Finite Group DatabasebetaFinite Group Databasebeta| order | 25652 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C121⋊#6157 |
| Fitting, derived, Hall | C53×C121 ⋊ C4 |
| Sylow | C121 ⋊ #6157 |
| Sylow | C53 ⋊ Dic121 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C53×C121 | C4 |
| Frattini | C11 | C11⋊#6157 |
| socle | C11×C53 | Dic11 |
| prime radical | C11×D53 | D11 |
| cosocle | D53×C121 | C2 |
| LCS | G ▷ C53×C121 | |
| UCS | C1 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6413 |
Polycyclic presentation:
2^2,11,53,11|a^2=b,c^11=e^10,c^a=c^10e,d^a=d^30,e^a=e^10,d^b=d^521697 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25652, 7);