Finite Group DatabasebetaFinite Group Databasebeta| order | 5901 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C7 · Schur multiplier (H2) = C1 |
| direct product | C3×C281⋊C7 |
| unambiguous semidirect product | C281⋊(C3×C7) |
| unambiguous semidirect product | (C3×C281)⋊C7 |
| Fitting, socle, Hall | C3×C281 ⋊ C7 |
| derived, Sylow | C281 ⋊ C3×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C281⋊C7 |
| commutator, hypocenter | C281 | C3×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C281 | C7 |
| LCS | G ▷ C281 | |
| UCS | C1 ◁ C3 | |
8 conjugacy classes of subgroups.
141 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C3×C281⋊C7, C3×D281⋊C7, D3×C281⋊C7, … |
| maximal normal subgroup of | C2×C3×C281⋊C7, C3×D281⋊C7, D3×C281⋊C7, … |
| maximal quotient of | C2×C3×C281⋊C7, C9×C281⋊C7, C32×C281⋊C7, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5901, 1);