Finite Group DatabasebetaFinite Group Databasebeta| order | 7936 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #7318 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C31 · Schur multiplier (H2) = C25 |
| direct product | C31×#7318 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C31 | #1304 |
| commutator | C22×C4 | C42×C31 |
| Frattini, cosocle | C22×#41 | C22×C31 |
| prime radical | C22×#41×C31 | C22 |
| LCS | G ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C31 ◁ C23×C31 ◁ C22×#41×C31 ◁ G | |
484 conjugacy classes of subgroups.
868 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7936, 306);