Finite Group DatabasebetaFinite Group Databasebeta| order | 10890 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C9⋊#11925896 |
| Fitting, derived, Hall | C9×C112 ⋊ C2×C5 |
| Hall | C9×#10597245 ⋊ C2 |
| Hall | C11×D99 ⋊ C5 |
| Hall | #10597245 ⋊ D9 |
| Sylow | C112 ⋊ C5×D9 |
| Sylow | C9 ⋊ #11925896 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C9×C112 | C2×C5 |
| Frattini | C3 | C3⋊#11925896 |
| socle | C3×C112 | C5×D3 |
| LCS | G ▷ C9×C112 | |
| UCS | C1 | |
51 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,3,11^2,3|c^3=f^2,c^a=c^2f,d^a=d^10,f^a=f^2,d^b=d^4,e^b=e^3141 conjugacy classes — view the full character table.
| maximal subgroup of | #11925896⋊D9, #36344841, D9×#11925896, … |
| maximal normal subgroup of | #11925896⋊D9, #36344841, D9×#11925896, … |
| maximal quotient of | C9⋊#14559055, C2×C9⋊#11925896 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10890, 52);