Finite Group DatabasebetaFinite Group Databasebeta| order | 7956 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×C13⋊C3×Dic17 |
| unambiguous semidirect product | (C13×Dic17)⋊C32 |
| unambiguous semidirect product | (C3×C13×Dic17)⋊C3 |
| derived, Hall | C13×C17 ⋊ C32×C4 |
| Hall | C3×C17×C13⋊C3 ⋊ C4 |
| Hall | C13×Dic17 ⋊ C32 |
| Sylow | C17 ⋊ C3×C4×C13⋊C3 |
| Sylow | C13 ⋊ C32×Dic17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D17×C13⋊C3 |
| commutator, hypocenter | C13×C17 | C32×C4 |
| Frattini | C2 | C3×D17×C13⋊C3 |
| Fitting, socle | C2×C3×C13×C17 | C2×C3 |
| LCS | G ▷ C13×C17 | |
| UCS | C1 ◁ C2×C3 | |
72 conjugacy classes of subgroups.
420 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7956, 56);