Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#5188 |
| Fitting | C2×C3×C5×Q16 ⋊ C2 |
| Hall | C3×C5 ⋊ #467 |
| Sylow | C3 ⋊ C5×#467 |
228 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 86 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)(6,7,8)(10,12)(13,15,17,23)(14,18,20,26)(16,24,25,22)(19,27,28,21);(13,14,16,19,17,20,25,28)(15,21,22,26,23,27,24,18);(7,8)(9,10)(11,12)180 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#71485, #14316174, C5×#71502, … |
| maximal normal subgroup of | C5×#71485, #14316174, C5×#71502, … |
| maximal quotient of | C5×#71305, C5×#71308, C5×#71372, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4882);