Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×Q8×AGL(1,𝔽5) |
| Fitting | C52×Q8 ⋊ C4 |
| Sylow | C52 ⋊ C4×Q8 |
146 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
125 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#688, #13103745, AGL(1,𝔽5)×#689, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#688, #13103745, AGL(1,𝔽5)×#689, … |
| maximal quotient of | C5×#65703, C5×#65707, C5×#65709, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 1075);