Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of C24⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C25 · Schur multiplier (H2) = C22 |
| direct product | C2×C24⋊C25 |
| unambiguous semidirect product | C25⋊C25 |
| derived | C24 ⋊ C2×C25 |
| Sylow | C25 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | C24⋊C5 |
| commutator, hypocenter | C24 | C2×C25 |
| Frattini | C5 | C2×C24⋊C5 |
| Fitting, socle, prime radical | C25×C5 | C5 |
| cosocle | C24×C5 | C2×C5 |
| LCS | G ▷ C24 | |
| UCS | C1 ◁ C2×C5 | |
160 conjugacy classes of subgroups.
| transitive degree | μt(G) = 50 |
80 conjugacy classes — view the full character table.
| maximal subgroup of | #13099657, C4×C24⋊C25, C2×(C24⋊C25)⋊C2, … |
| maximal normal subgroup of | #13099657, C4×C24⋊C25, C2×(C24⋊C25)⋊C2, … |
| maximal quotient of | C4×C24⋊C25, C2×2−1+4⋊C25, #585⋊C25, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 384);