Finite Group DatabasebetaFinite Group Databasebeta| order | 5154 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D859⋊C3 |
| unambiguous semidirect product | (C859⋊C3)⋊C2 |
| Fitting, socle, derived, Sylow | C859 ⋊ C2×C3 |
| Hall | C859⋊C3 ⋊ C2 |
| Hall | D859 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C859 | C2×C3 |
| LCS | G ▷ C859 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,859|c^a=c^858,c^b=c^260149 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D859⋊C3, C3⋊(D859⋊C3), C5×D859⋊C3, … |
| maximal normal subgroup of | C3×D859⋊C3, C5×D859⋊C3, C7×D859⋊C3 |
| maximal quotient of | D859⋊C9, C3×D859⋊C3, C3⋊(D859⋊C3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5154, 1);