Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3×C4 · Schur multiplier (H2) = C210 |
| direct product | C24×C3×AGL(1,𝔽5) |
| unambiguous semidirect product | D5⋊(C23×C3×C4) |
| Fitting, socle | C24×C3×C5 ⋊ C4 |
| derived, Sylow | C5 ⋊ C24×C3×C4 |
| Hall | C3×C5 ⋊ C24×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24×C3 | AGL(1,𝔽5) |
| commutator, hypocenter | C5 | C24×C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C24×C3×C5 | C4 |
| prime radical | C24×C3×D5 | C2 |
| cosocle | D5 | C25×C3 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C24×C3 | |
2724 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
240 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 11385);