Finite Group DatabasebetaFinite Group Databasebeta| order | 7956 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | D17×C3⋊(D13⋊C3) |
| unambiguous semidirect product | (C3×D17)⋊(D13⋊C3) |
| unambiguous semidirect product | (D17×C13⋊C3)⋊D3 |
| unambiguous semidirect product | (D17×D39)⋊C3 |
| Fitting, socle, derived | C3×C13×C17 ⋊ C22×C3 |
| Hall | C3×C17×C13⋊C3 ⋊ C22 |
| Hall | C13×C17 ⋊ C2×C3×D3 |
| Hall | C3×C13⋊C3 ⋊ C2×D17 |
| Sylow | C17 ⋊ C2×C3⋊(D13⋊C3) |
| Sylow | C13 ⋊ C3×D3×D17 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C13×C17 | C22×C3 |
| LCS | G ▷ C3×C13×C17 | |
| UCS | C1 | |
88 conjugacy classes of subgroups.
150 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7956, 86);