Finite Group DatabasebetaFinite Group Databasebeta| order | 14300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊#13049908 |
| Fitting, derived, Hall | C11×C13×C25 ⋊ C4 |
| Hall | C13×C25 ⋊ Dic11 |
| Hall | C11×C25 ⋊ #261 |
| Hall | C11×C13 ⋊ #1035 |
| Sylow | C25 ⋊ C11⋊#261 |
| Sylow | C13 ⋊ C11⋊#1035 |
| Sylow | C11 ⋊ #13049908 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C11×C13×C25 | C4 |
| Frattini | C5 | C11⋊#63122 |
| socle | C5×C11×C13 | AGL(1,𝔽5) |
| prime radical, cosocle | C11×D325 | C2 |
| LCS | G ▷ C11×C13×C25 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3575 |
Polycyclic presentation:
2^2,5,11,13,5|a^2=b,c^5=f,c^a=c^2f,d^a=d^10,e^a=e^5,f^a=f^2,c^b=c^4f^4,e^b=e^12,f^b=f^4905 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14300, 29);