Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| isoclinism | isoclinic class of #213 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C5 · Schur multiplier (H2) = C25 |
| direct product | C22×C5×#216 |
| Hall | C3×C5 ⋊ C22×Q16 |
| Sylow | C3 ⋊ C22×C5×Q16 |
516 conjugacy classes of subgroups; only the 254 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 254 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 960 |
240 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#70281, C5×#70239, C5×#71632, … |
| maximal normal subgroup of | C5×#70281, C5×#70239, C5×#71632, … |
| maximal quotient of | C22×C5×#810, C22×C5×#835, C22×C5×#807, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 10389);