Finite Group DatabasebetaFinite Group Databasebeta| order | 7692 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D3×D641 |
| unambiguous semidirect product | (D3×C641)⋊C2 |
| unambiguous semidirect product | (C3×D641)⋊C2 |
| unambiguous semidirect product | D1923⋊C2 |
| Fitting, socle, derived, Hall | C3×C641 ⋊ C22 |
| Sylow | C641 ⋊ C2×D3 |
| Sylow | C3 ⋊ C2×D641 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C641 | C22 |
| LCS | G ▷ C3×C641 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
966 conjugacy classes — view the full character table.
| maximal subgroup of | D9×D641, C3×D3×D641, D3×D1923, … |
| maximal normal subgroup of | C3×D3×D641, D3×D641⋊C5, C5×D3×D641 |
| maximal quotient of | D9×D641, C3×D3×D641, D3×D1923, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7692, 8);