Finite Group DatabasebetaFinite Group Databasebeta| order | 37791 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×#14555740 |
| Fitting, socle, Hall | C13×C17×C19 ⋊ C9 |
| derived, Hall | C13×C19 ⋊ C9×C17 |
| Hall | C17×C19 ⋊ C13⋊C9 |
| Hall | C13×C17 ⋊ #4296 |
| Sylow | C19 ⋊ C17×C13⋊C9 |
| Sylow | C13 ⋊ C17×#4296 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | #14555740 |
| commutator, hypocenter | C13×C19 | C9×C17 |
| Frattini | C1 | G |
| Fitting, socle | C13×C17×C19 | C9 |
| prime radical | C13×C17×C19⋊C3 | C3 |
| cosocle | C13×C19⋊C3 | C3×C17 |
| LCS | G ▷ C13×C19 | |
| UCS | C1 ◁ C17 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4199 |
799 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37791, 9);