Finite Group DatabasebetaFinite Group Databasebeta| order | 5652 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C9⋊#10597845 |
| Fitting, derived, Hall | C9×C157 ⋊ C4 |
| Sylow | C157 ⋊ Dic9 |
| Sylow | C9 ⋊ #10597845 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C9×C157 | C4 |
| Frattini | C3 | C3⋊#10597845 |
| socle | C3×C157 | Dic3 |
| LCS | G ▷ C9×C157 | |
| UCS | C1 | |
18 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,157,3|a^2=b,c^3=e^2,c^a=c^2e,d^a=d^28,e^a=e^2,d^b=d^156363 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, 11);