Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of #826 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×#4492 |
| Hall | C3×C5 ⋊ #358 |
| Sylow | C3 ⋊ C5×#358 |
116 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 116 conjugacy classes of subgroups — too many to draw. Only its 58 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 — 2 generators on 28 points:
(1,2,3,4,5)(6,7,8)(9,10,11,12)(14,18)(15,22)(16,23)(19,20)(21,27)(24,28)(25,26);(7,8)(13,14,17,21)(15,18,24,27)(16,25,23,20)(19,28,26,22)180 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D3×#358, C2×C5×#4492, D5×#4492, … |
| maximal normal subgroup of | C5×D3×#358, C2×C5×#4492, D5×#4492, … |
| maximal quotient of | C5×#67472, C5×#67486, C5×#67474, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 386);