Finite Group DatabasebetaFinite Group Databasebeta| order | 5373 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9 · Schur multiplier (H2) = C3 |
| direct product | C9×C199⋊C3 |
| Fitting | C9×C199 ⋊ C3 |
| derived, Sylow | C199 ⋊ C3×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | C199⋊C3 |
| commutator, hypocenter | C199 | C3×C9 |
| Frattini | C3 | C3×C199⋊C3 |
| Fitting | C9×C199 | C3 |
| socle | C3×C199 | C32 |
| LCS | G ▷ C199 | |
| UCS | C1 ◁ C9 | |
20 conjugacy classes of subgroups.
621 conjugacy classes — view the full character table.
| maximal subgroup of | C27×C199⋊C3, #30633130, #30633131, … |
| maximal normal subgroup of | C27×C199⋊C3, #30633130, #30633131, … |
| maximal quotient of | C9×#13184224, #30633123, #30633125, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5373, 7);