Finite Group DatabasebetaFinite Group Databasebeta| order | 5684 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 7056 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2 |
| abelian | C22×C29×C49 |
| multiplicative | (ℤ/8529)ˣ, (ℤ/11372)ˣ, (ℤ/17058)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini | C7 | C22×C7×C29 |
| socle | C22×C7×C29 | C7 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
30 conjugacy classes of subgroups.
5684 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5684, 7);