Finite Group DatabasebetaFinite Group Databasebeta| order | 20634 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C181⋊C3)⋊D19 |
| Fitting, socle, derived, Hall | C19×C181 ⋊ C2×C3 |
| Hall | C19×C181⋊C3 ⋊ C2 |
| Hall | D3439 ⋊ C3 |
| Hall | C181⋊C3 ⋊ D19 |
| Sylow | C181 ⋊ C3×D19 |
| Sylow | C19 ⋊ D181⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C19×C181 | C2×C3 |
| LCS | G ▷ C19×C181 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3439 |
Polycyclic presentation:
2,3,19,181|c^a=c^18,d^a=d^180,d^b=d^48603 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20634, 21);