Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| isoclinism | isoclinic class of C24⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C25 · Schur multiplier (H2) = C22 |
| direct product | C4×C24⋊C25 |
| unambiguous semidirect product | (C24×C4)⋊C25 |
| derived | C24 ⋊ C4×C25 |
| Sylow | C24×C4 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C5 | C24⋊C5 |
| commutator, hypocenter | C24 | C4×C25 |
| Frattini | C2×C5 | C2×C24⋊C5 |
| Fitting | C24×C4×C5 | C5 |
| socle, prime radical, cosocle | C25×C5 | C2×C5 |
| LCS | G ▷ C24 | |
| UCS | C1 ◁ C4×C5 | |
288 conjugacy classes of subgroups.
| transitive degree | μt(G) = 100 |
160 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 2010);