Finite Group DatabasebetaFinite Group Databasebeta| order | 31682 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C73 · Schur multiplier (H2) = C1 |
| direct product | C73×D217 |
| unambiguous semidirect product | C7⋊(D31×C73) |
| unambiguous semidirect product | C31⋊(D7×C73) |
| Fitting, socle, Hall | C7×C31×C73 ⋊ C2 |
| derived, Hall | C7×C31 ⋊ C2×C73 |
| Hall | C31×C73 ⋊ D7 |
| Hall | C7×C73 ⋊ D31 |
| Sylow | C31 ⋊ D7×C73 |
| Sylow | C7 ⋊ D31×C73 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C73 | D217 |
| commutator, cosocle, hypocenter | C7×C31 | C2×C73 |
| Frattini | C1 | G |
| Fitting, socle | C7×C31×C73 | C2 |
| LCS | G ▷ C7×C31 | |
| UCS | C1 ◁ C73 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15841 |
8030 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31682, 7);