Finite Group DatabasebetaFinite Group Databasebeta| order | 7684 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D17×D113 |
| unambiguous semidirect product | (D17×C113)⋊C2 |
| unambiguous semidirect product | (C17×D113)⋊C2 |
| unambiguous semidirect product | D1921⋊C2 |
| Fitting, socle, derived, Hall | C17×C113 ⋊ C22 |
| Sylow | C113 ⋊ C2×D17 |
| Sylow | C17 ⋊ C2×D113 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C17×C113 | C22 |
| LCS | G ▷ C17×C113 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
580 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D17×D113, D51×D113, D17×D339, … |
| maximal normal subgroup of | C3×D17×D113, C5×D17×D113 |
| maximal quotient of | C3×D17×D113, D51×D113, D17×D339, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7684, 12);