Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C3 · Schur multiplier (H2) = C29 |
| direct product | C22×C3×Q8×D5 |
| Fitting | C22×C3×C5×Q8 ⋊ C2 |
| Hall | C3×C5 ⋊ C23×Q8 |
| Sylow | C5 ⋊ C23×C3×Q8 |
1700 conjugacy classes of subgroups; only the 1006 normal subgroups are shown.
This group has 1700 conjugacy classes of subgroups — too many to draw. Only its 1006 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 | C3×#10604988, #14280297, C3×#10600906, … |
| maximal normal subgroup of | C3×#10604988, #14280297, C3×#10600906, … |
| maximal quotient of | C22×C3×D5×C4⋊C4, C2×C3×C4×Q8×D5, C22×C3×#4033, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 11295);