Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5×C8 · Schur multiplier (H2) = C23 |
| direct product | C22×C5×#168 |
| derived | C5 ⋊ C22×C5×C8 |
| Sylow | C52 ⋊ C22×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C4×C5 | D5 |
| commutator, hypocenter | C5 | C22×C5×C8 |
| Frattini | C4 | C22×C5×D5 |
| Fitting | C22×C4×C52 | C2 |
| socle, prime radical | C23×C52 | C4 |
| cosocle | C4×C5 | C23×C5 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C22×C4×C5 | |
206 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
320 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #13099325, #13099326, #13099334, … |
| maximal normal subgroup of | #13099325, #13099326, #13099334, … |
| maximal quotient of | C2×C4×C5×#168, C2×C5×C4⋊#168, C5×#65214, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 813);