Finite Group DatabasebetaFinite Group Databasebeta| order | 12564 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊(C3⋊#13063703) |
| Fitting, socle, derived, Hall | C32×C349 ⋊ C4 |
| Sylow | C349 ⋊ C3⋊Dic3 |
| Sylow | C32 ⋊ #13063703 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C349 | C4 |
| prime radical, cosocle | C32×D349 | C2 |
| LCS | G ▷ C32×C349 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3^2,349|a^2=b,c^a=c^2,d^a=d^2,e^a=e^136,e^b=e^348795 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12564, 40);