Finite Group DatabasebetaFinite Group Databasebeta| order | 37107 |
| automorphism | ? |
| homology | Abelianization (H1) = C7×C9 · Schur multiplier (H2) = C1 |
| direct product | C7×#19127101 |
| derived, Hall | C19×C31 ⋊ C7×C9 |
| Hall | C7×C19×C31 ⋊ C9 |
| Hall | C7×C31 ⋊ #4294 |
| Hall | C7×C19 ⋊ C31⋊C9 |
| Sylow | C31 ⋊ C7×#4294 |
| Sylow | C19 ⋊ C7×C31⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C7 | #13183714 |
| commutator, hypocenter | C19×C31 | C7×C9 |
| Frattini | C3 | C7×#13183714 |
| Fitting, socle, prime radical | C3×C7×C19×C31 | C3 |
| cosocle | C3×C19×C31 | C3×C7 |
| LCS | G ▷ C19×C31 | |
| UCS | C1 ◁ C3×C7 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 37107 |
4179 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37107, 5);