Finite Group DatabasebetaFinite Group Databasebeta| order | 21846 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊(D331⋊C3) |
| unambiguous semidirect product | (C331⋊C3)⋊D11 |
| unambiguous semidirect product | D3641⋊C3 |
| Fitting, socle, derived, Hall | C11×C331 ⋊ C2×C3 |
| Hall | C11×C331⋊C3 ⋊ C2 |
| Hall | D3641 ⋊ C3 |
| Hall | C331⋊C3 ⋊ D11 |
| Sylow | C331 ⋊ C3×D11 |
| Sylow | C11 ⋊ D331⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C331 | C2×C3 |
| LCS | G ▷ C11×C331 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3641 |
Polycyclic presentation:
2,3,11,331|c^a=c^10,d^a=d^330,d^b=d^299626 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21846, 17);