×C3⋊D123 | C7 |
| LCS | G ▷ C32×C41 | |
| UCS | C1 ◁ C49 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18081 |
9114 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36162, 30);