Finite Group DatabasebetaFinite Group Databasebeta| order | 32116 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7×C31 · Schur multiplier (H2) = C2 |
| direct product | C2×C7×C31×D37 |
| unambiguous semidirect product | C37⋊(C22×C7×C31) |
| unambiguous semidirect product | (C2×C37)⋊(C2×C7×C31) |
| Fitting, socle | C2×C7×C31×C37 ⋊ C2 |
| derived, Sylow | C37 ⋊ C22×C7×C31 |
| Hall | C7×C31×C37 ⋊ C22 |
| Hall | C31×C37 ⋊ C22×C7 |
| Hall | C7×C37 ⋊ C22×C31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7×C31 | D37 |
| commutator, cosocle, hypocenter | C37 | C22×C7×C31 |
| Frattini | C1 | G |
| Fitting, socle | C2×C7×C31×C37 | C2 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C2×C7×C31 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16058 |
8680 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32116, 21);