Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| isoclinism | isoclinic class of #1035 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C26 |
| direct product | C23×#6016 |
| derived, Sylow | C25 ⋊ C23×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24 | #1035 |
| commutator, hypocenter | C25 | C23×C8 |
| Frattini | C2×C5 | C23×AGL(1,𝔽5) |
| Fitting | C24×C25 | C4 |
| socle, prime radical | C24×C5 | AGL(1,𝔽5) |
| cosocle | Dic25 | C24 |
| LCS | G ▷ C25 | |
| UCS | C1 ◁ C24 | |
507 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, 2031);