Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | Dic5×#213 |
| Hall | C3×C5 ⋊ C4×D8 |
| Sylow | C5 ⋊ C4×#213 |
| Sylow | C3 ⋊ D8×Dic5 |
268 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 88 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 | #14286109, #170×#213, #14286476, … |
| maximal normal subgroup of | #14286109, #170×#213, #14286476, … |
| maximal quotient of | #168×#213, #14286529, #14286542, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 3168);