Finite Group DatabasebetaFinite Group Databasebeta| order | 10820 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic541⋊C5 |
| derived, Sylow | C541 ⋊ C4×C5 |
| Hall | C541⋊C5 ⋊ C4 |
| Hall | Dic541 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D541⋊C5 |
| commutator, hypocenter | C541 | C4×C5 |
| Fitting, socle, cosocle | C2×C541 | C2×C5 |
| prime radical | C2×C541⋊C5 | C2 |
| LCS | G ▷ C541 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,541,2|a^2=d,c^a=c^540,c^b=c^48128 conjugacy classes — view the full character table.
| maximal subgroup of | C3×Dic541⋊C5, C3⋊(Dic541⋊C5), (Dic541⋊C3)⋊C5 |
| maximal normal subgroup of | C3×Dic541⋊C5, (Dic541⋊C3)⋊C5 |
| maximal quotient of | C3×Dic541⋊C5, C3⋊(Dic541⋊C5) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10820, 2);