Finite Group DatabasebetaFinite Group Databasebeta| order | 27900 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | D52×C31⋊C9 |
| unambiguous semidirect product | (C5×D5)⋊(C2×C31⋊C9) |
| unambiguous semidirect product | (D52×C31)⋊C9 |
| derived, Hall | C52×C31 ⋊ C22×C9 |
| Hall | C52×C31⋊C9 ⋊ C22 |
| Hall | D52×C31 ⋊ C9 |
| Sylow | C31 ⋊ C9×D52 |
| Sylow | C52 ⋊ C22×C31⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | D52×C31⋊C3 |
| commutator, hypocenter | C52×C31 | C22×C9 |
| Fitting, socle, cosocle | C3×C52×C31 | C22×C3 |
| prime radical | C3×D52×C31 | C3 |
| LCS | G ▷ C52×C31 | |
| UCS | C1 ◁ C3 | |
144 conjugacy classes of subgroups.
624 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27900, 249);