Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of ΓL(1,𝔽16) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4 |
| direct product | C22×C4×ΓL(1,𝔽16) |
| Fitting | C22×C3×C4×C5 ⋊ C4 |
| derived, Hall | C3×C5 ⋊ C22×C42 |
| Sylow | C5 ⋊ C22×C4×Dic3 |
| Sylow | C3 ⋊ C22×C4×AGL(1,𝔽5) |
996 conjugacy classes of subgroups; only the 421 normal subgroups are shown.
This group has 996 conjugacy classes of subgroups — too many to draw. Only its 421 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | #95×ΓL(1,𝔽16), C4×#91235, ΓL(1,𝔽16)⋊#95, … |
| maximal normal subgroup of | #95×ΓL(1,𝔽16), C4×#91235, ΓL(1,𝔽16)⋊#95, … |
| maximal quotient of | C2×C42×ΓL(1,𝔽16), C22×#91235, C2×#11752345, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 11176);