Finite Group DatabasebetaFinite Group Databasebeta| order | 19782 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C7×C157 ⋊ C2×C9 |
| Hall | #23754675 ⋊ C2 |
| Hall | C7×D157 ⋊ C9 |
| Hall | D157 ⋊ C7⋊C9 |
| Sylow | C157 ⋊ C2×C7⋊C9 |
| Sylow | C7 ⋊ D157⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #20268646 |
| commutator, hypocenter | C7×C157 | C2×C9 |
| Fitting, socle, cosocle | C3×C7×C157 | C2×C3 |
| prime radical | C3×C7×D157 | C3 |
| LCS | G ▷ C7×C157 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9891 |
Polycyclic presentation:
2,3,7,157,3|b^3=e,d^a=d^156,c^b=c^2,d^b=d^144576 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19782, 16);