Finite Group DatabasebetaFinite Group Databasebeta| order | 5838 |
| automorphism | Aut(G) order 4833864 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D2919 |
| unambiguous semidirect product | C3⋊D973 |
| unambiguous semidirect product | C7⋊D417 |
| unambiguous semidirect product | C139⋊D21 |
| Fitting, socle, derived, Hall | C3×C7×C139 ⋊ C2 |
| Hall | C7×C139 ⋊ D3 |
| Hall | C3×C139 ⋊ D7 |
| Sylow | C139 ⋊ D21 |
| Hall | C3×C7 ⋊ D139 |
| Sylow | C7 ⋊ D417 |
| Sylow | C3 ⋊ D973 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C7×C139 | C2 |
| LCS | G ▷ C3×C7×C139 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,7,139|b^a=b^2,c^a=c^6,d^a=d^1381461 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D21×D139, D7×D417, D3×D973, … |
| maximal normal subgroup of | D21×D139, D7×D417, D3×D973, … |
| maximal quotient of | Dic2919, C2×D2919, D8757, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5838, 12);