Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 79872 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C22×C32×C53 |
| multiplicative | (ℤ/13576)ˣ, (ℤ/13696)ˣ, (ℤ/20364)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini | C16 | C23×C53 |
| socle | C23×C53 | C16 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
120 conjugacy classes of subgroups.
6784 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 988);