Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C5 · Schur multiplier (H2) = C25 |
| direct product | C5×#5798 |
| Hall | C3×C5 ⋊ #518 |
| Sylow | C3 ⋊ C5×#518 |
676 conjugacy classes of subgroups; only the 382 normal subgroups are shown.
This group has 676 conjugacy classes of subgroups — too many to draw. Only its 382 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 4 generators on 20 points:
(1,2,3,4,5)(6,7,8)(14,18)(17,20);(15,19)(17,20);(13,15)(14,17)(16,19)(18,20);(7,8)(9,10,11,12)(13,14)(15,17)(16,18)(19,20)270 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×#70020, #14298647, C5×#70067, … |
| maximal normal subgroup of | C5×#70020, #14298647, C5×#70067, … |
| maximal quotient of | C5×#82083, C5×#82144, C5×#82317, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 10378);