Finite Group DatabasebetaFinite Group Databasebeta| order | 31569 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×C619⋊C3 |
| unambiguous semidirect product | C619⋊(C3×C17) |
| unambiguous semidirect product | (C17×C619)⋊C3 |
| Fitting, socle, Hall | C17×C619 ⋊ C3 |
| derived, Sylow | C619 ⋊ C3×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | C619⋊C3 |
| commutator, cosocle, hypocenter | C619 | C3×C17 |
| Frattini | C1 | G |
| Fitting, socle | C17×C619 | C3 |
| LCS | G ▷ C619 | |
| UCS | C1 ◁ C17 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10523 |
3553 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31569, 1);