Finite Group DatabasebetaFinite Group Databasebeta| order | 7692 |
| automorphism | Aut(G) order 4922880 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D3846 |
| direct product | C2×D1923 |
| unambiguous semidirect product | (C2×C3)⋊D641 |
| unambiguous semidirect product | (C2×C641)⋊D3 |
| Fitting, socle | C2×C3×C641 ⋊ C2 |
| derived, Hall | C3×C641 ⋊ C22 |
| Sylow | C641 ⋊ C2×D3 |
| Sylow | C3 ⋊ C2×D641 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D1923 |
| commutator, hypocenter | C3×C641 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C641 | C2 |
| LCS | G ▷ C3×C641 | |
| UCS | C1 ◁ C2 | |
20 conjugacy classes of subgroups.
1926 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D5769, D3×D1923, C2×C3×D1923, … |
| maximal normal subgroup of | C2×C3×D1923, C2×C3⋊(D641⋊C5), C2×C5×D1923, … |
| maximal quotient of | C2×D5769, D3×D1923, C2×C3×D1923, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7692, 10);