Finite Group DatabasebetaFinite Group Databasebeta| order | 7956 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D51⋊(D13⋊C3) |
| unambiguous semidirect product | (C3⋊(D13⋊C3))⋊D17 |
| unambiguous semidirect product | (C17⋊(D13⋊C3))⋊D3 |
| unambiguous semidirect product | (D39⋊D17)⋊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 ⋊ D3×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.
Polycyclic presentation:
2^2,3^2,13,17|e^a=e^12,f^a=f^16,d^b=d^2,e^b=e^12,e^c=e^3144 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7956, 90);