Finite Group DatabasebetaFinite Group Databasebeta| order | 16900 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5×C169 · Schur multiplier (H2) = C2 |
| direct product | C2×C5×D5×C169 |
| unambiguous semidirect product | C5⋊(C22×C5×C169) |
| unambiguous semidirect product | (C2×C5)⋊(C2×C5×C169) |
| Fitting | C2×C52×C169 ⋊ C2 |
| derived | C5 ⋊ C22×C5×C169 |
| Hall | C52×C169 ⋊ C22 |
| Sylow | C52 ⋊ C22×C169 |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3380 |
6760 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16900, 47);