Finite Group DatabasebetaFinite Group Databasebeta| order | 10522 |
| automorphism | Aut(G) order 27672860 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D5261 |
| unambiguous semidirect product | C5261⋊C2 |
| Fitting, socle, derived, Sylow | C5261 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5261 | C2 |
| LCS | G ▷ C5261 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
Polycyclic presentation:
2,5261|b^a=b^52602632 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35230935, C2×D5261, C3×D5261, … |
| maximal normal subgroup of | #35230935, C2×D5261, C3×D5261 |
| maximal quotient of | Dic5261, C2×D5261, C3×D5261, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10522, 1);