Finite Group DatabasebetaFinite Group Databasebeta| order | 5850 |
| isoclinism | isoclinic class of D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C52×C13 · Schur multiplier (H2) = C5 |
| direct product | C52×C13×D9 |
| unambiguous semidirect product | C9⋊(C2×C52×C13) |
| Fitting, Hall | C52×C9×C13 ⋊ C2 |
| derived, Sylow | C9 ⋊ C2×C52×C13 |
| Hall | C52×C9 ⋊ C2×C13 |
| Hall | C9×C13 ⋊ C2×C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52×C13 | D9 |
| commutator, hypocenter | C9 | C2×C52×C13 |
| Frattini | C3 | C52×D3×C13 |
| Fitting | C52×C9×C13 | C2 |
| socle | C3×C52×C13 | D3 |
| LCS | G ▷ C9 | |
| UCS | C1 ◁ C52×C13 | |
96 conjugacy classes of subgroups.
1950 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C52×D9×D13, C5×D5×C13×D9, C5×D9×D65, … |
| maximal normal subgroup of | C52×D9×D13, C5×D5×C13×D9, C5×D9×D65, … |
| maximal quotient of | C52×C13×Dic9, C2×C52×C13×D9 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5850, 55);