Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of #64671 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | C3×#64702 |
| Hall | C3×C5 ⋊ #332 |
| Sylow | C5 ⋊ C3×#332 |
128 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 66 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)(17,18,19,21,20,22,23,24);(5,6)(7,8)(9,10,11,14,12,15,16,13)(18,21)(19,23)(22,24)177 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D5×#332, C2×C3×#64702, #14284563, … |
| maximal normal subgroup of | C3×D5×#332, C2×C3×#64702, #14284563, … |
| maximal quotient of | C3×#10597969, C3×#10598193, C3×#10597959, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 254);