Finite Group DatabasebetaFinite Group Databasebeta| order | 21813 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C11 · Schur multiplier (H2) = C1 |
| direct product | C3×C661⋊C11 |
| unambiguous semidirect product | (C3×C661)⋊C11 |
| Fitting, socle, Hall | C3×C661 ⋊ C11 |
| derived, Sylow | C661 ⋊ C3×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C661⋊C11 |
| commutator, cosocle, hypocenter | C661 | C3×C11 |
| Frattini | C1 | G |
| Fitting, socle | C3×C661 | C11 |
| LCS | G ▷ C661 | |
| UCS | C1 ◁ C3 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1983 |
213 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21813, 2);