Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#91521 |
| Hall | C3×C5 ⋊ C2×#135 |
| Sylow | C5 ⋊ C2×#916 |
| Sylow | C3 ⋊ C2×#4065 |
532 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 532 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 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#91521, #14416296, #14416574, … |
| maximal normal subgroup of | C4×#91521, #14416296, #14416574, … |
| maximal quotient of | C2×#11747506, C2×#11749215, C2×#11747440, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 9312);