Finite Group DatabasebetaFinite Group Databasebeta| order | 37548 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C149 · Schur multiplier (H2) = C1 |
| direct product | C3×Dic21×C149 |
| unambiguous semidirect product | C3⋊(C3×Dic7×C149) |
| derived | C3×C7 ⋊ C3×C4×C149 |
| Hall | C32×C7×C149 ⋊ C4 |
| Hall | C32×C149 ⋊ Dic7 |
| Hall | C7×C149 ⋊ C3×Dic3 |
| Hall | C32×C7 ⋊ C4×C149 |
| Sylow | C32 ⋊ Dic7×C149 |
| Sylow | C7 ⋊ C3×Dic3×C149 |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12516 |
10728 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37548, 55);