Finite Group DatabasebetaFinite Group Databasebeta| order | 10890 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C3 |
| direct product | C3⋊D3×#10597243 |
| unambiguous semidirect product | C3⋊(D3×#10597243) |
| Fitting, socle, derived, Hall | C32×C112 ⋊ C2×C5 |
| Hall | C32×#10597243 ⋊ C2 |
| Hall | C112×C3⋊D3 ⋊ C5 |
| Sylow | C112 ⋊ C5×C3⋊D3 |
| Sylow | C32 ⋊ C2×#10597243 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C112 | C2×C5 |
| LCS | G ▷ C32×C112 | |
| UCS | C1 | |
336 conjugacy classes of subgroups.
174 conjugacy classes — view the full character table.
| maximal subgroup of | #157×#10597243, #36345068, #36345069, … |
| maximal normal subgroup of | #157×#10597243, #36345068, #36345069, … |
| maximal quotient of | C3⋊Dic3×#10597243, C2×C3⋊D3×#10597243 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10890, 125);