Finite Group DatabasebetaFinite Group Databasebeta| order | 27900 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C31 · Schur multiplier (H2) = C2 |
| direct product | C31×D45⋊D5 |
| unambiguous semidirect product | D45⋊(D5×C31) |
| Fitting, Hall | C52×C9×C31 ⋊ C22 |
| derived, Hall | C52×C9 ⋊ C22×C31 |
| Hall | C52×C31 ⋊ C2×D9 |
| Hall | C9×C31 ⋊ D52 |
| Sylow | C52 ⋊ C2×D9×C31 |
| Sylow | C9 ⋊ D52×C31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31 | D45⋊D5 |
| commutator, cosocle, hypocenter | C52×C9 | C22×C31 |
| Frattini | C3 | C31×D15⋊D5 |
| Fitting | C52×C9×C31 | C22 |
| socle | C3×C52×C31 | C2×D3 |
| LCS | G ▷ C52×C9 | |
| UCS | C1 ◁ C31 | |
144 conjugacy classes of subgroups.
2232 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27900, 319);