Finite Group DatabasebetaFinite Group Databasebeta| order | 7936 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of D32 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8×C31 · Schur multiplier (H2) = C2 |
| direct product | C31×#7387 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C31 | D16 |
| commutator | C16 | C2×C8×C31 |
| Frattini, cosocle | C4×C16 | C22×C31 |
| socle | C2×C31 | #1331 |
| prime radical | C31×#508 | C4 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C31 ◁ C2×C8×C31 ◁ C4×C8×C31 ◁ C4×C16×C31 ◁ G | |
120 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
2356 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7936, 375);