Finite Group DatabasebetaFinite Group Databasebeta| order | 12564 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C22×C3×C349⋊C3 |
| Fitting, socle | C22×C3×C349 ⋊ C3 |
| derived, Sylow | C349 ⋊ C22×C32 |
| Hall | C22×C349 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3 | C349⋊C3 |
| commutator, cosocle, hypocenter | C349 | C22×C32 |
| Frattini | C1 | G |
| Fitting, socle | C22×C3×C349 | C3 |
| LCS | G ▷ C349 | |
| UCS | C1 ◁ C22×C3 | |
60 conjugacy classes of subgroups.
1428 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12564, 50);