Finite Group DatabasebetaFinite Group Databasebeta| order | 12564 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| Fitting, socle, derived | C3×C349 ⋊ C22×C3 |
| Hall | C3×C349⋊C3 ⋊ C22 |
| Sylow | C349 ⋊ C2×C3×D3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C349 | C22×C3 |
| LCS | G ▷ C3×C349 | |
| UCS | C1 | |
44 conjugacy classes of subgroups.
192 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12564, 32);