Finite Group DatabasebetaFinite Group Databasebeta| order | 3600 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C3×#11925360 |
| Hall | C32×C52 ⋊ C22⋊C4 |
| Sylow | C52 ⋊ C3×(C2×D3)⋊C4 |
| Sylow | C32 ⋊ #87831 |
378 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 62 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
126 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#72224578, C3×D3×#87831, C3×#72224581, … |
| maximal normal subgroup of | C3×#72224578, C3×D3×#87831, C3×#72224581 |
| maximal quotient of | #72254712 |
Past the SmallGroups library coverage — no SmallGroups id.