Finite Group DatabasebetaFinite Group Databasebeta| order | 7726 |
| automorphism | Aut(G) order 14918906 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D3863 |
| unambiguous semidirect product | C3863⋊C2 |
| Fitting, socle, derived, Sylow | C3863 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3863 | C2 |
| LCS | G ▷ C3863 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
Polycyclic presentation:
2,3863|b^a=b^38621933 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D3863, C3×D3863, D11589, … |
| maximal normal subgroup of | C2×D3863, C3×D3863, C5×D3863 |
| maximal quotient of | Dic3863, C2×D3863, C3×D3863, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7726, 1);