Finite Group DatabasebetaFinite Group Databasebeta| order | 5850 |
| isoclinism | isoclinic class of C3⋊D39 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C52 · Schur multiplier (H2) = C3×C5 |
| direct product | C52×C3⋊D39 |
| unambiguous semidirect product | C3⋊(C52×D39) |
| unambiguous semidirect product | C13⋊(C52×C3⋊D3) |
| Fitting, socle, Hall | C32×C52×C13 ⋊ C2 |
| derived, Hall | C32×C13 ⋊ C2×C52 |
| Hall | C52×C13 ⋊ C3⋊D3 |
| Hall | C32×C52 ⋊ D13 |
| Sylow | C13 ⋊ C52×C3⋊D3 |
| Sylow | C32 ⋊ C52×D13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52 | C3⋊D39 |
| commutator, hypocenter | C32×C13 | C2×C52 |
| Frattini | C1 | G |
| Fitting, socle | C32×C52×C13 | C2 |
| LCS | G ▷ C32×C13 | |
| UCS | C1 ◁ C52 | |
192 conjugacy classes of subgroups.
1500 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C52×C3⋊D3×D13, C5×D5×C3⋊D39, C5×D65⋊(C3⋊D3), … |
| maximal normal subgroup of | C52×C3⋊D3×D13, C5×D5×C3⋊D39, C5×D65⋊(C3⋊D3), … |
| maximal quotient of | C52×C3⋊Dic39, C2×C52×C3⋊D39 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5850, 112);