Finite Group DatabasebetaFinite Group Databasebeta| order | 5850 |
| isoclinism | isoclinic class of C3⋊D15 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C13 · Schur multiplier (H2) = C3 |
| direct product | C5×C13×C3⋊D15 |
| unambiguous semidirect product | C3⋊(C5×C13×D15) |
| unambiguous semidirect product | C5⋊(C5×C13×C3⋊D3) |
| Fitting, socle, Hall | C32×C52×C13 ⋊ C2 |
| derived | C32×C5 ⋊ C2×C5×C13 |
| Hall | C52×C13 ⋊ C3⋊D3 |
| Hall | C32×C52 ⋊ C2×C13 |
| Hall | C32×C13 ⋊ C5×D5 |
| Sylow | C52 ⋊ C13×C3⋊D3 |
| Sylow | C32 ⋊ C5×D5×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C13 | C3⋊D15 |
| commutator, hypocenter | C32×C5 | C2×C5×C13 |
| Frattini | C1 | G |
| Fitting, socle | C32×C52×C13 | C2 |
| LCS | G ▷ C32×C5 | |
| UCS | C1 ◁ C5×C13 | |
120 conjugacy classes of subgroups.
1560 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D13×C3⋊D15, C5×D5×C13×C3⋊D3, C5×D65⋊(C3⋊D3), … |
| maximal normal subgroup of | C5×D13×C3⋊D15, C5×D5×C13×C3⋊D3, C5×D65⋊(C3⋊D3), … |
| maximal quotient of | C5×C13×C3⋊Dic15, C2×C5×C13×C3⋊D15 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5850, 113);