Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | Q8×D5×A4 |
| Fitting | C22×C5×Q8 ⋊ C2×C3 |
| Hall | C22×Q8×D5 ⋊ C3 |
| Sylow | C5 ⋊ C2×Q8×A4 |
410 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 75 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
80 conjugacy classes — view the full character table.
| maximal subgroup of | #14512492, A4×#4009, D5×#5416, … |
| maximal normal subgroup of | #14512492, A4×#4009, D5×#5416, … |
| maximal quotient of | A4×#4033, A4×#4042, A4×#4034, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 11132);