Finite Group DatabasebetaFinite Group Databasebeta| order | 7936 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1812 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C31 · Schur multiplier (H2) = C22 |
| direct product | C31×#12896 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C31 | #117 |
| commutator | C2×C4 | C22×C8×C31 |
| Frattini, cosocle | C22×C8 | C23×C31 |
| socle | C22×C31 | #432 |
| prime radical | C23×C31 | C2×M16 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C31 ◁ C2×C31×#97 ◁ G | |
294 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 142 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1984 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7936, 5884);