Finite Group DatabasebetaFinite Group Databasebeta| order | 7956 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×C9⋊#595 |
| unambiguous semidirect product | C9⋊(C13×#595) |
| Fitting, Hall | C9×C13×C17 ⋊ C4 |
| derived, Hall | C9×C17 ⋊ C4×C13 |
| Hall | C13×C17 ⋊ Dic9 |
| Hall | C9×C13 ⋊ #595 |
| Sylow | C17 ⋊ C13×Dic9 |
| Sylow | C9 ⋊ C13×#595 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | C9⋊#595 |
| commutator, hypocenter | C9×C17 | C4×C13 |
| Frattini | C3 | C13×C3⋊#595 |
| Fitting | C9×C13×C17 | C4 |
| socle | C3×C13×C17 | Dic3 |
| LCS | G ▷ C9×C17 | |
| UCS | C1 ◁ C13 | |
36 conjugacy classes of subgroups.
624 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7956, 31);