Finite Group DatabasebetaFinite Group Databasebeta| order | 31740 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C23 |
| direct product | C2×C3×C5⋊(C23⋊D23) |
| unambiguous semidirect product | (C2×C5)⋊(C3×C23⋊D23) |
| unambiguous semidirect product | (C2×C23)⋊(C3×D115) |
| Fitting, socle | C2×C3×C5×C232 ⋊ C2 |
| derived, Hall | C5×C232 ⋊ C22×C3 |
| Hall | C3×C5×C232 ⋊ C22 |
| Hall | C3×C232 ⋊ C2×D5 |
| Sylow | C232 ⋊ C2×C3×D5 |
| Hall | C3×C5 ⋊ C2×C23⋊D23 |
| Sylow | C5 ⋊ C2×C3×C23⋊D23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | C5⋊(C23⋊D23) |
| commutator, cosocle, hypocenter | C5×C232 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C5×C232 | C2 |
| LCS | G ▷ C5×C232 | |
| UCS | C1 ◁ C2×C3 | |
520 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, 109);