Finite Group DatabasebetaFinite Group Databasebeta| order | 7936 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C31 · Schur multiplier (H2) = C29 |
| direct product | C31×#62635 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C31 | C22×D8 |
| commutator, Frattini, cosocle | C8 | C25×C31 |
| socle | C2×C31 | C23×D8 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C31 ◁ C2×#41×C31 ◁ C2×C31×#131 ◁ G | |
2038 conjugacy classes of subgroups.
1984 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7936, 55623);