Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C5 · Schur multiplier (H2) = C26 |
| direct product | C23×C5×AGL(1,𝔽5) |
| unambiguous semidirect product | D5⋊(C22×C4×C5) |
| Fitting, socle | C23×C52 ⋊ C4 |
| derived | C5 ⋊ C23×C4×C5 |
| Sylow | C52 ⋊ C23×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C5 | AGL(1,𝔽5) |
| commutator, hypocenter | C5 | C23×C4×C5 |
| Frattini | C1 | G |
| Fitting, socle | C23×C52 | C4 |
| prime radical | C23×C5×D5 | C2 |
| cosocle | D5 | C24×C5 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C23×C5 | |
488 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
200 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 1204);