Finite Group DatabasebetaFinite Group Databasebeta| order | 20826 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C89⋊(D13⋊C9) |
| unambiguous semidirect product | (C13⋊C9)⋊D89 |
| unambiguous semidirect product | D1157⋊C9 |
| derived, Hall | C13×C89 ⋊ C2×C9 |
| Hall | C89×C13⋊C9 ⋊ C2 |
| Hall | D1157 ⋊ C9 |
| Hall | C13⋊C9 ⋊ D89 |
| Sylow | C89 ⋊ D13⋊C9 |
| Sylow | C13 ⋊ C9×D89 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | (C13⋊C3)⋊D89 |
| commutator, hypocenter | C13×C89 | C2×C9 |
| Fitting, socle, cosocle | C3×C13×C89 | C2×C3 |
| prime radical | C3×D1157 | C3 |
| LCS | G ▷ C13×C89 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10413 |
Polycyclic presentation:
2,3,13,89,3|b^3=e,c^a=c^12,d^a=d^88,c^b=c^3948 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20826, 12);