Finite Group DatabasebetaFinite Group Databasebeta| order | 12564 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(#13063703⋊C3) |
| unambiguous semidirect product | (C3⋊#13063703)⋊C3 |
| Fitting, socle, derived | C3×C349 ⋊ C3×C4 |
| Hall | C3×C349⋊C3 ⋊ C4 |
| Sylow | C349 ⋊ C3×Dic3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C349 | C3×C4 |
| prime radical | C3×D349⋊C3 | C2 |
| cosocle | C3×D349 | C2×C3 |
| LCS | G ▷ C3×C349 | |
| UCS | C1 | |
28 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,2,3,349|a^2=c,d^a=d^2,e^a=e^136,e^b=e^122,e^c=e^348105 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12564, 31);