Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of Dic10 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C8 · Schur multiplier (H2) = C23 |
| direct product | C3×#64744 |
| Hall | C3×C5 ⋊ #336 |
| Sylow | C5 ⋊ C3×#336 |
236 conjugacy classes of subgroups; only the 150 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 150 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 960 |
A minimal faithful permutation representation — 2 generators on 24 points:
(1,2,3)(4,5,7,8,6)(9,10,11,12)(14,16);(5,6)(7,8)(13,14)(15,16)(17,18,19,21,20,22,23,24)312 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#10597970, C3×#10598130, #14276647, … |
| maximal normal subgroup of | C3×#10597970, C3×#10598130, #14276647, … |
| maximal quotient of | C3×#10598144, C3×#10598105, C3×#10598151, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 296);