Finite Group DatabasebetaFinite Group Databasebeta| order | 5400 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×#67082⋊C3 |
| Hall | C52×3−1+2 ⋊ D4 |
| Sylow | 3−1+2 ⋊ C5×C22⋊D5 |
| Sylow | C52 ⋊ #611⋊C3 |
276 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 180 |
355 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #72254700, C5×C22⋊D5×AGL(1,ℤ/9), #72254771 |
| maximal normal subgroup of | #72254700, C5×C22⋊D5×AGL(1,ℤ/9), #72254771 |
Past the SmallGroups library coverage — no SmallGroups id.