Finite Group DatabasebetaFinite Group Databasebeta| order | 21780 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊(C3⋊((C11⋊C5)⋊Dic11)) |
| unambiguous semidirect product | (C11⋊C5)⋊(C3⋊Dic33) |
| derived, Hall | C32×C112 ⋊ C4×C5 |
| Hall | C32×C11×C11⋊C5 ⋊ C4 |
| Hall | C3⋊(C3⋊(C11⋊Dic11)) ⋊ C5 |
| Hall | C11×C11⋊C5 ⋊ C3⋊Dic3 |
| Sylow | C112 ⋊ C5×C3⋊Dic3 |
| Sylow | C32 ⋊ (C11⋊C5)⋊Dic11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊(C3⋊((C11⋊C5)⋊D11)) |
| commutator, hypocenter | C32×C112 | C4×C5 |
| Fitting, socle, cosocle | C2×C32×C112 | C2×C5 |
| prime radical | C2×C32×C11×C11⋊C5 | C2 |
| LCS | G ▷ C32×C112 | |
| UCS | C1 ◁ C2 | |
180 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,3^2,11^2,2|a^2=g,c^a=c^2,d^a=d^2,e^a=e^10,f^a=f^10,e^b=e^4708 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21780, 354);