Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of ΓL(1,𝔽16) |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | C24×ΓL(1,𝔽16) |
| unambiguous semidirect product | D5⋊(C23×Dic3) |
| Fitting, socle | C24×C3×C5 ⋊ C4 |
| derived, Hall | C3×C5 ⋊ C24×C4 |
| Sylow | C5 ⋊ C24×Dic3 |
| Sylow | C3 ⋊ C24×AGL(1,𝔽5) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24 | ΓL(1,𝔽16) |
| commutator, hypocenter | C3×C5 | C24×C4 |
| Frattini | C1 | G |
| Fitting, socle | C24×C3×C5 | C4 |
| prime radical | C24×C3×D5 | C2 |
| cosocle | C3×D5 | C25 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C24 | |
2724 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | #14279866, #14279880, C22×#91235, … |
| maximal normal subgroup of | #14279866, #14279880, C22×#91235, … |
| maximal quotient of | C23×C4×ΓL(1,𝔽16), C23×#6763, C23×C4⋊ΓL(1,𝔽16), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 11386);