Finite Group DatabasebetaFinite Group Databasebeta| order | 31558 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C31 · Schur multiplier (H2) = C1 |
| direct product | C31×D509 |
| unambiguous semidirect product | C509⋊(C2×C31) |
| Fitting, socle, Hall | C31×C509 ⋊ C2 |
| derived, Sylow | C509 ⋊ C2×C31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31 | D509 |
| commutator, cosocle, hypocenter | C509 | C2×C31 |
| Frattini | C1 | G |
| Fitting, socle | C31×C509 | C2 |
| LCS | G ▷ C509 | |
| UCS | C1 ◁ C31 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15779 |
7936 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31558, 2);