Finite Group DatabasebetaFinite Group Databasebeta| order | 5844 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×D487⋊C3 |
| unambiguous semidirect product | D487⋊(C2×C3) |
| unambiguous semidirect product | (C487⋊C3)⋊C22 |
| unambiguous semidirect product | (C2×D487)⋊C3 |
| unambiguous semidirect product | (C2×C487⋊C3)⋊C2 |
| Fitting, socle | C2×C487 ⋊ C2×C3 |
| derived, Sylow | C487 ⋊ C22×C3 |
| Hall | C2×D487 ⋊ C3 |
| Hall | C487⋊C3 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D487⋊C3 |
| commutator, hypocenter | C487 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C487 | C2×C3 |
| LCS | G ▷ C487 | |
| UCS | C1 ◁ C2 | |
20 conjugacy classes of subgroups.
174 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#17983940⋊C2, D3×D487⋊C3, C2×C3×D487⋊C3, … |
| maximal normal subgroup of | C2×#17983940⋊C2, C2×C3×D487⋊C3, C2×C5×D487⋊C3 |
| maximal quotient of | C2×#17983938⋊C2, D3×D487⋊C3, C2×C3×D487⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5844, 8);