Finite Group DatabasebetaFinite Group Databasebeta| order | 5394 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D899 |
| unambiguous semidirect product | C29⋊(C3×D31) |
| Fitting, socle, Hall | C3×C29×C31 ⋊ C2 |
| derived, Hall | C29×C31 ⋊ C2×C3 |
| Hall | C3×C31 ⋊ D29 |
| Hall | C3×C29 ⋊ D31 |
| Sylow | C31 ⋊ C3×D29 |
| Sylow | C29 ⋊ C3×D31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D899 |
| commutator, hypocenter | C29×C31 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C29×C31 | C2 |
| LCS | G ▷ C29×C31 | |
| UCS | C1 ◁ C3 | |
16 conjugacy classes of subgroups.
1353 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C9×D899, C29⋊(D31⋊C9), C3×C29⋊(D31⋊C3), … |
| maximal normal subgroup of | C9×D899, C29⋊(D31⋊C9), C3×C29⋊(D31⋊C3), … |
| maximal quotient of | C9×D899, C3×D2697, C32×D899, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5394, 5);