Finite Group DatabasebetaFinite Group Databasebeta| order | 19684 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×Dic703 |
| unambiguous semidirect product | C19⋊(C7×Dic37) |
| derived, Hall | C19×C37 ⋊ C4×C7 |
| Hall | C7×C19×C37 ⋊ C4 |
| Hall | C7×C37 ⋊ Dic19 |
| Hall | C7×C19 ⋊ Dic37 |
| Sylow | C37 ⋊ C7×Dic19 |
| Sylow | C19 ⋊ C7×Dic37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | D703 |
| commutator, hypocenter | C19×C37 | C4×C7 |
| Frattini | C2 | C7×D703 |
| Fitting, socle, prime radical | C2×C7×C19×C37 | C2 |
| cosocle | C2×C19×C37 | C2×C7 |
| LCS | G ▷ C19×C37 | |
| UCS | C1 ◁ C2×C7 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 19684 |
4942 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19684, 4);