Finite Group DatabasebetaFinite Group Databasebeta| order | 12564 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C2×C3 |
| direct product | A4×C349⋊C3 |
| unambiguous semidirect product | (C22×C349⋊C3)⋊C3 |
| unambiguous semidirect product | (A4×C349)⋊C3 |
| unambiguous semidirect product | (C22⋊(C349⋊C3))⋊C3 |
| Fitting, socle, derived, Hall | C22×C349 ⋊ C32 |
| Sylow | C349 ⋊ C3×A4 |
| Sylow | C22 ⋊ C3×C349⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C22×C349 | C32 |
| LCS | G ▷ C22×C349 | |
| UCS | C1 | |
28 conjugacy classes of subgroups.
476 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12564, 33);