Finite Group DatabasebetaFinite Group Databasebeta| order | 18876 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C121⋊AGL(1,𝔽13) |
| unambiguous semidirect product | (C121⋊#261)⋊C3 |
| Fitting, derived, Hall | C13×C121 ⋊ C3×C4 |
| Hall | C121⋊#261 ⋊ C3 |
| Hall | C13⋊C3×C121 ⋊ C4 |
| Sylow | C121 ⋊ AGL(1,𝔽13) |
| Hall | C13⋊C3 ⋊ Dic121 |
| Sylow | C13 ⋊ C3×Dic121 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C13×C121 | C3×C4 |
| Frattini | C11 | C11⋊AGL(1,𝔽13) |
| socle | C11×C13 | C3×Dic11 |
| prime radical | C11×D13⋊C3 | D11 |
| cosocle | D13×C121 | C2×C3 |
| LCS | G ▷ C13×C121 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1573 |
Polycyclic presentation:
2,3,2,11,13,11|a^2=c,d^11=f^10,d^a=d^10f,e^a=e^8,f^a=f^10,e^b=e^9,e^c=e^12493 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18876, 15);