Finite Group DatabasebetaFinite Group Databasebeta| order | 21780 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊(C3⋊(#92150⋊C5)) |
| unambiguous semidirect product | (C3⋊(C3⋊#92150))⋊C5 |
| Fitting, socle, derived, Hall | C32×C112 ⋊ C4×C5 |
| Hall | C32×#10597243 ⋊ C4 |
| Hall | C3⋊(C3⋊#92150) ⋊ C5 |
| Hall | #10597243 ⋊ C3⋊Dic3 |
| Sylow | C112 ⋊ C5×C3⋊Dic3 |
| Sylow | C32 ⋊ #92150⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C112 | C4×C5 |
| prime radical | C32×#11925892 | C2 |
| cosocle | C32×C11⋊D11 | C2×C5 |
| LCS | G ▷ C32×C112 | |
| UCS | C1 | |
216 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,2,3^2,11^2|a^2=c,d^a=d^2,e^a=e^2,f^a=f^5g^7,g^a=fg^6,f^b=f^3,g^b=g^3,f^c=f^10,g^c=g^10114 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21780, 500);