Finite Group DatabasebetaFinite Group Databasebeta| order | 34540 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×C11⋊#10597845 |
| Fitting, socle, Hall | C5×C11×C157 ⋊ C4 |
| derived, Hall | C11×C157 ⋊ C4×C5 |
| Hall | C5×C157 ⋊ Dic11 |
| Sylow | C157 ⋊ C5×Dic11 |
| Hall | C5×C11 ⋊ #10597845 |
| Sylow | C11 ⋊ C5×#10597845 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C11⋊#10597845 |
| commutator, hypocenter | C11×C157 | C4×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C11×C157 | C4 |
| prime radical | C5×C11×D157 | C2 |
| cosocle | C11×D157 | C2×C5 |
| LCS | G ▷ C11×C157 | |
| UCS | C1 ◁ C5 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8635 |
2215 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34540, 22);