Finite Group DatabasebetaFinite Group Databasebeta| order | 5820 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D5×D291 |
| unambiguous semidirect product | (C3×D5)⋊D97 |
| unambiguous semidirect product | (D5×C97)⋊D3 |
| Fitting, socle, derived, Hall | C3×C5×C97 ⋊ C22 |
| Hall | C5×C97 ⋊ C2×D3 |
| Hall | C3×C97 ⋊ C2×D5 |
| Sylow | C97 ⋊ D3×D5 |
| Hall | C3×C5 ⋊ C2×D97 |
| Sylow | C5 ⋊ C2×D291 |
| Sylow | C3 ⋊ D5×D97 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C5×C97 | C22 |
| LCS | G ▷ C3×C5×C97 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
588 conjugacy classes — view the full character table.
| maximal subgroup of | D5×D873, D5×C3⋊(D97⋊C3), C3×D5×D291, … |
| maximal normal subgroup of | D5×C3⋊(D97⋊C3), C3×D5×D291, C5×D5×D291 |
| maximal quotient of | D5×D873, C3×D5×D291, D5×C3⋊D291, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5820, 40);