Finite Group DatabasebetaFinite Group Databasebeta| order | 32116 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×C31⋊#3866 |
| unambiguous semidirect product | C31⋊(C7×#3866) |
| Fitting, socle, Hall | C7×C31×C37 ⋊ C4 |
| derived, Hall | C31×C37 ⋊ C4×C7 |
| Hall | C7×C37 ⋊ Dic31 |
| Hall | C7×C31 ⋊ #3866 |
| Sylow | C37 ⋊ C7×Dic31 |
| Sylow | C31 ⋊ C7×#3866 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | C31⋊#3866 |
| commutator, hypocenter | C31×C37 | C4×C7 |
| Frattini | C1 | G |
| Fitting, socle | C7×C31×C37 | C4 |
| prime radical | C7×C31×D37 | C2 |
| cosocle | C31×D37 | C2×C7 |
| LCS | G ▷ C31×C37 | |
| UCS | C1 ◁ C7 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8029 |
2191 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32116, 11);