Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4×C5 · Schur multiplier (H2) = C23 |
| direct product | C5×A4×C22⋊C4 |
| unambiguous semidirect product | (C22×C22⋊C4)⋊(C3×C5) |
| unambiguous semidirect product | (C22×C5×C22⋊C4)⋊C3 |
| Fitting, Hall | C22×C5×C22⋊C4 ⋊ C3 |
| Sylow | C22×C22⋊C4 ⋊ C3×C5 |
338 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
200 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#73049, C5×A4×#99, C5×#85292, … |
| maximal normal subgroup of | C5×#73049, C5×A4×#99, C5×#85292, … |
| maximal quotient of | C5×A4×#95, C5×C22⋊C4×SL(2,𝔽3), C5×#2341⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 9641);