Finite Group DatabasebetaFinite Group Databasebeta| order | 15210 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×D585 |
| unambiguous semidirect product | C5⋊(C13×D117) |
| unambiguous semidirect product | C9⋊(C13×D65) |
| unambiguous semidirect product | C13⋊(C13×D45) |
| Fitting, Hall | C5×C9×C132 ⋊ C2 |
| derived | C5×C9×C13 ⋊ C2×C13 |
| Hall | C9×C132 ⋊ D5 |
| Hall | C5×C132 ⋊ D9 |
| Sylow | C132 ⋊ D45 |
| Hall | C5×C9 ⋊ C13×D13 |
| Sylow | C9 ⋊ C13×D65 |
| Sylow | C5 ⋊ C13×D117 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | D585 |
| commutator, cosocle, hypocenter | C5×C9×C13 | C2×C13 |
| Frattini | C3 | C13×D195 |
| Fitting | C5×C9×C132 | C2 |
| socle | C3×C5×C132 | D3 |
| LCS | G ▷ C5×C9×C13 | |
| UCS | C1 ◁ C13 | |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1170 |
3822 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C13×D13×D45, D13×D585, #44477768, … |
| maximal normal subgroup of | C13×D13×D45, D13×D585, #44477768, … |
| maximal quotient of | C13×Dic585, C2×C13×D585 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15210, 65);