Finite Group DatabasebetaFinite Group Databasebeta| order | 20538 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #13091814⋊D7 |
| Fitting, socle, derived, Hall | C7×C163 ⋊ C2×C9 |
| Hall | C7×#13091814 ⋊ C2 |
| Hall | D1141 ⋊ C9 |
| Hall | #13091814 ⋊ D7 |
| Sylow | C163 ⋊ C9×D7 |
| Sylow | C7 ⋊ #13091814⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C163 | C2×C9 |
| prime radical | (C163⋊C3)⋊D7 | C3 |
| cosocle | C7×C163⋊C3 | C2×C3 |
| LCS | G ▷ C7×C163 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1141 |
Polycyclic presentation:
2,3^2,7,163|b^3=c,d^a=d^6,e^a=e^162,e^b=e^40,e^c=e^104108 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20538, 36);