Finite Group DatabasebetaFinite Group Databasebeta| order | 21726 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×D1207 |
| unambiguous semidirect product | C17⋊(C9×D71) |
| unambiguous semidirect product | C71⋊(C9×D17) |
| Fitting, Hall | C9×C17×C71 ⋊ C2 |
| derived, Hall | C17×C71 ⋊ C2×C9 |
| Hall | C9×C71 ⋊ D17 |
| Hall | C9×C17 ⋊ D71 |
| Sylow | C71 ⋊ C9×D17 |
| Sylow | C17 ⋊ C9×D71 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | D1207 |
| commutator, hypocenter | C17×C71 | C2×C9 |
| Frattini | C3 | C3×D1207 |
| Fitting | C9×C17×C71 | C2 |
| socle, cosocle | C3×C17×C71 | C2×C3 |
| prime radical | C3×D1207 | C3 |
| LCS | G ▷ C17×C71 | |
| UCS | C1 ◁ C9 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10863 |
5445 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21726, 4);