Finite Group DatabasebetaFinite Group Databasebeta| order | 27900 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C31 · Schur multiplier (H2) = C2 |
| direct product | C31×(C3⋊D3)⋊D25 |
| unambiguous semidirect product | (C3⋊D3)⋊(C31×D25) |
| unambiguous semidirect product | D75⋊(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 | (C3⋊D3)⋊D25 |
| commutator, cosocle, hypocenter | C32×C25 | C22×C31 |
| Frattini | C5 | C31×(C3⋊D3)⋊D5 |
| Fitting | C32×C25×C31 | C22 |
| socle | C32×C5×C31 | C2×D5 |
| LCS | G ▷ C32×C25 | |
| UCS | C1 ◁ C31 | |
132 conjugacy classes of subgroups.
2511 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27900, 193);