Finite Group DatabasebetaFinite Group Databasebeta| order | 8146 |
| automorphism | Aut(G) order 16585256 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D4073 |
| unambiguous semidirect product | C4073⋊C2 |
| Fitting, socle, derived, Sylow | C4073 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C4073 | C2 |
| LCS | G ▷ C4073 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
Polycyclic presentation:
2,4073|b^a=b^40722038 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30654363, C2×D4073, C3×D4073, … |
| maximal normal subgroup of | #30654363, C2×D4073, C3×D4073 |
| maximal quotient of | Dic4073, C2×D4073, C3×D4073, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8146, 1);