Finite Group DatabasebetaFinite Group Databasebeta| order | 7936 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12117 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C31 · Schur multiplier (H2) = C23 |
| direct product | C31×#12117 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C31 | #1595 |
| commutator, Frattini, cosocle | C2×M16 | C23×C31 |
| LCS | G ▷ C2×M16 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C31 ◁ C2×C4×C31 ◁ C2×M16×C31 ◁ G | |
424 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
775 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7936, 5105);