Finite Group DatabasebetaFinite Group Databasebeta| order | 31186 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C31 · Schur multiplier (H2) = C1 |
| direct product | C31×D503 |
| unambiguous semidirect product | C503⋊(C2×C31) |
| Fitting, socle, Hall | C31×C503 ⋊ C2 |
| derived, Sylow | C503 ⋊ C2×C31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31 | D503 |
| commutator, cosocle, hypocenter | C503 | C2×C31 |
| Frattini | C1 | G |
| Fitting, socle | C31×C503 | C2 |
| LCS | G ▷ C503 | |
| UCS | C1 ◁ C31 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15593 |
7843 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31186, 2);