Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| isoclinism | isoclinic class of #1035 |
| automorphism | ? |
| homology | Abelianization (H1) = C82 · Schur multiplier (H2) = C8 |
| direct product | C8×#6016 |
| derived, Sylow | C25 ⋊ C82 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | #1035 |
| commutator, hypocenter | C25 | C82 |
| Frattini | C2×C4×C5 | C2×AGL(1,𝔽5) |
| Fitting | C2×C8×C25 | C4 |
| socle, prime radical | C22×C5 | C4×AGL(1,𝔽5) |
| cosocle | C4×Dic25 | C22 |
| LCS | G ▷ C25 | |
| UCS | C1 ◁ C2×C8 | |
111 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1600 |
160 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 223);