Finite Group DatabasebetaFinite Group Databasebeta| order | 5170 |
| isoclinism | isoclinic class of D55 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C47 · Schur multiplier (H2) = C1 |
| direct product | C47×D55 |
| unambiguous semidirect product | C5⋊(D11×C47) |
| unambiguous semidirect product | C11⋊(D5×C47) |
| Fitting, socle, Hall | C5×C11×C47 ⋊ C2 |
| derived, Hall | C5×C11 ⋊ C2×C47 |
| Hall | C11×C47 ⋊ D5 |
| Hall | C5×C47 ⋊ D11 |
| Sylow | C11 ⋊ D5×C47 |
| Sylow | C5 ⋊ D11×C47 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C47 | D55 |
| commutator, hypocenter | C5×C11 | C2×C47 |
| Frattini | C1 | G |
| Fitting, socle | C5×C11×C47 | C2 |
| LCS | G ▷ C5×C11 | |
| UCS | C1 ◁ C47 | |
16 conjugacy classes of subgroups.
1363 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C47×D55, C47×D165, C47×D275, … |
| maximal normal subgroup of | C3×C47×D55, C47×C5⋊AGL(1,𝔽11), C5×C47×D55, … |
| maximal quotient of | C3×C47×D55, C47×D165, C47×D275, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5170, 8);