Finite Group DatabasebetaFinite Group Databasebeta| order | 7684 |
| isoclinism | isoclinic class of #90673 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×#90673 |
| Fitting, socle, Hall | C17×C113 ⋊ C4 |
| derived, Sylow | C113 ⋊ C4×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | #90673 |
| commutator, hypocenter | C113 | C4×C17 |
| Frattini | C1 | G |
| Fitting, socle | C17×C113 | C4 |
| LCS | G ▷ C113 | |
| UCS | C1 ◁ C17 | |
12 conjugacy classes of subgroups.
544 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C17×#90673, C17×C3⋊#90673, C5×C17×#90673, … |
| maximal normal subgroup of | C3×C17×#90673, C5×C17×#90673 |
| maximal quotient of | C3×C17×#90673, C17×C3⋊#90673, C5×C17×#90673, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7684, 6);