Finite Group DatabasebetaFinite Group Databasebeta| order | 7740 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×C5⋊(D43⋊C9) |
| unambiguous semidirect product | (C2×C5)⋊(D43⋊C9) |
| unambiguous semidirect product | (C2×C43⋊C9)⋊D5 |
| unambiguous semidirect product | (C2×D215)⋊C9 |
| derived, Hall | C5×C43 ⋊ C22×C9 |
| Hall | C5×C43⋊C9 ⋊ C22 |
| Hall | C2×D215 ⋊ C9 |
| Hall | C43⋊C9 ⋊ C2×D5 |
| Sylow | C43 ⋊ C2×C9×D5 |
| Sylow | C5 ⋊ C2×D43⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | C5⋊(D43⋊C3) |
| commutator, hypocenter | C5×C43 | C22×C9 |
| Frattini | C3 | C2×C5⋊(D43⋊C3) |
| Fitting, socle | C2×C3×C5×C43 | C2×C3 |
| LCS | G ▷ C5×C43 | |
| UCS | C1 ◁ C2×C3 | |
60 conjugacy classes of subgroups.
282 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7740, 18);