Finite Group DatabasebetaFinite Group Databasebeta| order | 21894 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D3649 |
| unambiguous semidirect product | C41⋊(C3×D89) |
| unambiguous semidirect product | C89⋊(C3×D41) |
| Fitting, socle, Hall | C3×C41×C89 ⋊ C2 |
| derived, Hall | C41×C89 ⋊ C2×C3 |
| Hall | C3×C89 ⋊ D41 |
| Hall | C3×C41 ⋊ D89 |
| Sylow | C89 ⋊ C3×D41 |
| Sylow | C41 ⋊ C3×D89 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D3649 |
| commutator, cosocle, hypocenter | C41×C89 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C41×C89 | C2 |
| LCS | G ▷ C41×C89 | |
| UCS | C1 ◁ C3 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10947 |
5478 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21894, 4);