Finite Group DatabasebetaFinite Group Databasebeta| order | 37386 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C31 · Schur multiplier (H2) = C1 |
| direct product | C31×D603 |
| unambiguous semidirect product | C9⋊(C31×D67) |
| unambiguous semidirect product | C67⋊(D9×C31) |
| Fitting, Hall | C9×C31×C67 ⋊ C2 |
| derived, Hall | C9×C67 ⋊ C2×C31 |
| Hall | C31×C67 ⋊ D9 |
| Hall | C9×C31 ⋊ D67 |
| Sylow | C67 ⋊ D9×C31 |
| Sylow | C9 ⋊ C31×D67 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31 | D603 |
| commutator, cosocle, hypocenter | C9×C67 | C2×C31 |
| Frattini | C3 | C31×D201 |
| Fitting | C9×C31×C67 | C2 |
| socle | C3×C31×C67 | D3 |
| LCS | G ▷ C9×C67 | |
| UCS | C1 ◁ C31 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18693 |
9393 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37386, 10);