Finite Group DatabasebetaFinite Group Databasebeta| order | 8534 |
| isoclinism | isoclinic class of D251 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×D251 |
| unambiguous semidirect product | C251⋊(C2×C17) |
| Fitting, socle, Hall | C17×C251 ⋊ C2 |
| derived, Sylow | C251 ⋊ C2×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | D251 |
| commutator, hypocenter | C251 | C2×C17 |
| Frattini | C1 | G |
| Fitting, socle | C17×C251 | C2 |
| LCS | G ▷ C251 | |
| UCS | C1 ◁ C17 | |
8 conjugacy classes of subgroups.
2159 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D17×D251, C2×C17×D251, C3×C17×D251, … |
| maximal normal subgroup of | D17×D251, C2×C17×D251, C3×C17×D251 |
| maximal quotient of | C17×Dic251, C2×C17×D251, C3×C17×D251, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8534, 2);