Finite Group DatabasebetaFinite Group Databasebeta| order | 31740 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D15⋊D529 |
| unambiguous semidirect product | D1587⋊D5 |
| unambiguous semidirect product | D2645⋊D3 |
| Fitting, derived, Hall | C3×C5×C529 ⋊ C22 |
| Hall | C5×C529 ⋊ C2×D3 |
| Hall | C3×C529 ⋊ C2×D5 |
| Sylow | C529 ⋊ D3×D5 |
| Hall | C3×C5 ⋊ C2×D529 |
| Sylow | C5 ⋊ D3×D529 |
| Sylow | C3 ⋊ D5×D529 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C3×C5×C529 | C22 |
| Frattini | C23 | D15⋊D23 |
| socle | C3×C5×C23 | C2×D23 |
| LCS | G ▷ C3×C5×C529 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7935 |
Polycyclic presentation:
2^2,3,5,23^2|e^23=f^22,d^a=d^4,e^a=e^22f,f^a=f^22,c^b=c^2,d^b=d^42388 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31740, 20);