Finite Group DatabasebetaFinite Group Databasebeta| order | 3600 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×C3×#10597126 |
| derived | C3×C52 ⋊ C22×C3×C4 |
| Hall | C32×C52 ⋊ C22×C4 |
| Sylow | C52 ⋊ C22×C3×Dic3 |
| Sylow | C32 ⋊ C2×#6036 |
688 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 158 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
360 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C3×#11925664, C2×#72224600, C2×C3×#11925356, … |
| maximal normal subgroup of | C2×C3×#11925664, C2×#72224600, C2×C3×#11925356, … |
| maximal quotient of | C3×#72229453 |
Past the SmallGroups library coverage — no SmallGroups id.