Finite Group DatabasebetaFinite Group Databasebeta| order | 6480 |
| automorphism | ? |
| homology | Abelianization (H1) = C33×C5 · Schur multiplier (H2) = C22×C32 |
| direct product | C5×#13049240 |
| Hall | C24×C5 ⋊ C3×3−1+2 |
| Sylow | C24 ⋊ C3×C5×3−1+2 |
500 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 180 |
320 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D5×#13049240, C5×#72213207, #72269593 |
| maximal normal subgroup of | D5×#13049240, C5×#72213207, #72269593 |
Past the SmallGroups library coverage — no SmallGroups id.