Finite Group DatabasebetaFinite Group Databasebeta| order | 5373 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9 · Schur multiplier (H2) = C3 |
| direct product | C3×#13184224 |
| derived, Sylow | C199 ⋊ C3×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | C199⋊C3 |
| commutator, hypocenter | C199 | C3×C9 |
| Frattini | C3 | C3×C199⋊C3 |
| Fitting, socle | C32×C199 | C3 |
| LCS | G ▷ C199 | |
| UCS | C1 ◁ C32 | |
20 conjugacy classes of subgroups.
621 conjugacy classes — view the full character table.
| maximal subgroup of | C9×#13184224, #30633123, C32⋊#13184224, … |
| maximal normal subgroup of | C9×#13184224, #30633123, C32⋊#13184224, … |
| maximal quotient of | C9×#13184224, C32⋊#13184224, #30633126, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5373, 8);