Finite Group DatabasebetaFinite Group Databasebeta| order | 7936 |
| automorphism | ? |
| homology | Abelianization (H1) = C82 · Schur multiplier (H2) = C2×C42 |
| unambiguous semidirect product | C31⋊#7014 |
| Sylow | C31 ⋊ #7014 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C4×Dic31 |
| commutator | C4×C31 | C82 |
| Frattini | C43 | C2×D31 |
| Fitting | C31×#1744 | C2 |
| socle | C23×C31 | #95 |
| hypercenter | #1744 | D31 |
| hypocenter | C31 | #7014 |
| LCS | G ▷ C4×C31 ▷ C31 | |
| UCS | C1 ◁ C22×C4 ◁ #1744 | |
338 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 159 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^8,31|a^2=d,b^2=e,c^2=f,d^2=g,e^2=h,b^a=bc,e^a=ef,d^b=df,i^b=i^301288 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7936, 56094);