Finite Group DatabasebetaFinite Group Databasebeta| order | 8820 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×C5⋊(D49⋊C9) |
| unambiguous semidirect product | (C2×C5)⋊(D49⋊C9) |
| unambiguous semidirect product | (C2×C49⋊C9)⋊D5 |
| unambiguous semidirect product | (C2×D245)⋊C9 |
| derived, Hall | C5×C49 ⋊ C22×C9 |
| Hall | C5×C49⋊C9 ⋊ C22 |
| Hall | C2×D245 ⋊ C9 |
| Hall | C49⋊C9 ⋊ C2×D5 |
| Sylow | C49 ⋊ C2×C9×D5 |
| Sylow | C5 ⋊ C2×D49⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | C5⋊(D49⋊C3) |
| commutator, hypocenter | C5×C49 | C22×C9 |
| Frattini | C3×C7 | C2×C5⋊AGL(1,𝔽7) |
| Fitting | C2×C3×C5×C49 | C2×C3 |
| socle | C2×C3×C5×C7 | AGL(1,𝔽7) |
| LCS | G ▷ C5×C49 | |
| UCS | C1 ◁ C2×C3 | |
90 conjugacy classes of subgroups.
312 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8820, 19);