Finite Group DatabasebetaFinite Group Databasebeta| order | 7684 |
| automorphism | Aut(G) order 6884864 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D3842 |
| direct product | C2×D1921 |
| unambiguous semidirect product | (C2×C17)⋊D113 |
| unambiguous semidirect product | (C2×C113)⋊D17 |
| Fitting, socle | C2×C17×C113 ⋊ C2 |
| derived, Hall | C17×C113 ⋊ C22 |
| Sylow | C113 ⋊ C2×D17 |
| Sylow | C17 ⋊ C2×D113 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D1921 |
| commutator, hypocenter | C17×C113 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C17×C113 | C2 |
| LCS | G ▷ C17×C113 | |
| UCS | C1 ◁ C2 | |
20 conjugacy classes of subgroups.
1924 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×D1921, C2×C3×D1921, C2×D5763, … |
| maximal normal subgroup of | C2×C3×D1921, C2×C5×D1921, D7684 |
| maximal quotient of | D3×D1921, C2×C3×D1921, C2×D5763, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7684, 13);