Finite Group DatabasebetaFinite Group Databasebeta| order | 10140 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C13 · Schur multiplier (H2) = C2 |
| direct product | C13×D15⋊D13 |
| unambiguous semidirect product | D15⋊(C13×D13) |
| unambiguous semidirect product | D39⋊(D5×C13) |
| unambiguous semidirect product | D65⋊(D3×C13) |
| Fitting, socle, Hall | C3×C5×C132 ⋊ C22 |
| derived | C3×C5×C13 ⋊ C22×C13 |
| Hall | C5×C132 ⋊ C2×D3 |
| Hall | C3×C132 ⋊ C2×D5 |
| Sylow | C132 ⋊ D3×D5 |
| Hall | C3×C5 ⋊ C2×C13×D13 |
| Sylow | C5 ⋊ D3×C13×D13 |
| Sylow | C3 ⋊ D5×C13×D13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | D15⋊D13 |
| commutator, cosocle, hypocenter | C3×C5×C13 | C22×C13 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C132 | C22 |
| LCS | G ▷ C3×C5×C13 | |
| UCS | C1 ◁ C13 | |
128 conjugacy classes of subgroups.
858 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10140, 248);