Finite Group DatabasebetaFinite Group Databasebeta| order | 3600 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C23×C3 |
| direct product | C5×C3⋊D3×C22⋊D5 |
| Fitting | C22×C32×C52 ⋊ C22 |
| Hall | C32×C52 ⋊ C2×D4 |
| Sylow | C52 ⋊ D4×C3⋊D3 |
| Sylow | C32 ⋊ C2×C5×C22⋊D5 |
840 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 840 conjugacy classes of subgroups — too many to draw. Only its 144 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 180 |
390 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3⋊D3×#87886, C2×C5×C3⋊D3×C22⋊D5 |
| maximal normal subgroup of | C3⋊D3×#87886, C2×C5×C3⋊D3×C22⋊D5 |
| maximal quotient of | C2×C5×C3⋊D3×C22⋊D5 |
Past the SmallGroups library coverage — no SmallGroups id.