Finite Group DatabasebetaFinite Group Databasebeta| order | 7917 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C7 · Schur multiplier (H2) = C1 |
| Fitting, socle, derived, Hall | C13×C29 ⋊ C3×C7 |
| Hall | C13×C29⋊C7 ⋊ C3 |
| Hall | C29×C13⋊C3 ⋊ C7 |
| Sylow | C29 ⋊ C7×C13⋊C3 |
| Sylow | C13 ⋊ C3×C29⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C13×C29 | C3×C7 |
| LCS | G ▷ C13×C29 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
77 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7917, 7);