Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C3×#65116 |
| Fitting | C3×C5×#104 ⋊ C2 |
| Hall | C3×C5 ⋊ #454 |
| Sylow | C5 ⋊ C3×#454 |
292 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 78 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,3)(4,5,7,8,6)(9,12,23,11,14,20,13,21)(10,16,18,24,19,15,17,22);(9,11,14,21)(10,15,19,16)(12,23,20,13)(17,24,18,22);(5,6)(7,8)(9,10)(11,15)(12,22)(13,18)(14,19)(16,21)(17,23)(20,24)132 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D5×#454, C2×C3×#65116, #14425090, … |
| maximal normal subgroup of | C3×D5×#454, C2×C3×#65116, #14425090, … |
| maximal quotient of | C3×#10599085, C3×#10599117, C3×#10599086, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 3919);