Finite Group DatabasebetaFinite Group Databasebeta| order | 12564 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(Dic349⋊C3) |
| unambiguous semidirect product | Dic1047⋊C3 |
| derived | C3×C349 ⋊ C3×C4 |
| Hall | C3×C349⋊C3 ⋊ C4 |
| Sylow | C349 ⋊ C3×Dic3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊(D349⋊C3) |
| commutator, hypocenter | C3×C349 | C3×C4 |
| Fitting, socle, cosocle | C2×C3×C349 | C2×C3 |
| prime radical | C2×C3×C349⋊C3 | C2 |
| LCS | G ▷ C3×C349 | |
| UCS | C1 ◁ C2 | |
28 conjugacy classes of subgroups.
Polycyclic presentation:
2,3^2,349,2|a^2=e,c^a=c^2,d^a=d^348,d^b=d^122366 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12564, 21);