Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#4848 |
| Fitting | C3×C5×C4⋊C8 ⋊ C2 |
| Hall | C3×C5 ⋊ #460 |
| Sylow | C3 ⋊ C5×#460 |
256 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 3 generators on 20 points:
(1,2,3,4,5)(6,7,8)(10,12)(13,15,16,14,17,18,20,19);(9,10,11,12);(7,8)(13,14,17,19)(15,20,18,16)195 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#68402, C5×#68258, #14288877, … |
| maximal normal subgroup of | C5×#68402, C5×#68258, #14288877, … |
| maximal quotient of | C5×#68546, C5×#68586, C5×#68587, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4542);