Finite Group DatabasebetaFinite Group Databasebeta| order | 26820 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C149 · Schur multiplier (H2) = C1 |
| direct product | C3×Dic15×C149 |
| unambiguous semidirect product | C3⋊(C3×Dic5×C149) |
| derived | C3×C5 ⋊ C3×C4×C149 |
| Hall | C32×C5×C149 ⋊ C4 |
| Hall | C32×C149 ⋊ Dic5 |
| Hall | C5×C149 ⋊ C3×Dic3 |
| Hall | C32×C5 ⋊ C4×C149 |
| Sylow | C32 ⋊ Dic5×C149 |
| Sylow | C5 ⋊ C3×Dic3×C149 |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8940 |
8046 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26820, 43);