Finite Group DatabasebetaFinite Group Databasebeta| order | 37107 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C31 · Schur multiplier (H2) = C3 |
| direct product | C3×C31×#87705 |
| Fitting, socle | C3×C7×C19×C31 ⋊ C3 |
| derived, Hall | C7×C19 ⋊ C32×C31 |
| Hall | C7×C19×C31 ⋊ C32 |
| Hall | C19×C31 ⋊ C3×ΓL(1,𝔽8) |
| Hall | C7×C31 ⋊ C3×C19⋊C3 |
| Sylow | C19 ⋊ C3×ΓL(1,𝔽8)×C31 |
| Sylow | C7 ⋊ C3×C31×C19⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C31 | #87705 |
| commutator, cosocle, hypocenter | C7×C19 | C32×C31 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C19×C31 | C3 |
| LCS | G ▷ C7×C19 | |
| UCS | C1 ◁ C3×C31 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12369 |
4371 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37107, 48);