Finite Group DatabasebetaFinite Group Databasebeta| order | 7936 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C31 · Schur multiplier (H2) = C24 |
| direct product | C31×#12561 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C31 | C2×D8 |
| commutator | C8 | C2×C42×C31 |
| Frattini, cosocle | C22×C8 | C23×C31 |
| socle | C22×C31 | C2×#102 |
| prime radical | C24×C31 | SD16 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C31 ◁ C23×C4×C31 ◁ C23×C8×C31 ◁ G | |
570 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, 5549);