Finite Group DatabasebetaFinite Group Databasebeta| order | 7936 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #560 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C31 · Schur multiplier (H2) = C28 |
| direct product | C4×C31×#563 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C31 | C24 |
| commutator | C22 | C24×C4×C31 |
| Frattini, cosocle | C23 | C25×C31 |
| socle | C23×C31 | C25 |
| prime radical | C22×D4×C31 | C23 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C31 ◁ G | |
2024 conjugacy classes of subgroups.
2356 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7936, 27342);