Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| isoclinism | isoclinic class of C24⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C52 · Schur multiplier (H2) = C23×C5 |
| direct product | C22×C5×C24⋊C5 |
| unambiguous semidirect product | C26⋊C52 |
| unambiguous semidirect product | (C26×C5)⋊C5 |
| Fitting, socle | C26×C5 ⋊ C5 |
| derived | C24 ⋊ C22×C52 |
| Sylow | C26 ⋊ C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C5 | C24⋊C5 |
| commutator, cosocle, hypocenter | C24 | C22×C52 |
| Frattini | C1 | G |
| Fitting, socle | C26×C5 | C5 |
| LCS | G ▷ C24 | |
| UCS | C1 ◁ C22×C5 | |
1206 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, 10273);