Finite Group DatabasebetaFinite Group Databasebeta| order | 26820 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9×C149 · Schur multiplier (H2) = C2 |
| direct product | C2×C9×D5×C149 |
| unambiguous semidirect product | C5⋊(C22×C9×C149) |
| unambiguous semidirect product | (C2×C5)⋊(C2×C9×C149) |
| Fitting | C2×C5×C9×C149 ⋊ C2 |
| derived, Sylow | C5 ⋊ C22×C9×C149 |
| Hall | C5×C9×C149 ⋊ C22 |
| Hall | C5×C149 ⋊ C22×C9 |
| Hall | C5×C9 ⋊ C22×C149 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13410 |
10728 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26820, 35);