Finite Group DatabasebetaFinite Group Databasebeta| order | 31617 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9 · Schur multiplier (H2) = C3 |
| direct product | C3×#24902008 |
| unambiguous semidirect product | (C1171⋊C3)⋊C9 |
| Fitting, socle | C3×C1171 ⋊ C9 |
| derived, Sylow | C1171 ⋊ C3×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #24902008 |
| commutator, hypocenter | C1171 | C3×C9 |
| Frattini | C1 | G |
| Fitting, socle | C3×C1171 | C9 |
| prime radical | C3×C1171⋊C3 | C3 |
| cosocle | C1171⋊C3 | C32 |
| LCS | G ▷ C1171 | |
| UCS | C1 ◁ C3 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3513 |
417 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31617, 15);