Finite Group DatabasebetaFinite Group Databasebeta| order | 31581 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C29 · Schur multiplier (H2) = C11 |
| direct product | C29×C112⋊C9 |
| unambiguous semidirect product | C112⋊(C9×C29) |
| unambiguous semidirect product | (C112×C29)⋊C9 |
| derived, Sylow | C112 ⋊ C9×C29 |
| Hall | C112×C29 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C29 | C112⋊C3 |
| commutator, hypocenter | C112 | C9×C29 |
| Frattini | C3 | C29×C112⋊C3 |
| Fitting, socle, prime radical | C3×C112×C29 | C3 |
| cosocle | C3×C112 | C3×C29 |
| LCS | G ▷ C112 | |
| UCS | C1 ◁ C3×C29 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2871 |
3741 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31581, 4);