Finite Group DatabasebetaFinite Group Databasebeta| order | 5170 |
| isoclinism | isoclinic class of D47 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C11 · Schur multiplier (H2) = C1 |
| direct product | C5×C11×D47 |
| unambiguous semidirect product | C47⋊(C2×C5×C11) |
| Fitting, socle, Hall | C5×C11×C47 ⋊ C2 |
| derived, Sylow | C47 ⋊ C2×C5×C11 |
| Hall | C11×C47 ⋊ C2×C5 |
| Hall | C5×C47 ⋊ C2×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C11 | D47 |
| commutator, hypocenter | C47 | C2×C5×C11 |
| Frattini | C1 | G |
| Fitting, socle | C5×C11×C47 | C2 |
| LCS | G ▷ C47 | |
| UCS | C1 ◁ C5×C11 | |
16 conjugacy classes of subgroups.
1375 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C5×C11×D47, C5×C11×D141, C11×C25×D47, … |
| maximal normal subgroup of | C3×C5×C11×D47, C11×C25×D47, D47×C11⋊C25, … |
| maximal quotient of | C3×C5×C11×D47, C5×C11×D141, C11×C25×D47, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5170, 3);