Finite Group DatabasebetaFinite Group Databasebeta| order | 10890 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊#14546095 |
| derived, Hall | C5×C112⋊C9 ⋊ C2 |
| Hall | C112⋊C9 ⋊ D5 |
| Hall | C5×C112 ⋊ D9 |
| Sylow | C112 ⋊ D45 |
| Sylow | C5 ⋊ #14546095 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C5×C112⋊C9 | C2 |
| Frattini | C3 | C5⋊#10624391 |
| Fitting, socle | C3×C5×C112 | D3 |
| LCS | G ▷ C5×C112⋊C9 | |
| UCS | C1 | |
44 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5,11^2,3|b^3=f^2,b^a=b^2f,c^a=c^4,e^a=d^4e^10,f^a=f^2,d^b=d^7e^10,e^b=d^2e^3339 conjugacy classes — view the full character table.
| maximal subgroup of | #14546095⋊D5, ((C11⋊D11)⋊C9)⋊D5, D5×#14546095, … |
| maximal normal subgroup of | #14546095⋊D5, ((C11⋊D11)⋊C9)⋊D5, D5×#14546095, … |
| maximal quotient of | #36344802, C2×C5⋊#14546095 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10890, 63);