Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of #6652 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C22×#6661 |
| Hall | C3×C5 ⋊ C22×Q16 |
| Sylow | C5 ⋊ C22×#216 |
| Sylow | C3 ⋊ C22×#689 |
516 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 192 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 960 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | #14300955, #14300957, #14300961, … |
| maximal normal subgroup of | #14300955, #14300957, #14300961, … |
| maximal quotient of | C22×#90970, C22×#90972, C22×#90989, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 8354);