Finite Group DatabasebetaFinite Group Databasebeta| order | 10140 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C13 |
| direct product | C2×C5⋊#11759816 |
| unambiguous semidirect product | (C2×C5)⋊#11759816 |
| Fitting, socle | C2×C5×C132 ⋊ C2×C3 |
| derived, Hall | C5×C132 ⋊ C22×C3 |
| Hall | C2×C5⋊(C13⋊D13) ⋊ C3 |
| Hall | C5×#92789 ⋊ C22 |
| Hall | #92789 ⋊ C2×D5 |
| Sylow | C132 ⋊ C2×C3×D5 |
| Sylow | C5 ⋊ C2×#11759816 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C5⋊#11759816 |
| commutator, cosocle, hypocenter | C5×C132 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C132 | C2×C3 |
| LCS | G ▷ C5×C132 | |
| UCS | C1 ◁ C2 | |
120 conjugacy classes of subgroups.
304 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10140, 188);