Finite Group DatabasebetaFinite Group Databasebeta| order | 31740 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×C3×D2645 |
| unambiguous semidirect product | (C2×C5)⋊(C3×D529) |
| unambiguous semidirect product | (C2×C529)⋊(C3×D5) |
| Fitting | C2×C3×C5×C529 ⋊ C2 |
| derived, Hall | C5×C529 ⋊ C22×C3 |
| Hall | C3×C5×C529 ⋊ C22 |
| 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 | C2×C3 | D2645 |
| commutator, cosocle, hypocenter | C5×C529 | C22×C3 |
| Frattini | C23 | C2×C3×D115 |
| Fitting | C2×C3×C5×C529 | C2 |
| socle | C2×C3×C5×C23 | D23 |
| LCS | G ▷ C5×C529 | |
| UCS | C1 ◁ C2×C3 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15870 |
7944 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31740, 24);