Finite Group DatabasebetaFinite Group Databasebeta| order | 7936 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13307 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C31 · Schur multiplier (H2) = C22 |
| direct product | C31×#13455 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C31 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C31 |
| prime radical | C23×C31 | AGL(1,ℤ/8) |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C31 ◁ C22×C4×C31 ◁ C31×#405 ◁ G | |
318 conjugacy classes of subgroups.
1240 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7936, 6443);