Finite Group DatabasebetaFinite Group Databasebeta| order | 31740 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×D5×D529 |
| unambiguous semidirect product | (D5×C529)⋊(C2×C3) |
| unambiguous semidirect product | (C5×D529)⋊(C2×C3) |
| unambiguous semidirect product | D2645⋊(C2×C3) |
| Fitting, Hall | C3×C5×C529 ⋊ C22 |
| derived, Hall | C5×C529 ⋊ C22×C3 |
| Hall | C3×C529 ⋊ C2×D5 |
| Sylow | C529 ⋊ C2×C3×D5 |
| Hall | C3×C5 ⋊ C2×D529 |
| Sylow | C5 ⋊ C2×C3×D529 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D5×D529 |
| commutator, cosocle, hypocenter | C5×C529 | C22×C3 |
| Frattini | C23 | C3×D5×D23 |
| Fitting | C3×C5×C529 | C22 |
| socle | C3×C5×C23 | C2×D23 |
| LCS | G ▷ C5×C529 | |
| UCS | C1 ◁ C3 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7935 |
3192 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31740, 14);