Finite Group DatabasebetaFinite Group Databasebeta| order | 6416 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 6400 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2 |
| abelian | C2×C8×C401 |
| multiplicative | (ℤ/9627)ˣ, (ℤ/12836)ˣ, (ℤ/19254)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini | C4 | C22×C401 |
| socle | C22×C401 | C4 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
22 conjugacy classes of subgroups.
6416 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6416, 5);