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×#3960 |
| Fitting | C2×C3×C5×Q16 ⋊ C2 |
| Hall | C3×C5 ⋊ C2×SD32 |
| Sylow | C5 ⋊ C2×C3×SD32 |
180 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 180 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) = 480 |
150 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10599999, C3×C4×#3960, #14315373, … |
| maximal normal subgroup of | C3×#10599999, C3×C4×#3960, #14315373, … |
| maximal quotient of | C2×C3×#64711, C2×C3×#64784, C2×C3×#64710, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4270);