Finite Group DatabasebetaFinite Group Databasebeta| order | 8619 |
| isoclinism | isoclinic class of C13⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C13×C17 · Schur multiplier (H2) = C1 |
| direct product | C13×C17×C13⋊C3 |
| unambiguous semidirect product | C13⋊(C3×C13×C17) |
| unambiguous semidirect product | (C13×C17)⋊(C3×C13) |
| Fitting, socle, Hall | C132×C17 ⋊ C3 |
| derived | C13 ⋊ C3×C13×C17 |
| Sylow | C132 ⋊ C3×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13×C17 | C13⋊C3 |
| commutator, hypocenter | C13 | C3×C13×C17 |
| Frattini | C1 | G |
| Fitting, socle | C132×C17 | C3 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C13×C17 | |
24 conjugacy classes of subgroups.
1547 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8619, 5);