Finite Group DatabasebetaFinite Group Databasebeta| order | 34540 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D55⋊D157 |
| unambiguous semidirect product | D785⋊D11 |
| unambiguous semidirect product | D1727⋊D5 |
| Fitting, socle, derived, Hall | C5×C11×C157 ⋊ C22 |
| Hall | C11×C157 ⋊ C2×D5 |
| Hall | C5×C157 ⋊ C2×D11 |
| Sylow | C157 ⋊ D5×D11 |
| Hall | C5×C11 ⋊ C2×D157 |
| Sylow | C11 ⋊ D5×D157 |
| Sylow | C5 ⋊ D11×D157 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C11×C157 | C22 |
| LCS | G ▷ C5×C11×C157 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8635 |
Polycyclic presentation:
2^2,5,11,157|d^a=d^10,e^a=e^156,c^b=c^4,d^b=d^102290 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34540, 39);