Finite Group DatabasebetaFinite Group Databasebeta| order | 8806 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×D259 |
| unambiguous semidirect product | C7⋊(C17×D37) |
| unambiguous semidirect product | C37⋊(D7×C17) |
| Fitting, socle, Hall | C7×C17×C37 ⋊ C2 |
| derived, Hall | C7×C37 ⋊ C2×C17 |
| Hall | C17×C37 ⋊ D7 |
| Hall | C7×C17 ⋊ D37 |
| Sylow | C37 ⋊ D7×C17 |
| Sylow | C7 ⋊ C17×D37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | D259 |
| commutator, hypocenter | C7×C37 | C2×C17 |
| Frattini | C1 | G |
| Fitting, socle | C7×C17×C37 | C2 |
| LCS | G ▷ C7×C37 | |
| UCS | C1 ◁ C17 | |
16 conjugacy classes of subgroups.
2227 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D7×C17×D37, D17×D259, D119⋊D37, … |
| maximal normal subgroup of | D7×C17×D37, D17×D259, D119⋊D37, … |
| maximal quotient of | C17×Dic259, C2×C17×D259, C3×C17×D259, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8806, 6);