Finite Group DatabasebetaFinite Group Databasebeta| order | 19348 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×Dic691 |
| unambiguous semidirect product | C691⋊(C4×C7) |
| derived, Sylow | C691 ⋊ C4×C7 |
| Hall | C7×C691 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | D691 |
| commutator, hypocenter | C691 | C4×C7 |
| Frattini | C2 | C7×D691 |
| Fitting, socle, prime radical | C2×C7×C691 | C2 |
| cosocle | C2×C691 | C2×C7 |
| LCS | G ▷ C691 | |
| UCS | C1 ◁ C2×C7 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 19348 |
4858 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19348, 3);