Finite Group DatabasebetaFinite Group Databasebeta| order | 7936 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13357 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C31 · Schur multiplier (H2) = C24 |
| direct product | C31×#13359 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C31 | B(4,𝔽2) |
| commutator, Frattini, cosocle | C22×Q8 | C23×C31 |
| prime radical | C2×C31×2−1+4 | C22 |
| LCS | G ▷ C22×Q8 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C31 ◁ C23×C31 ◁ C22×Q8×C31 ◁ G | |
704 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 704 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
961 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7936, 6347);