Finite Group DatabasebetaFinite Group Databasebeta| order | 5445 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C5 · Schur multiplier (H2) = C3 |
| direct product | C32×C121⋊C5 |
| unambiguous semidirect product | C121⋊(C32×C5) |
| unambiguous semidirect product | (C3×C121)⋊(C3×C5) |
| unambiguous semidirect product | (C32×C121)⋊C5 |
| Fitting, Hall | C32×C121 ⋊ C5 |
| derived, Sylow | C121 ⋊ C32×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | C121⋊C5 |
| commutator, hypocenter | C121 | C32×C5 |
| Frattini | C11 | C32×C11⋊C5 |
| Fitting | C32×C121 | C5 |
| socle | C32×C11 | C11⋊C5 |
| LCS | G ▷ C121 | |
| UCS | C1 ◁ C32 | |
36 conjugacy classes of subgroups.
261 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5445, 4);