Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | A4×#683 |
| unambiguous semidirect product | (C22×#683)⋊C3 |
| Hall | C22×#683 ⋊ C3 |
| Sylow | C5 ⋊ A4×C4⋊C4 |
226 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
104 conjugacy classes — view the full character table.
| maximal subgroup of | #14513005, #14513007, #14513008, … |
| maximal normal subgroup of | #14513005, #14513007, #14513008, … |
| maximal quotient of | A4×#3939, A4×#3940, SL(2,𝔽3)×#683, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 6379);