Finite Group DatabasebetaFinite Group Databasebeta| order | 7834 |
| automorphism | Aut(G) order 15338972 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D3917 |
| unambiguous semidirect product | C3917⋊C2 |
| Fitting, socle, derived, Sylow | C3917 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3917 | C2 |
| LCS | G ▷ C3917 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
Polycyclic presentation:
2,3917|b^a=b^39161960 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30627847, C2×D3917, C3×D3917, … |
| maximal normal subgroup of | #30627847, C2×D3917, C3×D3917 |
| maximal quotient of | Dic3917, C2×D3917, C3×D3917, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7834, 1);