Finite Group DatabasebetaFinite Group Databasebeta| order | 7956 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(#11725133⋊C3) |
| unambiguous semidirect product | (C3⋊#11725133)⋊C3 |
| Fitting, socle, derived | C3×C13×C17 ⋊ C3×C4 |
| Hall | C3×C17×C13⋊C3 ⋊ C4 |
| Hall | C13×C17 ⋊ C3×Dic3 |
| Hall | C3×C13⋊C3 ⋊ #595 |
| Sylow | C17 ⋊ C3⋊(Dic13⋊C3) |
| Sylow | C13 ⋊ C3×C3⋊#595 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C13×C17 | C3×C4 |
| LCS | G ▷ C3×C13×C17 | |
| UCS | C1 | |
56 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,2,3,13,17|a^2=c,d^a=d^2,e^a=e^12,f^a=f^13,e^b=e^3,f^c=f^16114 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7956, 85);