Finite Group DatabasebetaFinite Group Databasebeta| order | 820 |
| isoclinism | isoclinic class of AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C41 · Schur multiplier (H2) = C1 |
| direct product | AGL(1,𝔽5)×C41 |
| Fitting, socle, Hall | C5×C41 ⋊ C4 |
| derived, Sylow | C5 ⋊ C4×C41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C41 | AGL(1,𝔽5) |
| commutator, hypocenter | C5 | C4×C41 |
| Frattini | C1 | G |
| Fitting, socle | C5×C41 | C4 |
| prime radical | D5×C41 | C2 |
| cosocle | D5 | C2×C41 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C41 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 205 |
205 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(820, 11);