Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | D5×#821 |
| Fitting | C2×C3×C5×C8 ⋊ C22 |
| Hall | C3×C5 ⋊ C2×#102 |
| Sylow | C5 ⋊ C2×#821 |
| Sylow | C3 ⋊ D5×#102 |
404 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | #14295733, AGL(1,𝔽5)×#821, #14295839, … |
| maximal normal subgroup of | #14295733, AGL(1,𝔽5)×#821, #14295839, … |
| maximal quotient of | D5×#4459, #14281796, #14282094, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 2299);