Finite Group DatabasebetaFinite Group Databasebeta| order | 19684 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C7×D19×D37 |
| unambiguous semidirect product | (C37×D19)⋊(C2×C7) |
| unambiguous semidirect product | (C19×D37)⋊(C2×C7) |
| unambiguous semidirect product | D703⋊(C2×C7) |
| Fitting, socle, Hall | C7×C19×C37 ⋊ C22 |
| derived, Hall | C19×C37 ⋊ C22×C7 |
| Hall | C7×C37 ⋊ C2×D19 |
| Hall | C7×C19 ⋊ C2×D37 |
| Sylow | C37 ⋊ C2×C7×D19 |
| Sylow | C19 ⋊ C2×C7×D37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D19×D37 |
| commutator, cosocle, hypocenter | C19×C37 | C22×C7 |
| Frattini | C1 | G |
| Fitting, socle | C7×C19×C37 | C22 |
| LCS | G ▷ C19×C37 | |
| UCS | C1 ◁ C7 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4921 |
1540 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19684, 12);