Finite Group DatabasebetaFinite Group Databasebeta| order | 31347 |
| automorphism | ? |
| homology | Abelianization (H1) = C35 · Schur multiplier (H2) = C311 |
| direct product | C33×C32⋊(C43⋊C3) |
| Fitting | C35×C43 ⋊ C3 |
| Sylow | C43 ⋊ C33×H(3,𝔽3) |
| subgroup | G/H | |
|---|---|---|
| center | C34 | C3×C43⋊C3 |
| commutator, cosocle | C3×C43 | C35 |
| Frattini | C3 | C34×C43⋊C3 |
| Fitting | C35×C43 | C3 |
| socle | C34×C43 | C32 |
| hypercenter | C35 | C43⋊C3 |
| hypocenter | C43 | C33×H(3,𝔽3) |
| LCS | G ▷ C3×C43 ▷ C43 | |
| UCS | C1 ◁ C34 ◁ C35 | |
11744 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10449 |
3699 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31347, 4014);