Finite Group DatabasebetaFinite Group Databasebeta| order | 5148 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C9⋊(C11⋊#261) |
| unambiguous semidirect product | C11⋊(C9⋊#261) |
| Fitting, derived, Hall | C9×C11×C13 ⋊ C4 |
| Hall | C11×C13 ⋊ Dic9 |
| Hall | C9×C13 ⋊ Dic11 |
| Hall | C9×C11 ⋊ #261 |
| Sylow | C13 ⋊ Dic99 |
| Sylow | C11 ⋊ C9⋊#261 |
| Sylow | C9 ⋊ C11⋊#261 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C9×C11×C13 | C4 |
| Frattini | C3 | C3⋊(C11⋊#261) |
| socle | C3×C11×C13 | Dic3 |
| LCS | G ▷ C9×C11×C13 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,11,13,3|a^2=b,c^3=f^2,c^a=c^2f,d^a=d^10,e^a=e^8,f^a=f^2,e^b=e^12399 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5148, 23);