Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of #64757 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | C3×#64767 |
| Hall | C3×C5 ⋊ #332 |
| Sylow | C5 ⋊ C3×#332 |
128 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 70 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) = 960 |
A minimal faithful permutation representation — 2 generators on 24 points:
(1,2,3)(4,5,7,8,6)(10,13)(11,16)(14,15)(17,19,22,18)(20,23,21,24);(5,6)(7,8)(9,10)(11,13)(12,15)(14,16)(17,18,20,23,22,19,21,24)141 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D5×#332, C2×C3×#64767, #14284554, … |
| maximal normal subgroup of | C3×D5×#332, C2×C3×#64767, #14284554, … |
| maximal quotient of | C3×#10598129, C3×#10598125, C3×#10598290, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 319);