Finite Group DatabasebetaFinite Group Databasebeta| order | 10140 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×#11759818⋊C2 |
| unambiguous semidirect product | #11759818⋊(C2×C5) |
| Fitting, socle, Hall | C5×C132 ⋊ C22×C3 |
| derived, Sylow | C132 ⋊ C22×C3×C5 |
| Hall | C5×D132 ⋊ C3 |
| Hall | C5×#92789 ⋊ C22 |
| Hall | D132 ⋊ C3×C5 |
| Hall | #92789 ⋊ C22×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #11759818⋊C2 |
| commutator, cosocle, hypocenter | C132 | C22×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C132 | C22×C3 |
| LCS | G ▷ C132 | |
| UCS | C1 ◁ C5 | |
88 conjugacy classes of subgroups.
160 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D13⋊C32, C3×C5×#11759818⋊C2, C5×#11759818⋊D3, … |
| maximal normal subgroup of | C5×D13⋊C32, C3×C5×#11759818⋊C2 |
| maximal quotient of | C5×#15690151⋊C2, C3×C5×#11759818⋊C2, C5×#11759818⋊D3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10140, 101);