Finite Group DatabasebetaFinite Group Databasebeta| order | 10890 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C3×C3⋊#11925896 |
| unambiguous semidirect product | C3⋊(C3×#11925896) |
| Fitting, socle, Hall | C32×C112 ⋊ C2×C5 |
| derived | C3×C112 ⋊ C2×C3×C5 |
| Hall | C32×#10597245 ⋊ C2 |
| Hall | C3×C11×D33 ⋊ C5 |
| Hall | #10597245 ⋊ C3×D3 |
| Sylow | C112 ⋊ C3×C5×D3 |
| Sylow | C32 ⋊ #11925896 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C3⋊#11925896 |
| commutator, cosocle, hypocenter | C3×C112 | C2×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C32×C112 | C2×C5 |
| LCS | G ▷ C3×C112 | |
| UCS | C1 ◁ C3 | |
78 conjugacy classes of subgroups.
162 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×#11925896, C3×#11925896⋊D3, C3×#20300010, … |
| maximal normal subgroup of | C3×D3×#11925896, C3×#11925896⋊D3, C3×#20300010, … |
| maximal quotient of | C3×C3⋊#14559055, C2×C3×C3⋊#11925896 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10890, 106);