Finite Group DatabasebetaFinite Group Databasebeta| order | 5162 |
| automorphism | Aut(G) order 6359584 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D2581 |
| unambiguous semidirect product | C29⋊D89 |
| unambiguous semidirect product | C89⋊D29 |
| Fitting, socle, derived, Hall | C29×C89 ⋊ C2 |
| Sylow | C89 ⋊ D29 |
| Sylow | C29 ⋊ D89 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C29×C89 | C2 |
| LCS | G ▷ C29×C89 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,29,89|b^a=b^28,c^a=c^881292 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D2581, D7743, C5×D2581, … |
| maximal normal subgroup of | C3×D2581, C5×D2581, C7×D2581, … |
| maximal quotient of | C3×D2581, D7743, C5×D2581, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5162, 3);