Finite Group DatabasebetaFinite Group Databasebeta| order | 2160 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C5 · Schur multiplier (H2) = C24 |
| direct product | C5×#88907 |
| Hall | C24×C5 ⋊ 3−1+2 |
| Sylow | C24 ⋊ C5×3−1+2 |
352 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 180 |
280 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×#13049240, D5×#88907, C5×#11724050, … |
| maximal normal subgroup of | C5×#13049240, D5×#88907, C5×#11724050, … |
Past the SmallGroups library coverage — no SmallGroups id.