Finite Group DatabasebetaFinite Group Databasebeta| order | 31527 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C113 · Schur multiplier (H2) = C1 |
| direct product | C113×C31⋊C9 |
| unambiguous semidirect product | C31⋊(C9×C113) |
| unambiguous semidirect product | (C31×C113)⋊C9 |
| derived, Sylow | C31 ⋊ C9×C113 |
| Hall | C31×C113 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C113 | C31⋊C3 |
| commutator, hypocenter | C31 | C9×C113 |
| Frattini | C3 | C31⋊C3×C113 |
| Fitting, socle, prime radical | C3×C31×C113 | C3 |
| cosocle | C3×C31 | C3×C113 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C3×C113 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 31527 |
4407 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31527, 2);