Finite Group DatabasebetaFinite Group Databasebeta| order | 31740 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C23 |
| unambiguous semidirect product | D15⋊(C23⋊D23) |
| Fitting, socle, derived, Hall | C3×C5×C232 ⋊ C22 |
| Hall | C5×C232 ⋊ C2×D3 |
| Hall | C3×C232 ⋊ C2×D5 |
| Sylow | C232 ⋊ D3×D5 |
| Hall | C3×C5 ⋊ C2×C23⋊D23 |
| Sylow | C5 ⋊ D3×C23⋊D23 |
| Sylow | C3 ⋊ D5×C23⋊D23 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C5×C232 | C22 |
| LCS | G ▷ C3×C5×C232 | |
| UCS | C1 | |
520 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7935 |
Polycyclic presentation:
2^2,3,5,23^2|d^a=d^4,e^a=e^22,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, 101);