Finite Group DatabasebetaFinite Group Databasebeta| order | 7740 |
| isoclinism | isoclinic class of AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9×C43 · Schur multiplier (H2) = C1 |
| direct product | C9×AGL(1,𝔽5)×C43 |
| Fitting, Hall | C5×C9×C43 ⋊ C4 |
| derived, Sylow | C5 ⋊ C4×C9×C43 |
| Hall | C5×C43 ⋊ C4×C9 |
| Hall | C5×C9 ⋊ C4×C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9×C43 | AGL(1,𝔽5) |
| commutator, hypocenter | C5 | C4×C9×C43 |
| Frattini | C3 | C3×AGL(1,𝔽5)×C43 |
| Fitting | C5×C9×C43 | C4 |
| socle | C3×C5×C43 | C3×C4 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C9×C43 | |
36 conjugacy classes of subgroups.
1935 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7740, 20);