Finite Group DatabasebetaFinite Group Databasebeta| order | 12564 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×Dic349⋊C3 |
| unambiguous semidirect product | Dic349⋊C32 |
| unambiguous semidirect product | (C3×Dic349)⋊C3 |
| derived, Sylow | C349 ⋊ C32×C4 |
| Hall | C3×C349⋊C3 ⋊ C4 |
| Hall | Dic349 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D349⋊C3 |
| commutator, hypocenter | C349 | C32×C4 |
| Frattini | C2 | C3×D349⋊C3 |
| Fitting, socle | C2×C3×C349 | C2×C3 |
| prime radical | C2×C3×C349⋊C3 | C2 |
| cosocle | C2×C349 | C2×C32 |
| LCS | G ▷ C349 | |
| UCS | C1 ◁ C2×C3 | |
36 conjugacy classes of subgroups.
384 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12564, 20);