Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | A4×#676 |
| unambiguous semidirect product | (C22×#676)⋊C3 |
| Fitting | C22×C5×C8 ⋊ C2×C3 |
| Hall | C22×#676 ⋊ C3 |
| Sylow | C5 ⋊ A4×M16 |
166 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
104 conjugacy classes — view the full character table.
| maximal subgroup of | #14512903, #14512904, S4×#676, … |
| maximal normal subgroup of | #14512903, #14512904, S4×#676, … |
| maximal quotient of | #10611638⋊C3, #10611636⋊C3, SL(2,𝔽3)×#676, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 6367);