Finite Group DatabasebetaFinite Group Databasebeta| order | 27900 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C25 · Schur multiplier (H2) = C2 |
| derived | C3×C31 ⋊ C22×C3×C25 |
| Hall | C3×(C31⋊C3)⋊C25 ⋊ C22 |
| Hall | C2×D3×C31⋊C3 ⋊ C25 |
| Hall | C31⋊C25 ⋊ C2×C3×D3 |
| Hall | C3×C31⋊C3 ⋊ C22×C25 |
| Sylow | C31 ⋊ C2×C3×D3×C25 |
132 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
510 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27900, 131);