Finite Group DatabasebetaFinite Group Databasebeta| order | 7856 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C491 · Schur multiplier (H2) = C22 |
| direct product | C22⋊C4×C491 |
| unambiguous semidirect product | C22⋊(C4×C491) |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C491 | C22 |
| commutator | C2 | C2×C4×C491 |
| Frattini, cosocle | C22 | C22×C491 |
| prime radical | C23×C491 | C2 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C491 ◁ G | |
34 conjugacy classes of subgroups.
4910 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7856, 3);