Finite Group DatabasebetaFinite Group Databasebeta| order | 10140 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D13×D195 |
| unambiguous semidirect product | (C3×D13)⋊D65 |
| unambiguous semidirect product | (C5×D13)⋊D39 |
| unambiguous semidirect product | (C13×D13)⋊D15 |
| Fitting, socle, derived, Hall | C3×C5×C132 ⋊ C22 |
| Hall | C5×C132 ⋊ C2×D3 |
| Hall | C3×C132 ⋊ C2×D5 |
| Sylow | C132 ⋊ C2×D15 |
| Hall | C3×C5 ⋊ D132 |
| Sylow | C5 ⋊ D13×D39 |
| Sylow | C3 ⋊ D13×D65 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C5×C132 | C22 |
| LCS | G ▷ C3×C5×C132 | |
| UCS | C1 | |
128 conjugacy classes of subgroups.
792 conjugacy classes — view the full character table.
| maximal subgroup of | D13×D585, #11759813⋊D15, D13×C3⋊(C5⋊(D13⋊C3)), … |
| maximal normal subgroup of | D13×C3⋊(C5⋊(D13⋊C3)), D13⋊C3×D195, #11759817⋊D15, … |
| maximal quotient of | D13×D585, C3×D13×D195, D39×D195, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10140, 243);