Finite Group DatabasebetaFinite Group Databasebeta| order | 5522 |
| automorphism | Aut(G) order 6902500 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D2761 |
| unambiguous semidirect product | C11⋊D251 |
| unambiguous semidirect product | C251⋊D11 |
| Fitting, socle, derived, Hall | C11×C251 ⋊ C2 |
| Sylow | C251 ⋊ D11 |
| Sylow | C11 ⋊ D251 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C11×C251 | C2 |
| LCS | G ▷ C11×C251 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,11,251|b^a=b^10,c^a=c^2501382 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D11×D251, C2×D2761, C3×D2761, … |
| maximal normal subgroup of | D11×D251, C2×D2761, C3×D2761, … |
| maximal quotient of | Dic2761, C2×D2761, C3×D2761, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5522, 3);