Finite Group DatabasebetaFinite Group Databasebeta| order | 5373 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C33 |
| direct product | C32×C199⋊C3 |
| unambiguous semidirect product | C199⋊C33 |
| unambiguous semidirect product | (C3×C199)⋊C32 |
| Fitting, socle | C32×C199 ⋊ C3 |
| derived, Sylow | C199 ⋊ C33 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | C199⋊C3 |
| commutator, hypocenter | C199 | C33 |
| Frattini | C1 | G |
| Fitting, socle | C32×C199 | C3 |
| LCS | G ▷ C199 | |
| UCS | C1 ◁ C32 | |
56 conjugacy classes of subgroups.
621 conjugacy classes — view the full character table.
| maximal subgroup of | #30633123, #30633133, #30633135, … |
| maximal normal subgroup of | #30633123, #30633133, #30633135, … |
| maximal quotient of | C3×C9×C199⋊C3, C32×#13184224, H(3,𝔽3)×C199⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5373, 13);