Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C3×#65162 |
| Hall | C3×C5 ⋊ C4×Q16 |
| Sylow | C5 ⋊ C3×C4×Q16 |
220 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 220 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) = 28 |
| transitive degree | μt(G) = 960 |
A minimal faithful permutation representation — 3 generators on 28 points:
(1,2,3)(4,5,7,8,6)(9,11,12,10)(15,21)(16,24)(18,25)(19,28)(22,23)(26,27);(9,10,12,11)(13,15)(14,18)(16,21)(17,23)(19,25)(20,27)(22,24)(26,28);(5,6)(7,8)(9,10,12,11)(13,14,17,20)(15,18,23,27)(16,19,24,28)(21,25,22,26)168 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10598610, #14277830, C3×#10598608, … |
| maximal normal subgroup of | C3×#10598610, #14277830, C3×#10598608, … |
| maximal quotient of | C3×#10599350, C3×#10599353, C3×#10599357, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 3965);