Finite Group DatabasebetaFinite Group Databasebeta| order | 7740 |
| automorphism | Aut(G) order 3900960 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D3870 |
| direct product | C2×D1935 |
| unambiguous semidirect product | (C2×C5)⋊D387 |
| unambiguous semidirect product | (C2×C9)⋊D215 |
| unambiguous semidirect product | (C2×C43)⋊D45 |
| Fitting | C2×C5×C9×C43 ⋊ C2 |
| derived, Hall | C5×C9×C43 ⋊ C22 |
| Hall | C9×C43 ⋊ C2×D5 |
| Hall | C5×C43 ⋊ C2×D9 |
| Hall | C5×C9 ⋊ C2×D43 |
| Sylow | C43 ⋊ C2×D45 |
| Sylow | C9 ⋊ C2×D215 |
| Sylow | C5 ⋊ C2×D387 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D1935 |
| commutator, hypocenter | C5×C9×C43 | C22 |
| Frattini | C3 | C2×D645 |
| Fitting | C2×C5×C9×C43 | C2 |
| socle | C2×C3×C5×C43 | D3 |
| LCS | G ▷ C5×C9×C43 | |
| UCS | C1 ◁ C2 | |
60 conjugacy classes of subgroups.
1938 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D7740, C2×D5805, C2×D13545 |
| maximal normal subgroup of | D7740 |
| maximal quotient of | D7740, Dic3870, C2×D5805, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7740, 40);