Finite Group DatabasebetaFinite Group Databasebeta| order | 20988 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C53 · Schur multiplier (H2) = C2 |
| direct product | D9×D11×C53 |
| unambiguous semidirect product | (C11×D9)⋊(C2×C53) |
| unambiguous semidirect product | (C9×D11)⋊(C2×C53) |
| unambiguous semidirect product | D99⋊(C2×C53) |
| Fitting, Hall | C9×C11×C53 ⋊ C22 |
| derived, Hall | C9×C11 ⋊ C22×C53 |
| Hall | C11×C53 ⋊ C2×D9 |
| Hall | C9×C53 ⋊ C2×D11 |
| Sylow | C11 ⋊ C2×D9×C53 |
| Sylow | C9 ⋊ C2×D11×C53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C53 | D9×D11 |
| commutator, cosocle, hypocenter | C9×C11 | C22×C53 |
| Frattini | C3 | D3×D11×C53 |
| Fitting | C9×C11×C53 | C22 |
| socle | C3×C11×C53 | C2×D3 |
| LCS | G ▷ C9×C11 | |
| UCS | C1 ◁ C53 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5247 |
2226 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20988, 17);