Finite Group DatabasebetaFinite Group Databasebeta| order | 20988 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C1 |
| direct product | C3×C11×C3⋊#6157 |
| unambiguous semidirect product | C3⋊(C3×C11×#6157) |
| Fitting, socle, Hall | C32×C11×C53 ⋊ C4 |
| derived | C3×C53 ⋊ C3×C4×C11 |
| Hall | C11×C53 ⋊ C3×Dic3 |
| Hall | C32×C53 ⋊ C4×C11 |
| Hall | C32×C11 ⋊ #6157 |
| Sylow | C53 ⋊ C3×C11×Dic3 |
| Sylow | C32 ⋊ C11×#6157 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C11 | C3⋊#6157 |
| commutator, hypocenter | C3×C53 | C3×C4×C11 |
| Frattini | C1 | G |
| Fitting, socle | C32×C11×C53 | C4 |
| prime radical | C32×C11×D53 | C2 |
| cosocle | C3×D53 | C2×C3×C11 |
| LCS | G ▷ C3×C53 | |
| UCS | C1 ◁ C3×C11 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3498 |
1485 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20988, 51);