Finite Group DatabasebetaFinite Group Databasebeta| order | 12564 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C9⋊#13063703 |
| Fitting, derived, Hall | C9×C349 ⋊ C4 |
| Sylow | C349 ⋊ Dic9 |
| Sylow | C9 ⋊ #13063703 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C9×C349 | C4 |
| Frattini | C3 | C3⋊#13063703 |
| socle | C3×C349 | Dic3 |
| prime radical | C3×D349 | D3 |
| cosocle | C9×D349 | C2 |
| LCS | G ▷ C9×C349 | |
| UCS | C1 | |
18 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,349,3|a^2=b,c^3=e^2,c^a=c^2e,d^a=d^136,e^a=e^2,d^b=d^348795 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12564, 11);