Finite Group DatabasebetaFinite Group Databasebeta| order | 3600 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | C3×#11925351 |
| Hall | C32×C52 ⋊ C4⋊C4 |
| Sylow | C52 ⋊ C3×C4⋊Dic3 |
| Sylow | C32 ⋊ #87832 |
314 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
162 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#72224578, C3×#72224574, C3×D3×#87832, … |
| maximal normal subgroup of | C3×#72224578, C3×#72224574, C3×D3×#87832 |
| maximal quotient of | #72254705 |
Past the SmallGroups library coverage — no SmallGroups id.