Finite Group DatabasebetaFinite Group Databasebeta| order | 7684 |
| isoclinism | isoclinic class of #595 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C113 · Schur multiplier (H2) = C1 |
| direct product | #595×C113 |
| Fitting, socle, Hall | C17×C113 ⋊ C4 |
| derived, Sylow | C17 ⋊ C4×C113 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C113 | #595 |
| commutator, hypocenter | C17 | C4×C113 |
| Frattini | C1 | G |
| Fitting, socle | C17×C113 | C4 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C113 | |
12 conjugacy classes of subgroups.
904 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#595×C113, C113×C3⋊#595, C5×#595×C113, … |
| maximal normal subgroup of | C3×#595×C113, C5×#595×C113 |
| maximal quotient of | C3×#595×C113, C113×C3⋊#595, C5×#595×C113, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7684, 7);