Finite Group DatabasebetaFinite Group Databasebeta| order | 5390 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C11⋊C5×D49 |
| unambiguous semidirect product | C49⋊(C2×C11⋊C5) |
| unambiguous semidirect product | (C11×D49)⋊C5 |
| Fitting, derived, Hall | C11×C49 ⋊ C2×C5 |
| Hall | C49×C11⋊C5 ⋊ C2 |
| Hall | C11×D49 ⋊ C5 |
| Sylow | C49 ⋊ C2×C11⋊C5 |
| Sylow | C11 ⋊ C5×D49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C11×C49 | C2×C5 |
| Frattini | C7 | D7×C11⋊C5 |
| socle | C7×C11 | C5×D7 |
| LCS | G ▷ C11×C49 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
182 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C11⋊C5×D49, C11⋊C5×D147, C11⋊C5×D49⋊C3, … |
| maximal normal subgroup of | C3×C11⋊C5×D49, C11⋊C5×D49⋊C3, C5×C11⋊C5×D49 |
| maximal quotient of | C3×C11⋊C5×D49, C11⋊C5×D147, D49×C11⋊C25, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5390, 3);