Finite Group DatabasebetaFinite Group Databasebeta| order | 12564 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D3×D1047 |
| unambiguous semidirect product | (C3×D3)⋊D349 |
| unambiguous semidirect product | (D3×C349)⋊D3 |
| Fitting, socle, derived, Hall | C32×C349 ⋊ C22 |
| Sylow | C349 ⋊ D32 |
| Sylow | C32 ⋊ C2×D349 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C349 | C22 |
| LCS | G ▷ C32×C349 | |
| UCS | C1 | |
44 conjugacy classes of subgroups.
1575 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12564, 43);