Finite Group DatabasebetaFinite Group Databasebeta| order | 20538 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | D7×#13091814 |
| Fitting, socle, derived, Hall | C7×C163 ⋊ C2×C9 |
| Hall | C7×#13091814 ⋊ C2 |
| Hall | D7×C163 ⋊ C9 |
| Sylow | C163 ⋊ C9×D7 |
| Sylow | C7 ⋊ C2×#13091814 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C163 | C2×C9 |
| prime radical | D7×C163⋊C3 | C3 |
| cosocle | C7×C163⋊C3 | C2×C3 |
| LCS | G ▷ C7×C163 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1141 |
135 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20538, 37);