Finite Group DatabasebetaFinite Group Databasebeta| order | 21780 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | (C121⋊C5)⋊#157 |
| unambiguous semidirect product | (C121⋊#157)⋊C5 |
| Fitting, derived, Hall | C32×C121 ⋊ C4×C5 |
| Hall | C32×C121⋊C5 ⋊ C4 |
| Hall | C121⋊#157 ⋊ C5 |
| Hall | C121⋊C5 ⋊ #157 |
| Sylow | C121 ⋊ C5×#157 |
| Sylow | C32 ⋊ Dic121⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C32×C121 | C4×C5 |
| Frattini | C11 | (C11⋊C5)⋊#157 |
| socle | C32×C11 | Dic11⋊C5 |
| prime radical | C3⋊D3×C121⋊C5 | C2 |
| cosocle | C3⋊D3×C121 | C2×C5 |
| LCS | G ▷ C32×C121 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,2,3^2,11^2|a^2=c,f^11=g^10,d^a=de^2,e^a=d^2e^2,f^a=f^10g,g^a=g^10,f^b=f^9,g^b=g^9,d^c=d^2,e^c=e^2102 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21780, 59);