Finite Group DatabasebetaFinite Group Databasebeta| order | 5550 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C52×C37 · Schur multiplier (H2) = C5 |
| direct product | C52×D3×C37 |
| unambiguous semidirect product | C3⋊(C2×C52×C37) |
| Fitting, socle, Hall | C3×C52×C37 ⋊ C2 |
| derived, Sylow | C3 ⋊ C2×C52×C37 |
| Hall | C3×C37 ⋊ C2×C52 |
| Hall | C3×C52 ⋊ C2×C37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52×C37 | D3 |
| commutator, hypocenter | C3 | C2×C52×C37 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C37 | C2 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C52×C37 | |
64 conjugacy classes of subgroups.
2775 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C52×D3×D37, C5×D3×D5×C37, C5×D3×D185, … |
| maximal normal subgroup of | C52×D3×D37, C5×D3×D5×C37, C5×D3×D185, … |
| maximal quotient of | C52×Dic3×C37, C2×C52×D3×C37, C52×D9×C37, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5550, 35);