Finite Group DatabasebetaFinite Group Databasebeta| order | 5364 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D9×D149 |
| unambiguous semidirect product | (D9×C149)⋊C2 |
| unambiguous semidirect product | (C9×D149)⋊C2 |
| unambiguous semidirect product | D1341⋊C2 |
| Fitting, derived, Hall | C9×C149 ⋊ C22 |
| Sylow | C149 ⋊ C2×D9 |
| Sylow | C9 ⋊ C2×D149 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C9×C149 | C22 |
| Frattini | C3 | D3×D149 |
| socle | C3×C149 | C2×D3 |
| LCS | G ▷ C9×C149 | |
| UCS | C1 | |
30 conjugacy classes of subgroups.
456 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D9×D149, D45×D149, D9×D745, … |
| maximal normal subgroup of | C5×D9×D149, C7×D9×D149 |
| maximal quotient of | C5×D9×D149, D45×D149, D9×D745, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5364, 8);