Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | C3×#64865 |
| Fitting | C3×C5×C22⋊C4 ⋊ C4 |
| Hall | C3×C5 ⋊ #352 |
| Sylow | C5 ⋊ C3×#352 |
136 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 36 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 — 2 generators on 24 points:
(1,2,3)(4,5,6,8,7)(9,11)(10,14,17,24)(12,19)(13,21)(15,18,16,23)(20,22);(5,6,7,8)(9,10,12,15,13,17,22,16)(11,18,19,14,21,23,20,24)69 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C3×#64865, C3×D5⋊#352, D3×#64865, … |
| maximal normal subgroup of | C2×C3×#64865, C3×D5⋊#352, D3×#64865, … |
| maximal quotient of | C3×#10598703, C3×#10598704, C3×#10598496, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 837);