Finite Group DatabasebetaFinite Group Databasebeta| order | 8534 |
| automorphism | Aut(G) order 17068000 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D4267 |
| unambiguous semidirect product | C17⋊D251 |
| unambiguous semidirect product | C251⋊D17 |
| Fitting, socle, derived, Hall | C17×C251 ⋊ C2 |
| Sylow | C251 ⋊ D17 |
| Sylow | C17 ⋊ D251 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C17×C251 | C2 |
| LCS | G ▷ C17×C251 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,17,251|b^a=b^16,c^a=c^2502135 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D17×D251, C2×D4267, C3×D4267, … |
| maximal normal subgroup of | D17×D251, C2×D4267, C3×D4267 |
| maximal quotient of | Dic4267, C2×D4267, C3×D4267, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8534, 3);