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×#4567 |
| Hall | C3×C5 ⋊ #359 |
| Sylow | C3 ⋊ C5×#359 |
112 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 40 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 2 generators on 40 points:
(1,2,3,4,5)(6,7,8)(9,11)(10,16)(12,21)(13,26)(14,30)(15,23)(17,31)(18,34)(19,33)(20,25)(22,27)(24,38)(28,40)(29,32)(35,36)(37,39);(7,8)(9,10,12,17,15,19,14,29)(11,20,21,36,23,37,30,34)(13,25,24,35,28,39,27,18)(16,26,31,38,33,40,32,22)180 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D3×#359, C2×C5×#4567, D5×#4567, … |
| maximal normal subgroup of | C5×D3×#359, C2×C5×#4567, D5×#4567, … |
| maximal quotient of | C5×#67763, C5×#67765, C5×#67775, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 461);