Finite Group DatabasebetaFinite Group Databasebeta| order | 20961 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C17 · Schur multiplier (H2) = C1 |
| direct product | C9×C137⋊C17 |
| unambiguous semidirect product | C137⋊(C9×C17) |
| unambiguous semidirect product | (C9×C137)⋊C17 |
| Fitting, Hall | C9×C137 ⋊ C17 |
| derived, Sylow | C137 ⋊ C9×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | C137⋊C17 |
| commutator, hypocenter | C137 | C9×C17 |
| Frattini | C3 | C3×C137⋊C17 |
| Fitting | C9×C137 | C17 |
| socle, cosocle | C3×C137 | C3×C17 |
| prime radical | C3×C137⋊C17 | C3 |
| LCS | G ▷ C137 | |
| UCS | C1 ◁ C9 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1233 |
225 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20961, 2);