Finite Group DatabasebetaFinite Group Databasebeta| order | 10890 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C9⋊#11925890 |
| Fitting, Hall | C9×C112 ⋊ D5 |
| derived, Hall | C9×#10597245 ⋊ C2 |
| Hall | #10597245 ⋊ D9 |
| Sylow | C112 ⋊ D45 |
| Sylow | C9 ⋊ #11925890 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C9×#10597245 | C2 |
| Frattini | C3 | C3⋊#11925890 |
| Fitting | C9×C112 | D5 |
| socle | C3×C112 | D15 |
| LCS | G ▷ C9×#10597245 | |
| UCS | C1 | |
42 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5,11^2,3|b^3=f^2,b^a=b^2f,c^a=c^4,d^a=d^3e^3,e^a=de^8,f^a=f^2,d^c=d^4e^8,e^c=e^3147 conjugacy classes — view the full character table.
| maximal subgroup of | #11925890⋊D9, #36344855, D9×#11925890, … |
| maximal normal subgroup of | #11925890⋊D9, #36344855, D9×#11925890, … |
| maximal quotient of | C9⋊#14559049, C2×C9⋊#11925890 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10890, 60);