Finite Group DatabasebetaFinite Group Databasebeta| order | 6106 |
| automorphism | Aut(G) order 8975820 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D3053 |
| unambiguous semidirect product | C43⋊D71 |
| unambiguous semidirect product | C71⋊D43 |
| Fitting, socle, derived, Hall | C43×C71 ⋊ C2 |
| Sylow | C71 ⋊ D43 |
| Sylow | C43 ⋊ D71 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C43×C71 | C2 |
| LCS | G ▷ C43×C71 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,43,71|b^a=b^42,c^a=c^701528 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D43×D71, C2×D3053, C3×D3053, … |
| maximal normal subgroup of | D43×D71, C2×D3053, C3×D3053, … |
| maximal quotient of | Dic3053, C2×D3053, C3×D3053, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6106, 3);