Finite Group DatabasebetaFinite Group Databasebeta| order | 27900 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C25 · Schur multiplier (H2) = C2 |
| direct product | D3×C3⋊(D31⋊C25) |
| unambiguous semidirect product | (C3×D3)⋊(D31⋊C25) |
| unambiguous semidirect product | (D3×D93)⋊C25 |
| unambiguous semidirect product | (D3×C31⋊C25)⋊D3 |
| derived, Hall | C32×C31 ⋊ C22×C25 |
| Hall | C32×C31⋊C25 ⋊ C22 |
| Hall | D3×D93 ⋊ C25 |
| Hall | C31⋊C25 ⋊ D32 |
| Sylow | C31 ⋊ D32×C25 |
| Sylow | C32 ⋊ C2×D31⋊C25 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C5 | D3×C3⋊(D31⋊C5) |
| commutator, hypocenter | C32×C31 | C22×C25 |
| Fitting, socle, cosocle | C32×C5×C31 | C22×C5 |
| prime radical | C5×D3×D93 | C5 |
| LCS | G ▷ C32×C31 | |
| UCS | C1 ◁ C5 | |
132 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
360 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27900, 134);