Finite Group DatabasebetaFinite Group Databasebeta| order | 11420 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C4×C571⋊C5 |
| unambiguous semidirect product | (C4×C571)⋊C5 |
| Fitting, Hall | C4×C571 ⋊ C5 |
| derived, Sylow | C571 ⋊ C4×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | C571⋊C5 |
| commutator, hypocenter | C571 | C4×C5 |
| Frattini | C2 | C2×C571⋊C5 |
| Fitting | C4×C571 | C5 |
| socle, cosocle | C2×C571 | C2×C5 |
| prime radical | C2×C571⋊C5 | C2 |
| LCS | G ▷ C571 | |
| UCS | C1 ◁ C4 | |
12 conjugacy classes of subgroups.
476 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C4×C571⋊C5, C4×(C571⋊C3)⋊C5, Dic3×C571⋊C5 |
| maximal normal subgroup of | C3×C4×C571⋊C5, C4×(C571⋊C3)⋊C5 |
| maximal quotient of | C3×C4×C571⋊C5, Dic3×C571⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11420, 3);