Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | D5×#828 |
| Fitting | C3×C5×Q16 ⋊ C22 |
| Hall | C3×C5 ⋊ C2×SD32 |
| Sylow | C5 ⋊ C2×#828 |
| Sylow | C3 ⋊ D5×SD32 |
180 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
72 conjugacy classes — view the full character table.
| maximal subgroup of | #14315408, AGL(1,𝔽5)×#828, #14315526, … |
| maximal normal subgroup of | #14315408, AGL(1,𝔽5)×#828, #14315526, … |
| maximal quotient of | D5×#4491, D5×#4564, D5×#4490, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 2483);