Finite Group DatabasebetaFinite Group Databasebeta| order | 37518 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C13 · Schur multiplier (H2) = C1 |
| direct product | C2×C13×#13089649 |
| Fitting, socle, Hall | C2×C132×C37 ⋊ C3 |
| derived | C13×C37 ⋊ C2×C3×C13 |
| Hall | C132×C37 ⋊ C2×C3 |
| Hall | C2×C132 ⋊ C37⋊C3 |
| Sylow | C132 ⋊ C2×C37⋊C3 |
| Hall | C2×C37 ⋊ C13×C13⋊C3 |
| Sylow | C37 ⋊ C2×C13×C13⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C13 | #13089649 |
| commutator, cosocle, hypocenter | C13×C37 | C2×C3×C13 |
| Frattini | C1 | G |
| Fitting, socle | C2×C132×C37 | C3 |
| LCS | G ▷ C13×C37 | |
| UCS | C1 ◁ C2×C13 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2886 |
4238 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37518, 84);