Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#91280 |
| Hall | C3×C5 ⋊ C2×#137 |
| Sylow | C5 ⋊ C2×#918 |
| Sylow | C3 ⋊ C2×#4061 |
516 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 136 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 480 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#91280, #14416931, #14416946, … |
| maximal normal subgroup of | C4×#91280, #14416931, #14416946, … |
| maximal quotient of | C2×#11747644, C2×#11748146, C2×#11747640, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 8205);