Finite Group DatabasebetaFinite Group Databasebeta| order | 5066 |
| automorphism | Aut(G) order 5998144 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D2533 |
| unambiguous semidirect product | C17⋊D149 |
| unambiguous semidirect product | C149⋊D17 |
| Fitting, socle, derived, Hall | C17×C149 ⋊ C2 |
| Sylow | C149 ⋊ D17 |
| Sylow | C17 ⋊ D149 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C17×C149 | C2 |
| LCS | G ▷ C17×C149 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,17,149|b^a=b^16,c^a=c^1481268 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D2533, D7599, C5×D2533, … |
| maximal normal subgroup of | C3×D2533, C5×D2533, C7×D2533 |
| maximal quotient of | C3×D2533, D7599, C5×D2533, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5066, 3);