Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#5090 |
| Hall | C3×C5 ⋊ #462 |
| Sylow | C3 ⋊ C5×#462 |
216 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 90 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)(6,7,8)(10,12)(13,15,17,23)(14,18,20,27)(16,25,26,22)(19,28,24,21);(9,10,11,12);(7,8)(13,14,17,20)(15,21,23,28)(16,24,26,19)(18,25,27,22)165 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#71206, C5×#71128, #14289957, … |
| maximal normal subgroup of | C5×#71206, C5×#71128, #14289957, … |
| maximal quotient of | C5×#71348, C5×#71377, C5×#71378, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4784);