Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C4⋊C4×ΓL(1,𝔽16) |
| Fitting | C3×C5×C4⋊C4 ⋊ C4 |
| Hall | C3×C5 ⋊ C4×C4⋊C4 |
| Sylow | C5 ⋊ Dic3×C4⋊C4 |
| Sylow | C3 ⋊ C4⋊C4×AGL(1,𝔽5) |
388 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | #102×ΓL(1,𝔽16), #14295737, #103×ΓL(1,𝔽16), … |
| maximal normal subgroup of | #102×ΓL(1,𝔽16), #14295737, #103×ΓL(1,𝔽16), … |
| maximal quotient of | #95×ΓL(1,𝔽16), #14279896, #14279931, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 6564);