Finite Group DatabasebetaFinite Group Databasebeta| order | 36900 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C25 · Schur multiplier (H2) = C2 |
| derived | C3×C41 ⋊ C22×C3×C25 |
| Hall | C32×C41⋊C25 ⋊ C22 |
| Hall | C2×C3×D123 ⋊ C25 |
| Hall | C41⋊C25 ⋊ C2×C3×D3 |
| Hall | C32×C41 ⋊ C22×C25 |
| Sylow | C41 ⋊ C2×C3×D3×C25 |
| Sylow | C32 ⋊ C2×D41⋊C25 |
132 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 12300 |
810 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36900, 107);