Finite Group DatabasebetaFinite Group Databasebeta| order | 32116 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C37 · Schur multiplier (H2) = C2 |
| direct product | D7×C37×D31 |
| unambiguous semidirect product | (D7×C31)⋊(C2×C37) |
| unambiguous semidirect product | (C7×D31)⋊(C2×C37) |
| unambiguous semidirect product | D217⋊(C2×C37) |
| Fitting, socle, Hall | C7×C31×C37 ⋊ C22 |
| derived, Hall | C7×C31 ⋊ C22×C37 |
| Hall | C31×C37 ⋊ C2×D7 |
| Hall | C7×C37 ⋊ C2×D31 |
| Sylow | C31 ⋊ C2×D7×C37 |
| Sylow | C7 ⋊ C2×C37×D31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C37 | D7×D31 |
| commutator, cosocle, hypocenter | C7×C31 | C22×C37 |
| Frattini | C1 | G |
| Fitting, socle | C7×C31×C37 | C22 |
| LCS | G ▷ C7×C31 | |
| UCS | C1 ◁ C37 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8029 |
3145 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32116, 17);