Finite Group DatabasebetaFinite Group Databasebeta| order | 3600 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22×C5 |
| direct product | C3×(C2×D3)⋊#1044 |
| Hall | C32×C52 ⋊ C22⋊C4 |
| Sylow | C52 ⋊ C3×(C2×D3)⋊C4 |
| Sylow | C32 ⋊ C22⋊#1044 |
442 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 64 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×#72224586, C3×#72224578, C3×#72224584, … |
| maximal normal subgroup of | C3×#72224586, C3×#72224578, C3×#72224584, … |
| maximal quotient of | #72254709 |
Past the SmallGroups library coverage — no SmallGroups id.