Finite Group DatabasebetaFinite Group Databasebeta| order | 14300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C11⋊#13049931 |
| Fitting, socle, derived, Hall | C52×C11×C13 ⋊ C4 |
| Hall | C52×C13 ⋊ Dic11 |
| Hall | C52×C11 ⋊ #261 |
| Hall | C11×C13 ⋊ #1044 |
| Sylow | C52 ⋊ C11⋊#261 |
| Sylow | C13 ⋊ C11⋊#1044 |
| Sylow | C11 ⋊ #13049931 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C11×C13 | C4 |
| prime radical, cosocle | C11×C5⋊D65 | C2 |
| LCS | G ▷ C52×C11×C13 | |
| UCS | C1 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1430 |
Polycyclic presentation:
2^2,5^2,11,13|a^2=b,c^a=c^2,d^a=d^3,e^a=e^10,f^a=f^5,c^b=c^4,d^b=d^4,f^b=f^12905 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14300, 126);