Finite Group DatabasebetaFinite Group Databasebeta| order | 37518 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C13 |
| direct product | C2×C37⋊#92789 |
| unambiguous semidirect product | (C2×C37)⋊#92789 |
| Fitting, socle, Hall | C2×C132×C37 ⋊ C3 |
| derived, Hall | C132×C37 ⋊ C2×C3 |
| Hall | C2×C132 ⋊ C37⋊C3 |
| Sylow | C132 ⋊ C2×C37⋊C3 |
| Hall | C2×C37 ⋊ #92789 |
| Sylow | C37 ⋊ C2×#92789 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C37⋊#92789 |
| commutator, cosocle, hypocenter | C132×C37 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C132×C37 | C3 |
| LCS | G ▷ C132×C37 | |
| UCS | C1 ◁ C2 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2886 |
4174 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37518, 89);