Finite Group DatabasebetaFinite Group Databasebeta| order | 7936 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of AGL(1,ℤ/8) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8×C31 · Schur multiplier (H2) = C22×C4 |
| direct product | C31×#12615 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C31 | C2×D4 |
| commutator | C4 | C2×C4×C8×C31 |
| Frattini, cosocle | C22×C8 | C23×C31 |
| socle | C22×C31 | C8×D4 |
| prime radical | C2×#41×C31 | C2×C4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C31 ◁ C22×C16×C31 ◁ G | |
418 conjugacy classes of subgroups.
2728 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7936, 5603);