Finite Group DatabasebetaFinite Group Databasebeta| order | 5390 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×D7×C11⋊C5 |
| unambiguous semidirect product | C7⋊(C2×C7×C11⋊C5) |
| unambiguous semidirect product | (C11×D7)⋊(C5×C7) |
| unambiguous semidirect product | (C7×C11×D7)⋊C5 |
| Fitting, socle, Hall | C72×C11 ⋊ C2×C5 |
| derived | C7×C11 ⋊ C2×C5×C7 |
| Hall | C72×C11⋊C5 ⋊ C2 |
| Hall | C7×C11×D7 ⋊ C5 |
| Sylow | C72 ⋊ C2×C11⋊C5 |
| Sylow | C11 ⋊ C5×C7×D7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D7×C11⋊C5 |
| commutator, hypocenter | C7×C11 | C2×C5×C7 |
| Frattini | C1 | G |
| Fitting, socle | C72×C11 | C2×C5 |
| LCS | G ▷ C7×C11 | |
| UCS | C1 ◁ C7 | |
44 conjugacy classes of subgroups.
245 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5390, 16);