Finite Group DatabasebetaFinite Group Databasebeta| order | 31740 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C23 |
| direct product | C2×C3⋊(C5⋊(C23⋊D23)) |
| unambiguous semidirect product | (C2×C3)⋊(C5⋊(C23⋊D23)) |
| unambiguous semidirect product | (C2×C5)⋊(C3⋊(C23⋊D23)) |
| unambiguous semidirect product | (C2×C23)⋊D345 |
| Fitting, socle | C2×C3×C5×C232 ⋊ C2 |
| derived, Hall | C3×C5×C232 ⋊ C22 |
| Hall | C5×C232 ⋊ C2×D3 |
| Hall | C3×C232 ⋊ C2×D5 |
| Sylow | C232 ⋊ C2×D15 |
| Hall | C3×C5 ⋊ C2×C23⋊D23 |
| Sylow | C5 ⋊ C2×C3⋊(C23⋊D23) |
| Sylow | C3 ⋊ C2×C5⋊(C23⋊D23) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C3⋊(C5⋊(C23⋊D23)) |
| commutator, cosocle, hypocenter | C3×C5×C232 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C5×C232 | C2 |
| LCS | G ▷ C3×C5×C232 | |
| UCS | C1 ◁ C2 | |
520 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15870 |
7938 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31740, 115);