Finite Group DatabasebetaFinite Group Databasebeta| order | 10802 |
| automorphism | Aut(G) order 26464900 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D5401 |
| unambiguous semidirect product | C11⋊D491 |
| unambiguous semidirect product | C491⋊D11 |
| Fitting, socle, derived, Hall | C11×C491 ⋊ C2 |
| Sylow | C491 ⋊ D11 |
| Sylow | C11 ⋊ D491 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C491 | C2 |
| LCS | G ▷ C11×C491 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,11,491|b^a=b^10,c^a=c^4902702 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D11×D491, C2×D5401, C3×D5401, … |
| maximal normal subgroup of | D11×D491, C2×D5401, C3×D5401 |
| maximal quotient of | Dic5401, C2×D5401, C3×D5401, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10802, 3);