Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of #6057 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C5 |
| direct product | C22×#6057 |
| Fitting, socle | C22×C52 ⋊ Q8 |
| Sylow | C52 ⋊ C22×Q8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #6057 |
| commutator, cosocle | C5⋊D5 | C24 |
| Frattini | C1 | G |
| Fitting, socle | C22×C52 | Q8 |
| prime radical | C22×C5⋊D5 | C22 |
| hypocenter | C52 | C22×Q8 |
| LCS | G ▷ C5⋊D5 ▷ C52 | |
| UCS | C1 ◁ C22 | |
237 conjugacy classes of subgroups.
| transitive degree | μt(G) = 40 |
32 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 1202);