Finite Group DatabasebetaFinite Group Databasebeta| order | 37582 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C43 · Schur multiplier (H2) = C1 |
| direct product | C43×D437 |
| unambiguous semidirect product | C19⋊(C43×D23) |
| unambiguous semidirect product | C23⋊(D19×C43) |
| Fitting, socle, Hall | C19×C23×C43 ⋊ C2 |
| derived, Hall | C19×C23 ⋊ C2×C43 |
| Hall | C23×C43 ⋊ D19 |
| Hall | C19×C43 ⋊ D23 |
| Sylow | C23 ⋊ D19×C43 |
| Sylow | C19 ⋊ C43×D23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C43 | D437 |
| commutator, cosocle, hypocenter | C19×C23 | C2×C43 |
| Frattini | C1 | G |
| Fitting, socle | C19×C23×C43 | C2 |
| LCS | G ▷ C19×C23 | |
| UCS | C1 ◁ C43 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18791 |
9460 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37582, 7);