Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of #3958 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | C2×C3×#3961 |
| Hall | C3×C5 ⋊ C2×Q32 |
| Sylow | C5 ⋊ C2×C3×Q32 |
164 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 78 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 960 |
150 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10600000, C3×C4×#3961, #14315438, … |
| maximal normal subgroup of | C3×#10600000, C3×C4×#3961, #14315438, … |
| maximal quotient of | C2×C3×#64712, C2×C3×#64784, C2×C3×#64709, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4272);