Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C3×#64928 |
| Fitting | C2×C3×C5×Q8 ⋊ C4 |
| Hall | C3×C5 ⋊ #354 |
| Sylow | C5 ⋊ C3×#354 |
140 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 140 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)(9,11,13,18)(10,14,16,23)(12,21,22,19)(15,24,20,17);(5,6,7,8)(9,10)(11,17,18,24)(12,20,22,15)(13,16)(14,19)(21,23)69 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10598835, C3×#10598575, #14279359, … |
| maximal normal subgroup of | C3×#10598835, C3×#10598575, #14279359, … |
| maximal quotient of | C3×#10598827, C3×#10598710, C3×#10598716, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 900);