Finite Group DatabasebetaFinite Group Databasebeta| order | 31329 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3×C59 |
| direct product | C3×C592⋊C3 |
| unambiguous semidirect product | C592⋊C32 |
| unambiguous semidirect product | (C3×C592)⋊C3 |
| Fitting, socle | C3×C592 ⋊ C3 |
| derived, Sylow | C592 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C592⋊C3 |
| commutator, cosocle, hypocenter | C592 | C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C592 | C3 |
| LCS | G ▷ C592 | |
| UCS | C1 ◁ C3 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 531 |
3489 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31329, 6);