Finite Group DatabasebetaFinite Group Databasebeta| order | 12564 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×#13063703⋊C3 |
| unambiguous semidirect product | #13063703⋊C32 |
| unambiguous semidirect product | (C3×#13063703)⋊C3 |
| Fitting, socle | C3×C349 ⋊ C3×C4 |
| derived, Sylow | C349 ⋊ C32×C4 |
| Hall | C3×C349⋊C3 ⋊ C4 |
| Hall | #13063703 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #13063703⋊C3 |
| commutator, hypocenter | C349 | C32×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C349 | C3×C4 |
| prime radical | C3×D349⋊C3 | C2 |
| cosocle | D349 | C2×C32 |
| LCS | G ▷ C349 | |
| UCS | C1 ◁ C3 | |
36 conjugacy classes of subgroups.
123 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12564, 30);