Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×#4476 |
| Hall | C3×C5 ⋊ #352 |
| Sylow | C3 ⋊ C5×#352 |
136 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 42 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)(6,7,8)(9,11,12,18,13,20,21,19)(10,14,15,22,16,23,24,17);(7,8)(9,10,13,16)(11,17,20,22)(12,15,21,24)(14,18,23,19)120 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D3×#352, C2×C5×#4476, D5×#4476, … |
| maximal normal subgroup of | C5×D3×#352, C2×C5×#4476, D5×#4476, … |
| maximal quotient of | C5×#67445, C5×#67446, C5×#67450, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 370);