Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of #700 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C23×C4 |
| direct product | C3×C4×C22⋊AGL(1,𝔽5) |
| Fitting | C22×C3×C4×C5 ⋊ C4 |
| Hall | C3×C5 ⋊ C4×C22⋊C4 |
| Sylow | C5 ⋊ C3×C4×C22⋊C4 |
516 conjugacy classes of subgroups; only the 172 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 172 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
168 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10598559, C3×#10598766, #14276868, … |
| maximal normal subgroup of | C3×#10598559, C3×#10598766, #14276868, … |
| maximal quotient of | C3×C4×(C2×AGL(1,𝔽5))⋊C4, C3×#10604909, C3×#10604197, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 6491);