Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C3×#65391 |
| Hall | C3×C5 ⋊ #424 |
| Sylow | C5 ⋊ C3×#424 |
228 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 126 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) = 480 |
A minimal faithful permutation representation — 3 generators on 28 points:
(1,2,3)(4,5,7,8,6)(10,12)(13,15,16,21,17,22,23,27)(14,19,20,26,18,24,25,28);(14,18)(19,24)(20,25)(26,28);(5,6)(7,8)(9,10,11,12)(13,14)(15,19)(16,20)(17,18)(21,26)(22,24)(23,25)(27,28)276 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#10598016, #14277661, C3×#10598763, … |
| maximal normal subgroup of | C3×#10598016, #14277661, C3×#10598763, … |
| maximal quotient of | C3×#10601214, C3×#10601215, C3×#10601540, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4194);