Finite Group DatabasebetaFinite Group Databasebeta| order | 8820 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| direct product | AGL(1,𝔽5)×C49⋊C9 |
| unambiguous semidirect product | (AGL(1,𝔽5)×C49)⋊C9 |
| derived, Hall | C5×C49 ⋊ C4×C9 |
| Hall | C5×C49⋊C9 ⋊ C4 |
| Hall | AGL(1,𝔽5)×C49 ⋊ C9 |
| Sylow | C49 ⋊ C9×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C4×C49⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | AGL(1,𝔽5)×C49⋊C3 |
| commutator, hypocenter | C5×C49 | C4×C9 |
| Frattini | C3×C7 | AGL(1,𝔽5)×ΓL(1,𝔽8) |
| Fitting | C3×C5×C49 | C3×C4 |
| socle | C3×C5×C7 | C4×ΓL(1,𝔽8) |
| LCS | G ▷ C5×C49 | |
| UCS | C1 ◁ C3 | |
54 conjugacy classes of subgroups.
285 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8820, 14);