Finite Group DatabasebetaFinite Group Databasebeta| order | 31302 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×D1739 |
| unambiguous semidirect product | C47⋊(C9×D37) |
| Fitting, Hall | C9×C37×C47 ⋊ C2 |
| derived, Hall | C37×C47 ⋊ C2×C9 |
| Hall | C9×C47 ⋊ D37 |
| Hall | C9×C37 ⋊ D47 |
| Sylow | C47 ⋊ C9×D37 |
| Sylow | C37 ⋊ C9×D47 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | D1739 |
| commutator, hypocenter | C37×C47 | C2×C9 |
| Frattini | C3 | C3×D1739 |
| Fitting | C9×C37×C47 | C2 |
| socle, cosocle | C3×C37×C47 | C2×C3 |
| prime radical | C3×D1739 | C3 |
| LCS | G ▷ C37×C47 | |
| UCS | C1 ◁ C9 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15651 |
7839 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31302, 5);