Finite Group DatabasebetaFinite Group Databasebeta| order | 10170 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×D565 |
| unambiguous semidirect product | C5⋊(C9×D113) |
| unambiguous semidirect product | C113⋊(C9×D5) |
| Fitting, Hall | C5×C9×C113 ⋊ C2 |
| derived, Hall | C5×C113 ⋊ C2×C9 |
| Hall | C9×C113 ⋊ D5 |
| Sylow | C113 ⋊ C9×D5 |
| Hall | C5×C9 ⋊ D113 |
| Sylow | C5 ⋊ C9×D113 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | D565 |
| commutator, hypocenter | C5×C113 | C2×C9 |
| Frattini | C3 | C3×D565 |
| Fitting | C5×C9×C113 | C2 |
| socle, cosocle | C3×C5×C113 | C2×C3 |
| prime radical | C3×D565 | C3 |
| LCS | G ▷ C5×C113 | |
| UCS | C1 ◁ C9 | |
24 conjugacy classes of subgroups.
2556 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C9×#14555933, C9×#14555934, C9×D5×D113, … |
| maximal normal subgroup of | C9×#14555933, C9×#14555934, C9×D5×D113, … |
| maximal quotient of | C9×Dic565, C2×C9×D565 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10170, 4);