Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of D48 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×#4503 |
| 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)(9,11,12,10)(13,14,19,28,17,21,15,18,16,20,22,27,23,25,24,26);(7,8)(9,10,12,11)(14,18)(15,22)(17,23)(19,24)(20,26)(21,28)(25,27)270 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D3×#358, C2×C5×#4503, D5×#4503, … |
| maximal normal subgroup of | C5×D3×#358, C2×C5×#4503, D5×#4503, … |
| maximal quotient of | C5×#67505, C5×#67528, C5×#67561, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 397);