Finite Group DatabasebetaFinite Group Databasebeta| order | 5820 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×C5×D291 |
| unambiguous semidirect product | (C2×C3)⋊(C5×D97) |
| unambiguous semidirect product | (C2×C97)⋊(C5×D3) |
| Fitting, socle | C2×C3×C5×C97 ⋊ C2 |
| derived, Hall | C3×C97 ⋊ C22×C5 |
| Hall | C3×C5×C97 ⋊ C22 |
| Hall | C5×C97 ⋊ C2×D3 |
| Sylow | C97 ⋊ C2×C5×D3 |
| Hall | C3×C5 ⋊ C2×D97 |
| Sylow | C3 ⋊ C2×C5×D97 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D291 |
| commutator, hypocenter | C3×C97 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C5×C97 | C2 |
| LCS | G ▷ C3×C97 | |
| UCS | C1 ◁ C2×C5 | |
40 conjugacy classes of subgroups.
1470 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C5×D873, C2×C5×C3⋊(D97⋊C3), C5×D3×D291, … |
| maximal normal subgroup of | C2×C5×C3⋊(D97⋊C3), C2×C3×C5×D291, C2×C25×D291, … |
| maximal quotient of | C2×C5×D873, C5×D3×D291, C2×C5×C3⋊D291, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5820, 50);