Finite Group DatabasebetaFinite Group Databasebeta| order | 27900 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C31 · Schur multiplier (H2) = C2 |
| direct product | D3×C31×D75 |
| unambiguous semidirect product | (C3×D3)⋊(C31×D25) |
| unambiguous semidirect product | (D3×C25)⋊(D3×C31) |
| Fitting, Hall | C32×C25×C31 ⋊ C22 |
| derived, Hall | C32×C25 ⋊ C22×C31 |
| Hall | C25×C31 ⋊ D32 |
| Hall | C32×C31 ⋊ C2×D25 |
| Sylow | C25 ⋊ D32×C31 |
| Sylow | C32 ⋊ C2×C31×D25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31 | D3×D75 |
| commutator, cosocle, hypocenter | C32×C25 | C22×C31 |
| Frattini | C5 | D3×D15×C31 |
| Fitting | C32×C25×C31 | C22 |
| socle | C32×C5×C31 | C2×D5 |
| LCS | G ▷ C32×C25 | |
| UCS | C1 ◁ C31 | |
132 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
3627 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27900, 189);