Finite Group DatabasebetaFinite Group Databasebeta| order | 37107 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C31 · Schur multiplier (H2) = C1 |
| direct product | C31×#11924780 |
| Fitting, socle, Hall | C7×C19×C31 ⋊ C9 |
| derived, Hall | C7×C19 ⋊ C9×C31 |
| Hall | C19×C31 ⋊ C7⋊C9 |
| Hall | C7×C31 ⋊ #4296 |
| Sylow | C19 ⋊ C31×C7⋊C9 |
| Sylow | C7 ⋊ C31×#4296 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31 | #11924780 |
| commutator, hypocenter | C7×C19 | C9×C31 |
| Frattini | C1 | G |
| Fitting, socle | C7×C19×C31 | C9 |
| prime radical | C7×C31×C19⋊C3 | C3 |
| cosocle | C7×C19⋊C3 | C3×C31 |
| LCS | G ▷ C7×C19 | |
| UCS | C1 ◁ C31 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4123 |
899 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37107, 21);