Finite Group DatabasebetaFinite Group Databasebeta| order | 5754 |
| automorphism | Aut(G) order 4695264 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D2877 |
| unambiguous semidirect product | C3⋊D959 |
| unambiguous semidirect product | C7⋊D411 |
| unambiguous semidirect product | C137⋊D21 |
| Fitting, socle, derived, Hall | C3×C7×C137 ⋊ C2 |
| Hall | C7×C137 ⋊ D3 |
| Hall | C3×C137 ⋊ D7 |
| Sylow | C137 ⋊ D21 |
| Hall | C3×C7 ⋊ D137 |
| Sylow | C7 ⋊ D411 |
| Sylow | C3 ⋊ D959 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C7×C137 | C2 |
| LCS | G ▷ C3×C7×C137 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,7,137|b^a=b^2,c^a=c^6,d^a=d^1361440 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D21×D137, D7×D411, D3×D959, … |
| maximal normal subgroup of | D21×D137, D7×D411, D3×D959, … |
| maximal quotient of | Dic2877, C2×D2877, D8631, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5754, 9);