Finite Group DatabasebetaFinite Group Databasebeta| order | 31740 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C23 · Schur multiplier (H2) = C2 |
| direct product | C23×D15×D23 |
| unambiguous semidirect product | (C3×D23)⋊(D5×C23) |
| unambiguous semidirect product | (C5×D23)⋊(D3×C23) |
| Fitting, socle, Hall | C3×C5×C232 ⋊ C22 |
| derived | C3×C5×C23 ⋊ C22×C23 |
| Hall | C5×C232 ⋊ C2×D3 |
| Hall | C3×C232 ⋊ C2×D5 |
| Sylow | C232 ⋊ C2×D15 |
| Hall | C3×C5 ⋊ C2×C23×D23 |
| Sylow | C5 ⋊ D3×C23×D23 |
| Sylow | C3 ⋊ D5×C23×D23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D15×D23 |
| commutator, cosocle, hypocenter | C3×C5×C23 | C22×C23 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C232 | C22 |
| LCS | G ▷ C3×C5×C23 | |
| UCS | C1 ◁ C23 | |
168 conjugacy classes of subgroups.
| transitive degree | μt(G) = 690 |
2691 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31740, 88);