Finite Group DatabasebetaFinite Group Databasebeta| order | 10910 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D1091⋊C5 |
| unambiguous semidirect product | (C1091⋊C5)⋊C2 |
| Fitting, socle, derived, Sylow | C1091 ⋊ C2×C5 |
| Hall | C1091⋊C5 ⋊ C2 |
| Hall | D1091 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C1091 | C2×C5 |
| LCS | G ▷ C1091 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,1091|c^a=c^1090,c^b=c^93119 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D1091⋊C5, C3×D1091⋊C5, C3⋊(D1091⋊C5) |
| maximal normal subgroup of | C2×D1091⋊C5, C3×D1091⋊C5 |
| maximal quotient of | Dic1091⋊C5, C2×D1091⋊C5, C3×D1091⋊C5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10910, 1);