Finite Group DatabasebetaFinite Group Databasebeta| order | 19908 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×Dic711 |
| unambiguous semidirect product | C9⋊(C7×Dic79) |
| unambiguous semidirect product | C79⋊(C7×Dic9) |
| derived, Hall | C9×C79 ⋊ C4×C7 |
| Hall | C7×C9×C79 ⋊ C4 |
| Hall | C7×C79 ⋊ Dic9 |
| Sylow | C79 ⋊ C7×Dic9 |
| Hall | C7×C9 ⋊ Dic79 |
| Sylow | C9 ⋊ C7×Dic79 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | D711 |
| commutator, hypocenter | C9×C79 | C4×C7 |
| Frattini | C2×C3 | C7×D237 |
| Fitting | C2×C7×C9×C79 | C2 |
| socle, prime radical | C2×C3×C7×C79 | D3 |
| cosocle | C2×C9×C79 | C2×C7 |
| LCS | G ▷ C9×C79 | |
| UCS | C1 ◁ C2×C7 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 19908 |
4998 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19908, 10);