Finite Group DatabasebetaFinite Group Databasebeta| order | 10140 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×D13×D65 |
| Fitting, socle, Hall | C3×C5×C132 ⋊ C22 |
| derived, Hall | C5×C132 ⋊ C22×C3 |
| Hall | C3×C132 ⋊ C2×D5 |
| Sylow | C132 ⋊ C2×C3×D5 |
| Hall | C3×C5 ⋊ D132 |
| Sylow | C5 ⋊ C3×D132 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D13×D65 |
| commutator, cosocle, hypocenter | C5×C132 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C132 | C22 |
| LCS | G ▷ C5×C132 | |
| UCS | C1 ◁ C3 | |
128 conjugacy classes of subgroups.
816 conjugacy classes — view the full character table.
| maximal subgroup of | #15690150⋊D5, #15690151⋊D5, D65×D13⋊C9, … |
| maximal normal subgroup of | #15690150⋊D5, #15690151⋊D5, D65×D13⋊C9, … |
| maximal quotient of | C9×D13×D65, C32×D13×D65, C3×D13×D195, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10140, 217);