Finite Group DatabasebetaFinite Group Databasebeta| order | 10140 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×#63120⋊C3 |
| unambiguous semidirect product | #63120⋊(C3×C13) |
| Fitting, socle, Hall | C5×C132 ⋊ C3×C4 |
| derived | C5×C13 ⋊ C3×C4×C13 |
| Hall | C13×#63120 ⋊ C3 |
| Hall | C5×C13×C13⋊C3 ⋊ C4 |
| Hall | C13×C13⋊C3 ⋊ AGL(1,𝔽5) |
| Sylow | C132 ⋊ C3×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C13×Dic13⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | #63120⋊C3 |
| commutator, hypocenter | C5×C13 | C3×C4×C13 |
| Frattini | C1 | G |
| Fitting, socle | C5×C132 | C3×C4 |
| prime radical | D5×C13×C13⋊C3 | C2 |
| cosocle | D5×C13 | C2×C3×C13 |
| LCS | G ▷ C5×C13 | |
| UCS | C1 ◁ C13 | |
56 conjugacy classes of subgroups.
299 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10140, 109);