Finite Group DatabasebetaFinite Group Databasebeta| order | 31137 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C107 · Schur multiplier (H2) = C1 |
| direct product | C107×C97⋊C3 |
| unambiguous semidirect product | C97⋊(C3×C107) |
| unambiguous semidirect product | (C97×C107)⋊C3 |
| Fitting, socle, Hall | C97×C107 ⋊ C3 |
| derived, Sylow | C97 ⋊ C3×C107 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C107 | C97⋊C3 |
| commutator, cosocle, hypocenter | C97 | C3×C107 |
| Frattini | C1 | G |
| Fitting, socle | C97×C107 | C3 |
| LCS | G ▷ C97 | |
| UCS | C1 ◁ C107 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10379 |
3745 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31137, 1);