Finite Group DatabasebetaFinite Group Databasebeta| order | 10764 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×C23⋊#261 |
| unambiguous semidirect product | C23⋊(C9×#261) |
| Fitting, Hall | C9×C13×C23 ⋊ C4 |
| derived, Hall | C13×C23 ⋊ C4×C9 |
| Hall | C9×C23 ⋊ #261 |
| Hall | C9×C13 ⋊ Dic23 |
| Sylow | C23 ⋊ C9×#261 |
| Sylow | C13 ⋊ C9×Dic23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | C23⋊#261 |
| commutator, hypocenter | C13×C23 | C4×C9 |
| Frattini | C3 | C3×C23⋊#261 |
| Fitting | C9×C13×C23 | C4 |
| socle | C3×C13×C23 | C3×C4 |
| prime radical, cosocle | C3×C23×D13 | C2×C3 |
| LCS | G ▷ C13×C23 | |
| UCS | C1 ◁ C9 | |
36 conjugacy classes of subgroups.
855 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10764, 21);