Finite Group DatabasebetaFinite Group Databasebeta| order | 21780 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (#92150⋊C5)⋊C9 |
| unambiguous semidirect product | (#92150⋊C9)⋊C5 |
| derived, Sylow | C112 ⋊ C4×C5×C9 |
| Hall | #10597243⋊C9 ⋊ C4 |
| Hall | #92150⋊C9 ⋊ C5 |
| Hall | #92150⋊C5 ⋊ C9 |
| Hall | C112⋊C9 ⋊ C4×C5 |
| Hall | #10597243 ⋊ C4×C9 |
| Hall | #92150 ⋊ C5×C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | (#92150⋊C3)⋊C5 |
| commutator, hypocenter | C112 | C4×C5×C9 |
| Fitting, socle | C3×C112 | C3×C4×C5 |
| prime radical | C3×#11925892 | C2×C3 |
| cosocle | C3×C11⋊D11 | C2×C3×C5 |
| LCS | G ▷ C112 | |
| UCS | C1 ◁ C3 | |
52 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5,2,11^2,3|a^2=d,b^3=g,e^a=e^9f^3,f^a=e^2f^2,e^b=e^10f^9,f^b=e^6,e^c=e^4,f^c=f^4,e^d=e^10,f^d=f^10186 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21780, 173);