Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C3×#65078 |
| Hall | C3×C5 ⋊ #441 |
| Sylow | C5 ⋊ C3×#441 |
216 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 28 |
| transitive degree | μt(G) = 960 |
A minimal faithful permutation representation — 3 generators on 28 points:
(1,2,3)(4,5,7,8,6)(13,15,17,23)(14,18,20,21)(16,25,24,22)(19,28,27,26);(9,11,12,10)(15,22)(16,24)(18,26)(19,27)(21,28)(23,25);(5,6)(7,8)(9,10,12,11)(13,14,17,20)(15,21,23,18)(16,19,24,27)(22,28,25,26)150 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D5×#441, C2×C3×#65078, #14416425, … |
| maximal normal subgroup of | C3×D5×#441, C2×C3×#65078, #14416425, … |
| maximal quotient of | C3×#10599008, C3×#10599014, C3×#10599015, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 3881);