Finite Group DatabasebetaFinite Group Databasebeta| order | 6416 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 76800 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C22×C4×C401 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini | C2 | C23×C401 |
| socle | C23×C401 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
54 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, 10);