Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of ΓL(1,𝔽16) |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C43 |
| direct product | C42×ΓL(1,𝔽16) |
| Fitting | C3×C42×C5 ⋊ C4 |
| derived, Hall | C3×C5 ⋊ C43 |
| Sylow | C5 ⋊ C42×Dic3 |
| Sylow | C3 ⋊ C42×AGL(1,𝔽5) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C42 | ΓL(1,𝔽16) |
| commutator, hypocenter | C3×C5 | C43 |
| Frattini | C22 | C22×ΓL(1,𝔽16) |
| Fitting | C3×C42×C5 | C4 |
| socle | C22×C3×C5 | C22×C4 |
| prime radical, cosocle | C22×C3×D5 | C23 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C42 | |
516 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | #14276735, #14276742, C4×C8×ΓL(1,𝔽16), … |
| maximal normal subgroup of | #14276735, #14276742, C4×C8×ΓL(1,𝔽16), … |
| maximal quotient of | #95×ΓL(1,𝔽16), C4×#91235, C4×C8×ΓL(1,𝔽16), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 6539);