Finite Group DatabasebetaFinite Group Databasebeta| order | 34540 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×#15691171 |
| Fitting, socle, Hall | C5×C11×C157 ⋊ C4 |
| derived, Hall | C5×C157 ⋊ C4×C11 |
| Hall | C11×C157 ⋊ AGL(1,𝔽5) |
| Sylow | C157 ⋊ C11×AGL(1,𝔽5) |
| Hall | C5×C11 ⋊ Dic157 |
| Sylow | C5 ⋊ C11×Dic157 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | #15691171 |
| commutator, hypocenter | C5×C157 | C4×C11 |
| Frattini | C1 | G |
| Fitting, socle | C5×C11×C157 | C4 |
| prime radical | D5×C11×C157 | C2 |
| cosocle | D5×C157 | C2×C11 |
| LCS | G ▷ C5×C157 | |
| UCS | C1 ◁ C11 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8635 |
3487 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34540, 27);