Finite Group DatabasebetaFinite Group Databasebeta| order | 8670 |
| isoclinism | isoclinic class of D51 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C17 · Schur multiplier (H2) = C1 |
| direct product | C5×C17×D51 |
| unambiguous semidirect product | C3⋊(C5×C17×D17) |
| unambiguous semidirect product | C17⋊(C5×D3×C17) |
| Fitting, socle, Hall | C3×C5×C172 ⋊ C2 |
| derived | C3×C17 ⋊ C2×C5×C17 |
| Hall | C5×C172 ⋊ D3 |
| Hall | C3×C172 ⋊ C2×C5 |
| Sylow | C172 ⋊ C5×D3 |
| Hall | C3×C5 ⋊ C17×D17 |
| Sylow | C3 ⋊ C5×C17×D17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C17 | D51 |
| commutator, hypocenter | C3×C17 | C2×C5×C17 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C172 | C2 |
| LCS | G ▷ C3×C17 | |
| UCS | C1 ◁ C5×C17 | |
64 conjugacy classes of subgroups.
2295 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D3×C17×D17, C5×D17×D51, C5×D51⋊D17, … |
| maximal normal subgroup of | C5×D3×C17×D17, C5×D17×D51, C5×D51⋊D17, … |
| maximal quotient of | C5×C17×Dic51, C2×C5×C17×D51, C5×C17×D153, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8670, 22);