Finite Group DatabasebetaFinite Group Databasebeta| order | 10764 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×C3⋊(C23⋊#261) |
| unambiguous semidirect product | C3⋊(C3×C23⋊#261) |
| unambiguous semidirect product | C23⋊(C3×C3⋊#261) |
| Fitting, socle, Hall | C32×C13×C23 ⋊ C4 |
| derived | C3×C13×C23 ⋊ C3×C4 |
| Hall | C13×C23 ⋊ C3×Dic3 |
| Hall | C32×C23 ⋊ #261 |
| Hall | C32×C13 ⋊ Dic23 |
| Sylow | C23 ⋊ C3×C3⋊#261 |
| Sylow | C13 ⋊ C3×Dic69 |
| Sylow | C32 ⋊ C23⋊#261 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C3⋊(C23⋊#261) |
| commutator, hypocenter | C3×C13×C23 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C32×C13×C23 | C4 |
| prime radical | C32×C23×D13 | C2 |
| cosocle | C3×C23×D13 | C2×C3 |
| LCS | G ▷ C3×C13×C23 | |
| UCS | C1 ◁ C3 | |
56 conjugacy classes of subgroups.
837 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10764, 86);