Finite Group DatabasebetaFinite Group Databasebeta| order | 20826 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9×C89 · Schur multiplier (H2) = C1 |
| direct product | C2×C89×C13⋊C9 |
| unambiguous semidirect product | (C2×C13)⋊(C9×C89) |
| unambiguous semidirect product | (C2×C13×C89)⋊C9 |
| derived, Sylow | C13 ⋊ C2×C9×C89 |
| Hall | C2×C13×C89 ⋊ C9 |
| Hall | C13×C89 ⋊ C2×C9 |
| Hall | C2×C13 ⋊ C9×C89 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C89 | C13⋊C3 |
| commutator, hypocenter | C13 | C2×C9×C89 |
| Frattini | C3 | C2×C13⋊C3×C89 |
| Fitting, socle, prime radical | C2×C3×C13×C89 | C3 |
| cosocle | C3×C13 | C2×C3×C89 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C2×C3×C89 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 20826 |
3738 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20826, 2);