Finite Group DatabasebetaFinite Group Databasebeta| order | 27900 |
| isoclinism | isoclinic class of D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C52×C31 · Schur multiplier (H2) = C2×C5 |
| direct product | C2×C52×D9×C31 |
| unambiguous semidirect product | C9⋊(C22×C52×C31) |
| unambiguous semidirect product | (C2×C9)⋊(C2×C52×C31) |
| Fitting | C2×C52×C9×C31 ⋊ C2 |
| derived, Sylow | C9 ⋊ C22×C52×C31 |
| Hall | C52×C9×C31 ⋊ C22 |
| Hall | C9×C31 ⋊ C22×C52 |
| Hall | C52×C9 ⋊ C22×C31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C52×C31 | D9 |
| commutator, cosocle, hypocenter | C9 | C22×C52×C31 |
| Frattini | C3 | C2×C52×D3×C31 |
| Fitting | C2×C52×C9×C31 | C2 |
| socle | C2×C3×C52×C31 | D3 |
| LCS | G ▷ C9 | |
| UCS | C1 ◁ C2×C52×C31 | |
240 conjugacy classes of subgroups.
9300 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27900, 334);