Finite Group DatabasebetaFinite Group Databasebeta| order | 37582 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×D989 |
| unambiguous semidirect product | C23⋊(C19×D43) |
| unambiguous semidirect product | C43⋊(C19×D23) |
| Fitting, socle, Hall | C19×C23×C43 ⋊ C2 |
| derived, Hall | C23×C43 ⋊ C2×C19 |
| Hall | C19×C43 ⋊ D23 |
| Hall | C19×C23 ⋊ D43 |
| Sylow | C43 ⋊ C19×D23 |
| Sylow | C23 ⋊ C19×D43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | D989 |
| commutator, cosocle, hypocenter | C23×C43 | C2×C19 |
| Frattini | C1 | G |
| Fitting, socle | C19×C23×C43 | C2 |
| LCS | G ▷ C23×C43 | |
| UCS | C1 ◁ C19 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18791 |
9424 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37582, 4);