Finite Group DatabasebetaFinite Group Databasebeta| order | 20988 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C53 · Schur multiplier (H2) = C1 |
| direct product | C53×Dic99 |
| unambiguous semidirect product | C9⋊(Dic11×C53) |
| unambiguous semidirect product | C11⋊(Dic9×C53) |
| derived, Hall | C9×C11 ⋊ C4×C53 |
| Hall | C9×C11×C53 ⋊ C4 |
| Hall | C11×C53 ⋊ Dic9 |
| Hall | C9×C53 ⋊ Dic11 |
| Sylow | C11 ⋊ Dic9×C53 |
| Sylow | C9 ⋊ Dic11×C53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C53 | D99 |
| commutator, hypocenter | C9×C11 | C4×C53 |
| Frattini | C2×C3 | C53×D33 |
| Fitting | C2×C9×C11×C53 | C2 |
| socle, prime radical | C2×C3×C11×C53 | D3 |
| cosocle | C2×C9×C11 | C2×C53 |
| LCS | G ▷ C9×C11 | |
| UCS | C1 ◁ C2×C53 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 20988 |
5406 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20988, 7);