Finite Group DatabasebetaFinite Group Databasebeta| order | 27900 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2×C5 |
| direct product | C5⋊D5×D31⋊C9 |
| unambiguous semidirect product | D31⋊(C9×C5⋊D5) |
| unambiguous semidirect product | (C5×D31⋊C9)⋊D5 |
| derived, Hall | C52×C31 ⋊ C22×C9 |
| Hall | C52×C31⋊C9 ⋊ C22 |
| Hall | C5⋊D5×D31 ⋊ C9 |
| Hall | C31⋊C9 ⋊ C2×C5⋊D5 |
| Sylow | C31 ⋊ C2×C9×C5⋊D5 |
| Sylow | C52 ⋊ C2×D31⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C5⋊D5×D31⋊C3 |
| commutator, hypocenter | C52×C31 | C22×C9 |
| Fitting, socle, cosocle | C3×C52×C31 | C22×C3 |
| prime radical | C3×C5⋊D5×D31 | C3 |
| LCS | G ▷ C52×C31 | |
| UCS | C1 ◁ C3 | |
240 conjugacy classes of subgroups.
462 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27900, 246);