Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | Q8×#1220 |
| Fitting | C22×C3×C5×Q8 ⋊ C2 |
| Hall | C3×C5 ⋊ D4×Q8 |
| Sylow | C5 ⋊ Q8×#67 |
| Sylow | C3 ⋊ Q8×C22⋊D5 |
560 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 187 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 480 |
165 conjugacy classes — view the full character table.
| maximal subgroup of | #14453684, #14453687, #14453705, … |
| maximal normal subgroup of | #14453684, #14453687, #14453705, … |
| maximal quotient of | Q8×#6714, Q8×#6719, C4⋊C4×#1220, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 10769);