Finite Group DatabasebetaFinite Group Databasebeta| order | 7936 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #353 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16×C31 · Schur multiplier (H2) = C2 |
| direct product | C31×#7364 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C31 | #99 |
| commutator | C2×C4 | C2×C16×C31 |
| Frattini, cosocle | C2×M32 | C22×C31 |
| socle | C2×C31 | #1322 |
| prime radical | C23×C31 | M32 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C31 ◁ C2×C8×C31 ◁ C2×C31×M32 ◁ G | |
126 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 126 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.
1612 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7936, 352);