Finite Group DatabasebetaFinite Group Databasebeta| order | 12564 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| direct product | C4×C349⋊C9 |
| unambiguous semidirect product | (C4×C349)⋊C9 |
| derived, Sylow | C349 ⋊ C4×C9 |
| Hall | C4×C349 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C4 | C349⋊C3 |
| commutator, hypocenter | C349 | C4×C9 |
| Frattini | C2×C3 | C2×C349⋊C3 |
| Fitting | C3×C4×C349 | C3 |
| socle, prime radical, cosocle | C2×C3×C349 | C2×C3 |
| LCS | G ▷ C349 | |
| UCS | C1 ◁ C3×C4 | |
18 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, 3);