Finite Group DatabasebetaFinite Group Databasebeta| order | 21822 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D3637⋊C3 |
| unambiguous semidirect product | (C3637⋊C3)⋊C2 |
| Fitting, socle, derived, Sylow | C3637 ⋊ C2×C3 |
| Hall | C3637⋊C3 ⋊ C2 |
| Hall | D3637 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3637 | C2×C3 |
| LCS | G ▷ C3637 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3637 |
Polycyclic presentation:
2,3,3637|c^a=c^3636,c^b=c^2941612 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21822, 1);