Finite Group DatabasebetaFinite Group Databasebeta| order | 31006 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C37 · Schur multiplier (H2) = C1 |
| direct product | C37×D419 |
| unambiguous semidirect product | C419⋊(C2×C37) |
| Fitting, socle, Hall | C37×C419 ⋊ C2 |
| derived, Sylow | C419 ⋊ C2×C37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C37 | D419 |
| commutator, cosocle, hypocenter | C419 | C2×C37 |
| Frattini | C1 | G |
| Fitting, socle | C37×C419 | C2 |
| LCS | G ▷ C419 | |
| UCS | C1 ◁ C37 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15503 |
7807 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31006, 2);