Finite Group DatabasebetaFinite Group Databasebeta| order | 19684 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×C19⋊#3866 |
| unambiguous semidirect product | C19⋊(C7×#3866) |
| Fitting, socle, Hall | C7×C19×C37 ⋊ C4 |
| derived, Hall | C19×C37 ⋊ C4×C7 |
| Hall | C7×C37 ⋊ Dic19 |
| Hall | C7×C19 ⋊ #3866 |
| Sylow | C37 ⋊ C7×Dic19 |
| Sylow | C19 ⋊ C7×#3866 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | C19⋊#3866 |
| commutator, hypocenter | C19×C37 | C4×C7 |
| Frattini | C1 | G |
| Fitting, socle | C7×C19×C37 | C4 |
| prime radical | C7×C19×D37 | C2 |
| cosocle | C19×D37 | C2×C7 |
| LCS | G ▷ C19×C37 | |
| UCS | C1 ◁ C7 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4921 |
1351 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19684, 11);