Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×#65166 |
| Hall | C3×C5 ⋊ #479 |
| Sylow | C5 ⋊ C3×#479 |
180 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 78 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 960 |
A minimal faithful permutation representation — 3 generators on 32 points:
(1,2,3)(4,5,7,8,6)(9,12,13,11)(10,14,15,16)(19,25)(20,28)(22,29)(23,32)(26,27)(30,31);(9,11,13,12)(10,14,15,16)(17,19)(18,22)(20,25)(21,27)(23,29)(24,31)(26,28)(30,32);(5,6)(7,8)(9,10,13,15)(11,14,12,16)(17,18,21,24)(19,22,27,31)(20,23,28,32)(25,29,26,30)141 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D5×#479, C2×C3×#65166, #14430199, … |
| maximal normal subgroup of | C3×D5×#479, C2×C3×#65166, #14430199, … |
| maximal quotient of | C3×#10599698, C3×#10601435, C3×#10599700, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 3969);