Finite Group DatabasebetaFinite Group Databasebeta| order | 2160 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C3×#10624236 |
| Fitting | C22×C33×C5 ⋊ C22 |
| Hall | C33×C5 ⋊ C2×D4 |
| Sylow | C33 ⋊ C2×C22⋊D5 |
| Sylow | C5 ⋊ C3×#3811 |
580 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 580 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
216 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D5×#3811 |
| maximal normal subgroup of | C3×D5×#3811 |
Past the SmallGroups library coverage — no SmallGroups id.