Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | Q8×C5⋊S4 |
| Fitting | C22×C5×Q8 ⋊ D3 |
| Sylow | C5 ⋊ Q8×S4 |
312 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
65 conjugacy classes — view the full character table.
| maximal subgroup of | #14513320, #14513325, #14513328, … |
| maximal normal subgroup of | #14513320, #14513325, #14513328, … |
| maximal quotient of | #14513704, #14513705, #14513706, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 11097);