Finite Group DatabasebetaFinite Group Databasebeta| order | 27900 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C31 · Schur multiplier (H2) = C2×C3 |
| direct product | C31×((C5⋊D5)⋊C3)⋊D3 |
| unambiguous semidirect product | ((C5⋊D5)⋊C3)⋊(D3×C31) |
| Fitting, socle | C3×C52×C31 ⋊ C2×D3 |
| derived, Hall | C3×C52⋊C3 ⋊ C22×C31 |
| Hall | C3×C31×C52⋊C3 ⋊ C22 |
| Hall | C52×C31 ⋊ C2×C3⋊D3 |
| Sylow | C52 ⋊ C2×C3⋊D3×C31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31 | ((C5⋊D5)⋊C3)⋊D3 |
| commutator, cosocle, hypocenter | C3×C52⋊C3 | C22×C31 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C31 | C2×D3 |
| LCS | G ▷ C3×C52⋊C3 | |
| UCS | C1 ◁ C31 | |
160 conjugacy classes of subgroups.
744 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27900, 540);