Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| isoclinism | isoclinic class of AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C52×C8 · Schur multiplier (H2) = C2×C5 |
| direct product | C52×D5⋊C8 |
| unambiguous semidirect product | D5⋊(C52×C8) |
| derived | C5 ⋊ C2×C52×C8 |
| Sylow | C53 ⋊ C2×C8 |
212 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
500 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 744);