Finite Group DatabasebetaFinite Group Databasebeta| order | 31124 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D31×D251 |
| unambiguous semidirect product | (D31×C251)⋊C2 |
| unambiguous semidirect product | (C31×D251)⋊C2 |
| unambiguous semidirect product | D7781⋊C2 |
| Fitting, socle, derived, Hall | C31×C251 ⋊ C22 |
| Sylow | C251 ⋊ C2×D31 |
| Sylow | C31 ⋊ C2×D251 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C31×C251 | C22 |
| LCS | G ▷ C31×C251 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7781 |
2159 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31124, 6);