Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of D48 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C22 |
| direct product | C2×C5×#800 |
| Fitting | C2×C3×C5×C16 ⋊ C2 |
| Hall | C3×C5 ⋊ C2×SD32 |
| Sylow | C3 ⋊ C2×C5×SD32 |
180 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 78 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 480 |
270 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×#69337, C4×C5×#800, Dic5×#800, … |
| maximal normal subgroup of | C5×#69337, C4×C5×#800, Dic5×#800, … |
| maximal quotient of | C2×C5×#4509, C2×C5×#4503, C2×C5×#4505, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4597);