Finite Group DatabasebetaFinite Group Databasebeta| order | 10890 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C11 |
| unambiguous semidirect product | C3⋊(C5⋊((C11⋊D11)⋊C3)) |
| unambiguous semidirect product | C5⋊(C3⋊((C11⋊D11)⋊C3)) |
| unambiguous semidirect product | (C3⋊(C5⋊(C11⋊D11)))⋊C3 |
| Fitting, socle, derived | C3×C5×C112 ⋊ C2×C3 |
| Hall | C3×C5×C112⋊C3 ⋊ C2 |
| Hall | C3×C112⋊C3 ⋊ D5 |
| Hall | C5×C112 ⋊ C3×D3 |
| Sylow | C112 ⋊ C3×D15 |
| Sylow | C5 ⋊ C3⋊((C11⋊D11)⋊C3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C5×C112 | C2×C3 |
| LCS | G ▷ C3×C5×C112 | |
| UCS | C1 | |
68 conjugacy classes of subgroups.
Polycyclic presentation:
2,3^2,5,11^2|c^a=c^2,d^a=d^4,e^a=e^10,f^a=f^10,e^b=e^7f^5,f^b=e^4f^3327 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10890, 139);