Finite Group DatabasebetaFinite Group Databasebeta| order | 37023 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C7×C41 · Schur multiplier (H2) = C1 |
| direct product | C3×C41×C43⋊C7 |
| unambiguous semidirect product | (C3×C43)⋊(C7×C41) |
| unambiguous semidirect product | (C3×C41×C43)⋊C7 |
| Fitting, socle, Hall | C3×C41×C43 ⋊ C7 |
| derived, Sylow | C43 ⋊ C3×C7×C41 |
| Hall | C41×C43 ⋊ C3×C7 |
| Hall | C3×C43 ⋊ C7×C41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C41 | C43⋊C7 |
| commutator, cosocle, hypocenter | C43 | C3×C7×C41 |
| Frattini | C1 | G |
| Fitting, socle | C3×C41×C43 | C7 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C3×C41 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5289 |
1599 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37023, 2);