Finite Group DatabasebetaFinite Group Databasebeta| order | 19782 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C9 · Schur multiplier (H2) = C1 |
| direct product | C7×D157⋊C9 |
| unambiguous semidirect product | D157⋊(C7×C9) |
| unambiguous semidirect product | (C157⋊C9)⋊(C2×C7) |
| derived, Sylow | C157 ⋊ C2×C7×C9 |
| Hall | C7×C157⋊C9 ⋊ C2 |
| Hall | C7×D157 ⋊ C9 |
| Hall | C157⋊C9 ⋊ C2×C7 |
| Hall | C7×C157 ⋊ C2×C9 |
| Hall | D157 ⋊ C7×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C7 | D157⋊C3 |
| commutator, hypocenter | C157 | C2×C7×C9 |
| Frattini | C3 | C7×D157⋊C3 |
| Fitting, socle | C3×C7×C157 | C2×C3 |
| prime radical | C3×C7×D157 | C3 |
| cosocle | C3×C157 | C2×C3×C7 |
| LCS | G ▷ C157 | |
| UCS | C1 ◁ C3×C7 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9891 |
672 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19782, 13);