Finite Group DatabasebetaFinite Group Databasebeta| order | 20826 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊((C13⋊C3)⋊D89) |
| unambiguous semidirect product | (C13⋊C3)⋊D267 |
| unambiguous semidirect product | C89⋊(C3⋊(D13⋊C3)) |
| unambiguous semidirect product | D3471⋊C3 |
| Fitting, socle, derived | C3×C13×C89 ⋊ C2×C3 |
| Hall | C3×C13⋊C3×C89 ⋊ C2 |
| Hall | C13×C89 ⋊ C3×D3 |
| Hall | C3×C13⋊C3 ⋊ D89 |
| Sylow | C89 ⋊ C3⋊(D13⋊C3) |
| Sylow | C13 ⋊ C3×D267 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C13×C89 | C2×C3 |
| LCS | G ▷ C3×C13×C89 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3471 |
Polycyclic presentation:
2,3^2,13,89|c^a=c^2,d^a=d^12,e^a=e^88,d^b=d^3939 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20826, 18);