Finite Group DatabasebetaFinite Group Databasebeta| order | 5390 |
| isoclinism | isoclinic class of D245 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×D245 |
| unambiguous semidirect product | C5⋊(C11×D49) |
| unambiguous semidirect product | C49⋊(D5×C11) |
| Fitting, Hall | C5×C11×C49 ⋊ C2 |
| derived, Hall | C5×C49 ⋊ C2×C11 |
| Hall | C11×C49 ⋊ D5 |
| Hall | C5×C11 ⋊ D49 |
| Sylow | C49 ⋊ D5×C11 |
| Sylow | C5 ⋊ C11×D49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D245 |
| commutator, hypocenter | C5×C49 | C2×C11 |
| Frattini | C7 | C11×D35 |
| Fitting | C5×C11×C49 | C2 |
| socle | C5×C7×C11 | D7 |
| LCS | G ▷ C5×C49 | |
| UCS | C1 ◁ C11 | |
24 conjugacy classes of subgroups.
1364 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C11×D245, C11×D735, C11×C5⋊(D49⋊C3), … |
| maximal normal subgroup of | C3×C11×D245, C11×C5⋊(D49⋊C3), C11⋊C5×D245, … |
| maximal quotient of | C3×C11×D245, C11×D735, C11×D1225, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5390, 11);