Finite Group DatabasebetaFinite Group Databasebeta| order | 5154 |
| automorphism | Aut(G) order 4422132 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D2577 |
| unambiguous semidirect product | C3⋊D859 |
| unambiguous semidirect product | C859⋊D3 |
| Fitting, socle, derived, Hall | C3×C859 ⋊ C2 |
| Sylow | C859 ⋊ D3 |
| Sylow | C3 ⋊ D859 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C859 | C2 |
| LCS | G ▷ C3×C859 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,859|b^a=b^2,c^a=c^8581290 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D7731, C3⋊(D859⋊C3), C3⋊D2577, … |
| maximal normal subgroup of | C3⋊(D859⋊C3), C3×D2577, C5×D2577, … |
| maximal quotient of | D7731, C3⋊D2577, C3×D2577, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5154, 5);