Finite Group DatabasebetaFinite Group Databasebeta| order | 21780 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(((C11⋊Dic11)⋊C3)⋊C5) |
| unambiguous semidirect product | (C3⋊((C11⋊Dic11)⋊C3))⋊C5 |
| unambiguous semidirect product | (C3⋊#14559051)⋊C3 |
| derived | C3×C112 ⋊ C3×C4×C5 |
| Hall | C3×(C112⋊C3)⋊C5 ⋊ C4 |
| Hall | C3⋊((C11⋊Dic11)⋊C3) ⋊ C5 |
| Hall | C3×C112⋊C3 ⋊ C4×C5 |
| Hall | #10597243 ⋊ C3×Dic3 |
| Sylow | C112 ⋊ C3×C5×Dic3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊(((C11⋊D11)⋊C3)⋊C5) |
| commutator, hypocenter | C3×C112 | C3×C4×C5 |
| Fitting, socle, cosocle | C2×C3×C112 | C2×C3×C5 |
| prime radical | C2×C3×(C112⋊C3)⋊C5 | C2 |
| LCS | G ▷ C3×C112 | |
| UCS | C1 ◁ C2 | |
104 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5,3,11^2,2|a^2=g,d^a=d^2,e^a=e^10,f^a=f^10,e^b=e^3f^9,f^b=ef^7,e^c=e^3,f^c=f^3114 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21780, 316);