Finite Group DatabasebetaFinite Group Databasebeta| order | 6158 |
| automorphism | Aut(G) order 9477162 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D3079 |
| unambiguous semidirect product | C3079⋊C2 |
| Fitting, socle, derived, Sylow | C3079 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3079 | C2 |
| LCS | G ▷ C3079 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
Polycyclic presentation:
2,3079|b^a=b^30781541 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D3079, D3079⋊C3, C3×D3079, … |
| maximal normal subgroup of | C2×D3079, D3079⋊C3, C3×D3079, … |
| maximal quotient of | Dic3079, C2×D3079, C3×D3079, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6158, 1);