Finite Group DatabasebetaFinite Group Databasebeta| order | 15210 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×D845 |
| unambiguous semidirect product | C5⋊(C9×D169) |
| Fitting, Hall | C5×C9×C169 ⋊ C2 |
| derived, Hall | C5×C169 ⋊ C2×C9 |
| Hall | C9×C169 ⋊ D5 |
| Sylow | C169 ⋊ C9×D5 |
| Hall | C5×C9 ⋊ D169 |
| Sylow | C5 ⋊ C9×D169 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | D845 |
| commutator, hypocenter | C5×C169 | C2×C9 |
| Frattini | C3×C13 | C3×D65 |
| Fitting | C5×C9×C169 | C2 |
| socle | C3×C5×C13 | C3×D13 |
| prime radical | C3×D845 | C3 |
| cosocle | C3×C5×C169 | C2×C3 |
| LCS | G ▷ C5×C169 | |
| UCS | C1 ◁ C9 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7605 |
3816 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C9×#16809981, C9×#16809980, C9⋊#16809980, … |
| maximal normal subgroup of | C9×#16809981, C9×#16809980, C9⋊#16809980, … |
| maximal quotient of | C9×Dic845, C2×C9×D845 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15210, 8);