Finite Group DatabasebetaFinite Group Databasebeta| order | 5338 |
| automorphism | Aut(G) order 6661824 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D2669 |
| unambiguous semidirect product | C17⋊D157 |
| unambiguous semidirect product | C157⋊D17 |
| Fitting, socle, derived, Hall | C17×C157 ⋊ C2 |
| Sylow | C157 ⋊ D17 |
| Sylow | C17 ⋊ D157 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C17×C157 | C2 |
| LCS | G ▷ C17×C157 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,17,157|b^a=b^16,c^a=c^1561336 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D2669, D8007, C17⋊(D157⋊C3), … |
| maximal normal subgroup of | C3×D2669, C17⋊(D157⋊C3), C5×D2669, … |
| maximal quotient of | C3×D2669, D8007, C5×D2669, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5338, 3);