Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×#5401 |
| Fitting | C22×C5×C8 ⋊ D3 |
144 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 30 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 120 |
A minimal faithful permutation representation — 2 generators on 17 points:
(1,2,3,4,5)(6,7,9)(10,11,12,14,13,15,16,17);(7,8)(11,14)(12,16)(15,17)110 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C5×#5401, C5×#85440, C5×#85443, … |
| maximal normal subgroup of | C2×C5×#5401, C5×#85440, C5×#85443, … |
| maximal quotient of | C5×#73011, C5×#73012, C5×#73021, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 6267);