Finite Group DatabasebetaFinite Group Databasebeta| order | 7936 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of D16 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C31 · Schur multiplier (H2) = C210 |
| direct product | C23×C31×D16 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C31 | D8 |
| commutator, Frattini, cosocle | C8 | C25×C31 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24×C31 ◁ C23×C4×C31 ◁ C23×C8×C31 ◁ G | |
2590 conjugacy classes of subgroups; only the 1054 normal subgroups are shown.
This group has 2590 conjugacy classes of subgroups — too many to draw. Only its 1054 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
2728 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7936, 55613);