Finite Group DatabasebetaFinite Group Databasebeta| order | 31666 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C71 · Schur multiplier (H2) = C1 |
| direct product | C71×D223 |
| unambiguous semidirect product | C223⋊(C2×C71) |
| Fitting, socle, Hall | C71×C223 ⋊ C2 |
| derived, Sylow | C223 ⋊ C2×C71 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C71 | D223 |
| commutator, cosocle, hypocenter | C223 | C2×C71 |
| Frattini | C1 | G |
| Fitting, socle | C71×C223 | C2 |
| LCS | G ▷ C223 | |
| UCS | C1 ◁ C71 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15833 |
8023 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31666, 2);