Finite Group DatabasebetaFinite Group Databasebeta| order | 10800 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C22×#72222340 |
| Fitting | C22×C52×3−1+2 ⋊ C4 |
| derived | C52×C9 ⋊ C22×C3×C4 |
| Hall | C52×3−1+2 ⋊ C22×C4 |
| Sylow | 3−1+2 ⋊ C22×#1043 |
| Sylow | C52 ⋊ C22×3−1+2⋊C4 |
1424 conjugacy classes of subgroups; only the 277 normal subgroups are shown.
This group has 1424 conjugacy classes of subgroups — too many to draw. Only its 277 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 900 |
344 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22×AGL(1,ℤ/9)×#1043, #72254787, #72254816 |
| maximal normal subgroup of | C22×AGL(1,ℤ/9)×#1043, #72254787, #72254816 |
Past the SmallGroups library coverage — no SmallGroups id.