Finite Group DatabasebetaFinite Group Databasebeta| order | 15210 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D1521 |
| unambiguous semidirect product | C9⋊(C5×D169) |
| unambiguous semidirect product | C169⋊(C5×D9) |
| Fitting, Hall | C5×C9×C169 ⋊ C2 |
| derived, Hall | C9×C169 ⋊ C2×C5 |
| Hall | C5×C169 ⋊ D9 |
| Sylow | C169 ⋊ C5×D9 |
| Hall | C5×C9 ⋊ D169 |
| Sylow | C9 ⋊ C5×D169 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D1521 |
| commutator, cosocle, hypocenter | C9×C169 | C2×C5 |
| Frattini | C3×C13 | C5×D39 |
| Fitting | C5×C9×C169 | C2 |
| socle | C3×C5×C13 | D39 |
| LCS | G ▷ C9×C169 | |
| UCS | C1 ◁ C5 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7605 |
3810 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D9×D169, D5×D1521, D45⋊D169, … |
| maximal normal subgroup of | C5×D9×D169, D5×D1521, D45⋊D169, … |
| maximal quotient of | C5×Dic1521, C2×C5×D1521 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15210, 10);