Finite Group DatabasebetaFinite Group Databasebeta| order | 10140 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C13 |
| direct product | D5×C3⋊(C13⋊D13) |
| unambiguous semidirect product | (C3×D5)⋊(C13⋊D13) |
| unambiguous semidirect product | (D5×C13)⋊D39 |
| Fitting, socle, derived, Hall | C3×C5×C132 ⋊ C22 |
| Hall | C5×C132 ⋊ C2×D3 |
| Hall | C3×C132 ⋊ C2×D5 |
| Sylow | C132 ⋊ D3×D5 |
| Hall | C3×C5 ⋊ C2×C13⋊D13 |
| Sylow | C5 ⋊ C2×C3⋊(C13⋊D13) |
| Sylow | C3 ⋊ D5×C13⋊D13 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C5×C132 | C22 |
| LCS | G ▷ C3×C5×C132 | |
| UCS | C1 | |
320 conjugacy classes of subgroups.
1020 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10140, 249);