Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| isoclinism | isoclinic class of AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C52 · Schur multiplier (H2) = C4×C5 |
| direct product | C4×C52×AGL(1,𝔽5) |
| Fitting | C4×C53 ⋊ C4 |
| derived | C5 ⋊ C42×C52 |
| Sylow | C53 ⋊ C42 |
276 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
500 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×C5×AGL(1,ℤ/25) |
| maximal quotient of | C4×C5×AGL(1,ℤ/25) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 746);