Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C16 · Schur multiplier (H2) = C2 |
| direct product | C5×D5⋊C16 |
| unambiguous semidirect product | D5⋊(C5×C16) |
| derived | C5 ⋊ C2×C5×C16 |
| Sylow | C52 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C8 | AGL(1,𝔽5) |
| commutator, hypocenter | C5 | C2×C5×C16 |
| Frattini | C4 | C2×C5×AGL(1,𝔽5) |
| Fitting | C52×C8 | C4 |
| socle | C2×C52 | C2×C8 |
| prime radical | C2×C5×D5 | C8 |
| cosocle | #168 | C22×C5 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C5×C8 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
200 conjugacy classes — view the full character table.
| maximal subgroup of | #13099711, #13099713, #13099719, … |
| maximal normal subgroup of | #13099711, #13099713, #13099719, … |
| maximal quotient of | C5×D5⋊C32, C5×#64842, C5×#64885, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 466);