Finite Group DatabasebetaFinite Group Databasebeta| order | 7936 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #32870 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C31 · Schur multiplier (H2) = C23 |
| direct product | C31×#32871 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C31 | #2826 |
| commutator, Frattini, cosocle | C22×C4 | C24×C31 |
| prime radical | C2×C31×AGL(1,ℤ/8) | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C31 ◁ C22×C4×C31 ◁ G | |
492 conjugacy classes of subgroups.
868 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7936, 25859);