Finite Group DatabasebetaFinite Group Databasebeta| order | 31623 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C83 · Schur multiplier (H2) = C1 |
| direct product | C83×C127⋊C3 |
| unambiguous semidirect product | C127⋊(C3×C83) |
| unambiguous semidirect product | (C83×C127)⋊C3 |
| Fitting, socle, Hall | C83×C127 ⋊ C3 |
| derived, Sylow | C127 ⋊ C3×C83 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C83 | C127⋊C3 |
| commutator, cosocle, hypocenter | C127 | C3×C83 |
| Frattini | C1 | G |
| Fitting, socle | C83×C127 | C3 |
| LCS | G ▷ C127 | |
| UCS | C1 ◁ C83 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10541 |
3735 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31623, 1);