Finite Group DatabasebetaFinite Group Databasebeta| order | 26700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C25 · Schur multiplier (H2) = C2 |
| direct product | C2×C25×D267 |
| unambiguous semidirect product | (C2×C3)⋊(C25×D89) |
| unambiguous semidirect product | (C2×C89)⋊(D3×C25) |
| Fitting | C2×C3×C25×C89 ⋊ C2 |
| derived, Hall | C3×C89 ⋊ C22×C25 |
| Hall | C3×C25×C89 ⋊ C22 |
| Hall | C25×C89 ⋊ C2×D3 |
| Sylow | C89 ⋊ C2×D3×C25 |
| Hall | C3×C25 ⋊ C2×D89 |
| Sylow | C3 ⋊ C2×C25×D89 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13350 |
6750 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26700, 32);