Finite Group DatabasebetaFinite Group Databasebeta| order | 37518 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×(C37⋊C3)⋊D13 |
| unambiguous semidirect product | (C37⋊C3)⋊(C13×D13) |
| Fitting, socle, Hall | C132×C37 ⋊ C2×C3 |
| derived | C13×C37 ⋊ C2×C3×C13 |
| Hall | C132×C37⋊C3 ⋊ C2 |
| Hall | C13×D481 ⋊ C3 |
| Sylow | C132 ⋊ D37⋊C3 |
| Hall | C37⋊C3 ⋊ C13×D13 |
| Sylow | C37 ⋊ C3×C13×D13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | (C37⋊C3)⋊D13 |
| commutator, cosocle, hypocenter | C13×C37 | C2×C3×C13 |
| Frattini | C1 | G |
| Fitting, socle | C132×C37 | C2×C3 |
| LCS | G ▷ C13×C37 | |
| UCS | C1 ◁ C13 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 962 |
1326 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37518, 50);