Finite Group DatabasebetaFinite Group Databasebeta| order | 31347 |
| automorphism | ? |
| homology | Abelianization (H1) = C36 · Schur multiplier (H2) = C315 |
| direct product | C35×C43⋊C3 |
| unambiguous semidirect product | C43⋊C36 |
| unambiguous semidirect product | (C3×C43)⋊C35 |
| Fitting, socle | C35×C43 ⋊ C3 |
| derived, Sylow | C43 ⋊ C36 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C35 | C43⋊C3 |
| commutator, cosocle, hypocenter | C43 | C36 |
| Frattini | C1 | G |
| Fitting, socle | C35×C43 | C3 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C35 | |
113264 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10449 |
4131 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31347, 4033);