Finite Group DatabasebetaFinite Group Databasebeta| order | 10890 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3×C11 |
| unambiguous semidirect product | C3⋊(C3⋊(C5⋊(C11⋊D11))) |
| unambiguous semidirect product | C5⋊(C3⋊(C3⋊(C11⋊D11))) |
| unambiguous semidirect product | C11⋊(C3⋊D165) |
| Fitting, socle, derived, Hall | C32×C5×C112 ⋊ C2 |
| Hall | C32×C112 ⋊ D5 |
| Hall | C5×C112 ⋊ C3⋊D3 |
| Sylow | C112 ⋊ C3⋊D15 |
| Hall | C32×C5 ⋊ C11⋊D11 |
| Sylow | C32 ⋊ C5⋊(C11⋊D11) |
| Sylow | C5 ⋊ C3⋊(C3⋊(C11⋊D11)) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C5×C112 | C2 |
| LCS | G ▷ C32×C5×C112 | |
| UCS | C1 | |
336 conjugacy classes of subgroups.
Polycyclic presentation:
2,3^2,5,11^2|b^a=b^2,c^a=c^2,d^a=d^4,e^a=e^10,f^a=f^102724 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36345280, D33×D165, D3×C3⋊(C5⋊(C11⋊D11)), … |
| maximal normal subgroup of | #36345280, D33×D165, D3×C3⋊(C5⋊(C11⋊D11)), … |
| maximal quotient of | C3⋊(C3⋊(C11⋊Dic55)), C2×C3⋊(C3⋊(C5⋊(C11⋊D11))) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10890, 146);