Finite Group DatabasebetaFinite Group Databasebeta| order | 10038 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(D239⋊C7) |
| unambiguous semidirect product | D717⋊C7 |
| unambiguous semidirect product | (C239⋊C7)⋊D3 |
| Fitting, socle, derived, Hall | C3×C239 ⋊ C2×C7 |
| Hall | C3×C239⋊C7 ⋊ C2 |
| Hall | C239⋊C7 ⋊ D3 |
| Hall | D717 ⋊ C7 |
| Sylow | C239 ⋊ D3×C7 |
| Sylow | C3 ⋊ D239⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C239 | C2×C7 |
| LCS | G ▷ C3×C239 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,7,239|b^a=b^2,d^a=d^238,d^c=d^2472 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10038, 13);