Finite Group DatabasebetaFinite Group Databasebeta| order | 7740 |
| isoclinism | isoclinic class of C43⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5×C9 · Schur multiplier (H2) = C2 |
| direct product | C22×C5×C43⋊C9 |
| derived, Sylow | C43 ⋊ C22×C5×C9 |
| Hall | C22×C5×C43 ⋊ C9 |
| Hall | C5×C43 ⋊ C22×C9 |
| Hall | C22×C43 ⋊ C5×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3×C5 | C43⋊C3 |
| commutator, hypocenter | C43 | C22×C5×C9 |
| Frattini | C3 | C22×C5×C43⋊C3 |
| Fitting, socle | C22×C3×C5×C43 | C3 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C22×C3×C5 | |
60 conjugacy classes of subgroups.
1020 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7740, 31);