Finite Group DatabasebetaFinite Group Databasebeta| order | 5622 |
| automorphism | Aut(G) order 5262192 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D2811 |
| unambiguous semidirect product | C3⋊D937 |
| unambiguous semidirect product | C937⋊D3 |
| Fitting, socle, derived, Hall | C3×C937 ⋊ C2 |
| Sylow | C937 ⋊ D3 |
| Sylow | C3 ⋊ D937 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C937 | C2 |
| LCS | G ▷ C3×C937 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,937|b^a=b^2,c^a=c^9361407 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×D937, C2×D2811, D8433, … |
| maximal normal subgroup of | D3×D937, C2×D2811, C3⋊(D937⋊C3), … |
| maximal quotient of | Dic2811, C2×D2811, D8433, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5622, 5);