Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of D25 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| direct product | C16×D25 |
| Fitting | C16×C25 ⋊ C2 |
| derived, Sylow | C25 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C16 | D25 |
| commutator, hypocenter | C25 | C2×C16 |
| Frattini | C5×C8 | C2×D5 |
| Fitting | C16×C25 | C2 |
| socle | C2×C5 | C8×D5 |
| prime radical | C2×D25 | C8 |
| cosocle | C8×C25 | C22 |
| LCS | G ▷ C25 | |
| UCS | C1 ◁ C16 | |
42 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
224 conjugacy classes — view the full character table.
| maximal subgroup of | C32×D25, #13097653, D25⋊C32, … |
| maximal normal subgroup of | C32×D25, #13097653, D25⋊C32, … |
| maximal quotient of | C32×D25, #13097653, C16×Dic25, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 4);