Finite Group DatabasebetaFinite Group Databasebeta| order | 29524 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C121⋊#6923 |
| Fitting, derived, Hall | C61×C121 ⋊ C4 |
| Sylow | C121 ⋊ #6923 |
| Sylow | C61 ⋊ Dic121 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C61×C121 | C4 |
| Frattini | C11 | C11⋊#6923 |
| socle | C11×C61 | Dic11 |
| prime radical | C11×D61 | D11 |
| cosocle | C121×D61 | C2 |
| LCS | G ▷ C61×C121 | |
| UCS | C1 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7381 |
Polycyclic presentation:
2^2,11,61,11|a^2=b,c^11=e^10,c^a=c^10e,d^a=d^50,e^a=e^10,d^b=d^601939 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29524, 7);