Finite Group DatabasebetaFinite Group Databasebeta| order | 21780 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11 · Schur multiplier (H2) = C3 |
| direct product | C11×C11⋊#4380 |
| unambiguous semidirect product | C11⋊(C11×#4380) |
| Fitting, socle, Hall | C32×C5×C112 ⋊ C4 |
| derived | C32×C5×C11 ⋊ C4×C11 |
| Hall | C32×C112 ⋊ AGL(1,𝔽5) |
| Hall | C5×C112 ⋊ #157 |
| Sylow | C112 ⋊ #4380 |
| Hall | C32×C5 ⋊ C11×Dic11 |
| Sylow | C32 ⋊ C11×C11⋊AGL(1,𝔽5) |
| Sylow | C5 ⋊ C11×C11⋊#157 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | C11⋊#4380 |
| commutator, hypocenter | C32×C5×C11 | C4×C11 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C112 | C4 |
| prime radical | C112×C3⋊D15 | C2 |
| cosocle | C11×C3⋊D15 | C2×C11 |
| LCS | G ▷ C32×C5×C11 | |
| UCS | C1 ◁ C11 | |
200 conjugacy classes of subgroups.
1485 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21780, 631);