Finite Group DatabasebetaFinite Group Databasebeta| order | 32157 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C34 |
| direct product | C3×C32⋊(C397⋊C3) |
| unambiguous semidirect product | (C3×C397)⋊H(3,𝔽3) |
| Fitting | C33×C397 ⋊ C3 |
| Sylow | C397 ⋊ C3×H(3,𝔽3) |
| subgroup | G/H | |
|---|---|---|
| center | C32 | C3×C397⋊C3 |
| commutator, cosocle | C3×C397 | C33 |
| Frattini | C3 | C32×C397⋊C3 |
| Fitting | C33×C397 | C3 |
| socle | C32×C397 | C32 |
| hypercenter | C33 | C397⋊C3 |
| hypocenter | C397 | C3×H(3,𝔽3) |
| LCS | G ▷ C3×C397 ▷ C397 | |
| UCS | C1 ◁ C32 ◁ C33 | |
112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10719 |
3597 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32157, 41);