Finite Group DatabasebetaFinite Group Databasebeta| order | 980 |
| isoclinism | isoclinic class of AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C49 · Schur multiplier (H2) = C1 |
| direct product | AGL(1,𝔽5)×C49 |
| Fitting, Hall | C5×C49 ⋊ C4 |
| derived, Sylow | C5 ⋊ C4×C49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C49 | AGL(1,𝔽5) |
| commutator, hypocenter | C5 | C4×C49 |
| Frattini | C7 | C7×AGL(1,𝔽5) |
| Fitting | C5×C49 | C4 |
| socle | C5×C7 | C4×C7 |
| prime radical, cosocle | C7×D5 | C2×C7 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C49 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 245 |
245 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(980, 5);