Finite Group DatabasebetaFinite Group Databasebeta| order | 31126 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C79 · Schur multiplier (H2) = C1 |
| direct product | C79×D197 |
| unambiguous semidirect product | C197⋊(C2×C79) |
| Fitting, socle, Hall | C79×C197 ⋊ C2 |
| derived, Sylow | C197 ⋊ C2×C79 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C79 | D197 |
| commutator, cosocle, hypocenter | C197 | C2×C79 |
| Frattini | C1 | G |
| Fitting, socle | C79×C197 | C2 |
| LCS | G ▷ C197 | |
| UCS | C1 ◁ C79 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15563 |
7900 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31126, 2);