Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C2×C4 |
| direct product | C5×#5074 |
| Fitting | C3×C5×#127 ⋊ C2 |
| Hall | C3×C5 ⋊ #496 |
| Sylow | C3 ⋊ C5×#496 |
288 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 86 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)(14,18)(15,20)(17,19);(9,10,11,12)(14,17)(18,19);(7,8)(10,12)(13,14)(15,18)(16,17)(19,20)150 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#71326, #14290888, C5×#71327, … |
| maximal normal subgroup of | C5×#71326, #14290888, C5×#71327, … |
| maximal quotient of | C5×#71257, C5×#71259, C5×#71260, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4768);