Finite Group DatabasebetaFinite Group Databasebeta| order | 21846 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1 |
| direct product | C2×(C331⋊C3)⋊C11 |
| unambiguous semidirect product | (C2×C331⋊C3)⋊C11 |
| unambiguous semidirect product | (C2×C331⋊C11)⋊C3 |
| Fitting, socle, Hall | C2×C331 ⋊ C3×C11 |
| derived, Sylow | C331 ⋊ C2×C3×C11 |
| Hall | C2×C331⋊C11 ⋊ C3 |
| Hall | C331⋊C11 ⋊ C2×C3 |
| Hall | C2×C331⋊C3 ⋊ C11 |
| Hall | C331⋊C3 ⋊ C2×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | (C331⋊C3)⋊C11 |
| commutator, cosocle, hypocenter | C331 | C2×C3×C11 |
| Frattini | C1 | G |
| Fitting, socle | C2×C331 | C3×C11 |
| LCS | G ▷ C331 | |
| UCS | C1 ◁ C2 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 662 |
86 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21846, 4);