Finite Group DatabasebetaFinite Group Databasebeta| order | 7917 |
| isoclinism | isoclinic class of C13⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C7×C29 · Schur multiplier (H2) = C1 |
| direct product | C7×C29×C13⋊C3 |
| unambiguous semidirect product | C13⋊(C3×C7×C29) |
| Fitting, socle, Hall | C7×C13×C29 ⋊ C3 |
| derived, Sylow | C13 ⋊ C3×C7×C29 |
| Hall | C13×C29 ⋊ C3×C7 |
| Hall | C7×C13 ⋊ C3×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7×C29 | C13⋊C3 |
| commutator, hypocenter | C13 | C3×C7×C29 |
| Frattini | C1 | G |
| Fitting, socle | C7×C13×C29 | C3 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C7×C29 | |
16 conjugacy classes of subgroups.
1421 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7917, 3);