Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of AGL(1,𝔽5)×C22⋊A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C24 |
| direct product | AGL(1,𝔽5)×C22⋊A4 |
| Fitting, socle, derived | C24×C5 ⋊ C3×C4 |
| Hall | C24×AGL(1,𝔽5) ⋊ C3 |
| Sylow | C5 ⋊ C4×C22⋊A4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C24×C5 | C3×C4 |
| prime radical | D5×C22⋊A4 | C2 |
| cosocle | C24×D5 | C2×C3 |
| LCS | G ▷ C24×C5 | |
| UCS | C1 | |
524 conjugacy classes of subgroups.
| transitive degree | μt(G) = 60 |
40 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 11371);