Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | Dic5×#216 |
| Hall | C3×C5 ⋊ C4×Q16 |
| Sylow | C5 ⋊ C4×#216 |
| Sylow | C3 ⋊ Q16×Dic5 |
220 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 960 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | #14286263, #170×#216, #14286417, … |
| maximal normal subgroup of | #14286263, #170×#216, #14286417, … |
| maximal quotient of | #168×#216, #14286814, #14286827, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 3438);