Finite Group DatabasebetaFinite Group Databasebeta| order | 31506 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C89 · Schur multiplier (H2) = C1 |
| direct product | C89×D177 |
| unambiguous semidirect product | C3⋊(C89×D59) |
| unambiguous semidirect product | C59⋊(D3×C89) |
| Fitting, socle, Hall | C3×C59×C89 ⋊ C2 |
| derived, Hall | C3×C59 ⋊ C2×C89 |
| Hall | C59×C89 ⋊ D3 |
| Hall | C3×C89 ⋊ D59 |
| Sylow | C59 ⋊ D3×C89 |
| Sylow | C3 ⋊ C89×D59 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C89 | D177 |
| commutator, cosocle, hypocenter | C3×C59 | C2×C89 |
| Frattini | C1 | G |
| Fitting, socle | C3×C59×C89 | C2 |
| LCS | G ▷ C3×C59 | |
| UCS | C1 ◁ C89 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15753 |
8010 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31506, 7);