Finite Group DatabasebetaFinite Group Databasebeta| order | 6416 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C401 · Schur multiplier (H2) = C22 |
| direct product | C2×Q8×C401 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C401 | C22 |
| commutator, Frattini, cosocle | C2 | C23×C401 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C401 ◁ G | |
38 conjugacy classes of subgroups.
4010 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6416, 12);