Finite Group DatabasebetaFinite Group Databasebeta| order | 8820 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×(C49⋊C3)⋊Dic5 |
| unambiguous semidirect product | (C49⋊C3)⋊(C3×Dic5) |
| unambiguous semidirect product | Dic245⋊C32 |
| unambiguous semidirect product | (C3×Dic245)⋊C3 |
| derived, Hall | C5×C49 ⋊ C32×C4 |
| Hall | C3×C5×C49⋊C3 ⋊ C4 |
| Hall | Dic245 ⋊ C32 |
| Hall | C3×C49⋊C3 ⋊ Dic5 |
| Sylow | C49 ⋊ C32×Dic5 |
| Sylow | C5 ⋊ C3×(C49⋊C3)⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | C5⋊(D49⋊C3) |
| commutator, hypocenter | C5×C49 | C32×C4 |
| Frattini | C2×C7 | C3×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 | |
108 conjugacy classes of subgroups.
312 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8820, 44);