Finite Group DatabasebetaFinite Group Databasebeta| order | 7936 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10012 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C31 · Schur multiplier (H2) = C23 |
| direct product | C31×#10015 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C31 | #127 |
| commutator, Frattini, cosocle | C2×C42 | C23×C31 |
| socle | C22×C31 | #392 |
| prime radical | C31×#2397 | C2 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C31 ◁ C2×C42×C31 ◁ G | |
696 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 122 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1240 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7936, 3003);