Finite Group DatabasebetaFinite Group Databasebeta| order | 7956 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C9⋊#11725130 |
| Fitting, derived, Hall | C9×C13×C17 ⋊ C4 |
| Hall | C13×C17 ⋊ Dic9 |
| Hall | C9×C17 ⋊ #261 |
| Hall | C9×C13 ⋊ #595 |
| Sylow | C17 ⋊ C9⋊#261 |
| Sylow | C13 ⋊ C9⋊#595 |
| Sylow | C9 ⋊ #11725130 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C9×C13×C17 | C4 |
| Frattini | C3 | C3⋊#11725130 |
| socle | C3×C13×C17 | Dic3 |
| LCS | G ▷ C9×C13×C17 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,13,17,3|a^2=b,c^3=f^2,c^a=c^2f,d^a=d^5,e^a=e^13,f^a=f^2,d^b=d^12,e^b=e^16507 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7956, 34);