Finite Group DatabasebetaFinite Group Databasebeta| order | 5652 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×#10597845 |
| Fitting, Hall | C9×C157 ⋊ C4 |
| derived, Sylow | C157 ⋊ C4×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | #10597845 |
| commutator, hypocenter | C157 | C4×C9 |
| Frattini | C3 | C3×#10597845 |
| Fitting | C9×C157 | C4 |
| socle | C3×C157 | C3×C4 |
| LCS | G ▷ C157 | |
| UCS | C1 ◁ C9 | |
18 conjugacy classes of subgroups.
387 conjugacy classes — view the full character table.
| maximal subgroup of | C5×C9×#10597845, C9×#15691169, C9×#15691170, … |
| maximal normal subgroup of | C5×C9×#10597845 |
| maximal quotient of | C5×C9×#10597845, C9×#15691169, C9×#15691170, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5652, 10);