Finite Group DatabasebetaFinite Group Databasebeta| order | 10510 |
| automorphism | Aut(G) order 22071000 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D5255 |
| unambiguous semidirect product | C5⋊D1051 |
| unambiguous semidirect product | C1051⋊D5 |
| Fitting, socle, derived, Hall | C5×C1051 ⋊ C2 |
| Sylow | C1051 ⋊ D5 |
| Sylow | C5 ⋊ D1051 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C1051 | C2 |
| LCS | G ▷ C5×C1051 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,1051|b^a=b^4,c^a=c^10502629 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D5×D1051, C2×D5255, C3×D5255, … |
| maximal normal subgroup of | D5×D1051, C2×D5255, C3×D5255, … |
| maximal quotient of | Dic5255, C2×D5255, C3×D5255, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10510, 5);