Finite Group DatabasebetaFinite Group Databasebeta| order | 7936 |
| nilpotency class | 5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8×C31 · Schur multiplier (H2) = C2×C4 |
| direct product | C31×#7355 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C31 | #353 |
| commutator | C42 | C2×C8×C31 |
| Frattini, cosocle | #384 | C22×C31 |
| prime radical | C23×C31 | #99 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C31 ◁ C23×C31 ◁ C22×C4×C31 ◁ C31×#384 ◁ G | |
216 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1054 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7936, 343);