Finite Group DatabasebetaFinite Group Databasebeta| order | 7936 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11915 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C31 · Schur multiplier (H2) = C22 |
| direct product | C31×#11916 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C31 | #1533 |
| commutator | C42 | C22×C4×C31 |
| Frattini, cosocle | #97 | C23×C31 |
| prime radical | C23×C31 | #100 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C31 ◁ C2×C4×C31 ◁ C4×M16×C31 ◁ G | |
274 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
868 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7936, 4904);