Finite Group DatabasebetaFinite Group Databasebeta| order | 7936 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3585 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C31 · Schur multiplier (H2) = C210 |
| direct product | C31×#60087 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C31 | C23×D4 |
| commutator | C4 | C24×C4×C31 |
| Frattini, cosocle | C2×C4 | C25×C31 |
| prime radical | C22×C31×H(5,𝔽2) | C2 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C31 ◁ C22×#41×C31 ◁ G | |
5154 conjugacy classes of subgroups.
2542 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7936, 53075);