Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22×C4 |
| direct product | C3×#65029 |
| Fitting | C3×C5×#99 ⋊ C2 |
| Hall | C3×C5 ⋊ #410 |
| Sylow | C5 ⋊ C3×#410 |
316 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 102 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 — 3 generators on 24 points:
(1,2,3)(4,5,7,8,6)(9,12)(10,15)(11,17,18,19)(13,20)(14,21,22,23)(16,24);(9,11)(10,14)(12,19)(13,18)(15,23)(16,22)(17,20)(21,24);(5,6)(7,8)(9,10,13,16)(11,14,18,22)(12,15,20,24)(17,21,19,23)132 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10598569, #14279080, C3×#10598570, … |
| maximal normal subgroup of | C3×#10598569, #14279080, C3×#10598570, … |
| maximal quotient of | C3×#10598893, C3×#10598917, C3×#10598894, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 3832);