Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C5 · Schur multiplier (H2) = C25 |
| direct product | C5×#5834 |
| Fitting | C2×C3×C5×#41 ⋊ C2 |
| Hall | C3×C5 ⋊ #550 |
| Sylow | C3 ⋊ C5×#550 |
624 conjugacy classes of subgroups; only the 226 normal subgroups are shown.
This group has 624 conjugacy classes of subgroups — too many to draw. Only its 226 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 — 4 generators on 20 points:
(1,2,3,4,5)(6,7,8)(10,12)(13,15,16,19)(14,18,17,20);(10,12)(14,17)(18,20);(10,12)(13,14)(15,18)(16,17)(19,20);(7,8)(9,10)(11,12)(15,19)(18,20)225 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#80123, C5×#83955, C5×#83922, … |
| maximal normal subgroup of | C5×#80123, C5×#83955, C5×#83922, … |
| maximal quotient of | C5×#82457, C5×#84089, C5×Q8×Dic3⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 10414);