Finite Group DatabasebetaFinite Group Databasebeta| order | 7706 |
| automorphism | Aut(G) order 14841756 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D3853 |
| unambiguous semidirect product | C3853⋊C2 |
| Fitting, socle, derived, Sylow | C3853 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3853 | C2 |
| LCS | G ▷ C3853 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
Polycyclic presentation:
2,3853|b^a=b^38521928 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #29507078, C2×D3853, D3853⋊C3, … |
| maximal normal subgroup of | #29507078, C2×D3853, D3853⋊C3, … |
| maximal quotient of | Dic3853, C2×D3853, C3×D3853, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7706, 1);