Finite Group DatabasebetaFinite Group Databasebeta| order | 31740 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D15×D529 |
| unambiguous semidirect product | (C3×D529)⋊D5 |
| unambiguous semidirect product | (C5×D529)⋊D3 |
| Fitting, derived, Hall | C3×C5×C529 ⋊ C22 |
| Hall | C5×C529 ⋊ C2×D3 |
| Hall | C3×C529 ⋊ C2×D5 |
| Sylow | C529 ⋊ C2×D15 |
| Hall | C3×C5 ⋊ C2×D529 |
| Sylow | C5 ⋊ D3×D529 |
| Sylow | C3 ⋊ D5×D529 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C3×C5×C529 | C22 |
| Frattini | C23 | D15×D23 |
| socle | C3×C5×C23 | C2×D23 |
| LCS | G ▷ C3×C5×C529 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7935 |
2394 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31740, 16);