Finite Group DatabasebetaFinite Group Databasebeta| order | 5060 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊(C23⋊AGL(1,𝔽5)) |
| unambiguous semidirect product | C23⋊(C11⋊AGL(1,𝔽5)) |
| Fitting, socle, derived, Hall | C5×C11×C23 ⋊ C4 |
| Hall | C11×C23 ⋊ AGL(1,𝔽5) |
| Hall | C5×C23 ⋊ Dic11 |
| Hall | C5×C11 ⋊ Dic23 |
| Sylow | C23 ⋊ C11⋊AGL(1,𝔽5) |
| Sylow | C11 ⋊ C23⋊AGL(1,𝔽5) |
| Sylow | C5 ⋊ Dic253 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C11×C23 | C4 |
| LCS | G ▷ C5×C11×C23 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,5,11,23|a^2=b,c^a=c^2,d^a=d^10,e^a=e^22,c^b=c^4509 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5060, 34);