Finite Group DatabasebetaFinite Group Databasebeta| order | 7740 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D15⋊(D43⋊C3) |
| unambiguous semidirect product | (C3⋊(D43⋊C3))⋊D5 |
| unambiguous semidirect product | (C5⋊(D43⋊C3))⋊D3 |
| unambiguous semidirect product | (D15⋊D43)⋊C3 |
| Fitting, socle, derived | C3×C5×C43 ⋊ C22×C3 |
| Hall | C3×C5×C43⋊C3 ⋊ C22 |
| Hall | C3×C43⋊C3 ⋊ C2×D5 |
| Hall | C5×C43 ⋊ C2×C3×D3 |
| Sylow | C43 ⋊ C3×D3×D5 |
| Sylow | C5 ⋊ D3×D43⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C5×C43 | C22×C3 |
| LCS | G ▷ C3×C5×C43 | |
| UCS | C1 | |
88 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3^2,5,43|e^a=e^4,f^a=f^42,d^b=d^2,e^b=e^4,f^c=f^3699 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7740, 71);