Finite Group DatabasebetaFinite Group Databasebeta| order | 3600 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C42 · Schur multiplier (H2) = C4 |
| direct product | C3×#11925359 |
| derived | C3×C52 ⋊ C3×C42 |
| Hall | C32×C52 ⋊ C42 |
| Sylow | C52 ⋊ C3×C4×Dic3 |
| Sylow | C32 ⋊ #87830 |
346 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×#87830, C3×#72224584, C3×#72224581, … |
| maximal normal subgroup of | C3×D3×#87830, C3×#72224584, C3×#72224581 |
| maximal quotient of | #72254606 |
Past the SmallGroups library coverage — no SmallGroups id.