Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C3×#64940 |
| Hall | C3×C5 ⋊ #383 |
| Sylow | C5 ⋊ C3×#383 |
276 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 276 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) = 960 |
A minimal faithful permutation representation — 3 generators on 28 points:
(1,2,3)(4,5,7,8,6)(9,10,11,12)(14,18)(17,20)(23,27)(25,28);(13,15,16,19)(14,17,18,20)(21,23,24,27)(22,25,26,28);(5,6)(7,8)(13,14)(15,17)(16,18)(19,20)(21,22,24,26)(23,25,27,28)204 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10598505, #14277018, C3×#10599074, … |
| maximal normal subgroup of | C3×#10598505, #14277018, C3×#10599074, … |
| maximal quotient of | C3×#10600195, C3×#10600194, C3×#10600196, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 3743);