Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C5 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×C5×#947 |
| Fitting | C22×C3×C5×Q8 ⋊ C2 |
| Hall | C3×C5 ⋊ C2×#124 |
| Sylow | C3 ⋊ C2×C5×#124 |
660 conjugacy classes of subgroups; only the 254 normal subgroups are shown.
This group has 660 conjugacy classes of subgroups — too many to draw. Only its 254 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 480 |
240 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#70343, #14301466, C5×#70104, … |
| maximal normal subgroup of | C5×#70343, #14301466, C5×#70104, … |
| maximal quotient of | C2×C5×#4977, C2×C5×#4990, C2×C5×#4988, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 10394);