Finite Group DatabasebetaFinite Group Databasebeta| order | 5390 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D539 |
| unambiguous semidirect product | C49⋊(C5×D11) |
| Fitting, Hall | C5×C11×C49 ⋊ C2 |
| derived, Hall | C11×C49 ⋊ C2×C5 |
| Hall | C5×C49 ⋊ D11 |
| Hall | C5×C11 ⋊ D49 |
| Sylow | C49 ⋊ C5×D11 |
| Sylow | C11 ⋊ C5×D49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D539 |
| commutator, hypocenter | C11×C49 | C2×C5 |
| Frattini | C7 | C5×D77 |
| Fitting | C5×C11×C49 | C2 |
| socle | C5×C7×C11 | D7 |
| LCS | G ▷ C11×C49 | |
| UCS | C1 ◁ C5 | |
24 conjugacy classes of subgroups.
1355 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C5×D539, C5×D1617, C5×C11⋊(D49⋊C3), … |
| maximal normal subgroup of | C3×C5×D539, C5×C11⋊(D49⋊C3), C49⋊(D11⋊C25), … |
| maximal quotient of | C3×C5×D539, C5×D1617, C25×D539, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5390, 8);