Finite Group DatabasebetaFinite Group Databasebeta| order | 7740 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×C3×D645 |
| unambiguous semidirect product | (C2×C3)⋊(C3×D215) |
| unambiguous semidirect product | (C2×C5)⋊(C3×D129) |
| Fitting, socle | C2×C32×C5×C43 ⋊ C2 |
| derived | C3×C5×C43 ⋊ C22×C3 |
| Hall | C32×C5×C43 ⋊ C22 |
| Hall | C32×C43 ⋊ C2×D5 |
| Hall | C5×C43 ⋊ C2×C3×D3 |
| Hall | C32×C5 ⋊ C2×D43 |
| Sylow | C43 ⋊ C2×C3×D15 |
| Sylow | C32 ⋊ C2×D215 |
| Sylow | C5 ⋊ C2×C3×D129 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D645 |
| commutator, hypocenter | C3×C5×C43 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C5×C43 | C2 |
| LCS | G ▷ C3×C5×C43 | |
| UCS | C1 ◁ C2×C3 | |
88 conjugacy classes of subgroups.
1944 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7740, 123);