Finite Group DatabasebetaFinite Group Databasebeta| order | 31749 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C557 · Schur multiplier (H2) = C1 |
| direct product | C19⋊C3×C557 |
| unambiguous semidirect product | C19⋊(C3×C557) |
| unambiguous semidirect product | (C19×C557)⋊C3 |
| Fitting, socle, Hall | C19×C557 ⋊ C3 |
| derived, Sylow | C19 ⋊ C3×C557 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C557 | C19⋊C3 |
| commutator, cosocle, hypocenter | C19 | C3×C557 |
| Frattini | C1 | G |
| Fitting, socle | C19×C557 | C3 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C557 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10583 |
5013 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31749, 1);