Finite Group DatabasebetaFinite Group Databasebeta| order | 37791 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C17 · Schur multiplier (H2) = C3 |
| Fitting, socle, Hall | C13×C17×C19 ⋊ C32 |
| derived, Hall | C13×C19 ⋊ C32×C17 |
| Hall | C17×C19 ⋊ C3×C13⋊C3 |
| Hall | C13×C17 ⋊ C3×C19⋊C3 |
| Sylow | C19 ⋊ C3×C17×C13⋊C3 |
| Sylow | C13 ⋊ C3×C17×C19⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | C13⋊C3×C19⋊C3 |
| commutator, cosocle, hypocenter | C13×C19 | C32×C17 |
| Frattini | C1 | G |
| Fitting, socle | C13×C17×C19 | C32 |
| LCS | G ▷ C13×C19 | |
| UCS | C1 ◁ C17 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4199 |
1071 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37791, 10);